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Research ArticleCooperative Spectrum Sensing for Cognitive HeterogeneousNetworking Using Iterative Gauss-Seidel Process
Haleh Hosseini1 Kaamran Raahemifar1
Sharifah Kamilah Syed Yusof2 and Alagan Anpalagan1
1Department of Electrical Engineering Ryerson University Toronto Canada M5B 2K32Universiti Teknologi Malaysia 81310 Johor Malaysia
Correspondence should be addressed to Alagan Anpalagan alaganeeryersonca
Received 9 June 2015 Revised 14 September 2015 Accepted 29 September 2015
Academic Editor Qingqi Pei
Copyright copy 2015 Haleh Hosseini et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Heterogeneous networks with dense deployment of small cells can employ cognitive features to efficiently utilize the availablespectrum resources Spectrum sensing is the key enabler for cognitive radio to detect the unoccupied channels for data transmissionIn order to deal with shadowing and multipath fading in sensing channels cooperative spectrum sensing is designed to increasethe accuracy of the sensed signal In this paper an optimized local decision rule is implemented for the case that the received datafrom primary users are possibly correlated due to the sensing channel impairments Since the prior information is unavailable inthe real systems Neyman-Pearson criterion is used as the cost functionThen a discrete iterative algorithm based on Gauss-Seidelprocess is applied to optimize the local cognitive user decision rules under a fixed fusion rule This method with low complexitycan minimize the cost using the golden section search method in a finite number of iterations ROC curves are depicted usingthe achieved probability of detection and false alarm by numerical examples to illustrate the efficiency of the proposed algorithmSimulation results also confirm the superiority of the proposed method compared to the conventional topologies and decisionrules
1 Introduction
Heterogeneous networks are the next generation of cellu-lar networks with densely deployed low power small cellsthat may reuse spectrum resources across the space Sinceheterogeneous networks may experience spectral crowd-ing the main challenge is to coexist efficiently with otherlicensed users According to the Federal CommunicationCommissions (FCC) frequency allocation chart the spec-trum bands dedicated to the licensed or primary user (PU)are highly underutilized [1] Cognitive radio features mayequip heterogeneous networks with spectrum sensing withinthe small cells to acquire available channels and enhance theiroperations [2] Cognitive radio can provide opportunisticspectrum access for unlicensed or secondary users andoptimize the spectral efficiency [3 4] The most criticalrequirement of cognitive radio is the sensing mechanism
to exploit the spectrum holes while suppressing the mutualinterference with PUs [4ndash6]
An optimal spectrum sensingmechanism is necessary forcognitive radios tomaximize detection probability of the PUsrsquosignal subject to the constraint of the limited probability offalse alarm Among various signal detection schemes energydetection has been recognized with low computational com-plexity to be used for spectrum sensingThis method is basedon measuring and comparing the received signal strengthfrom the PUs with a threshold within the channels and acertain sensing time [7] However the performance of energydetector is degraded with sensing channel impairmentswhich leads to attenuation and variations of the sensed signalMultipath fading path loss shadowing and hidden nodeproblem inevitably compromise the sensing reliability Aneffective approach to overcoming these uncertainty problemsand improving the performance is cooperative sensing [8ndash11]
Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 319164 9 pageshttpdxdoiorg1011552015319164
2 International Journal of Distributed Sensor Networks
Cooperative sensing can be used to acquire informationof an intelligent wireless network with various applicationsincluding radar and sensor networks [12 13] The designof cooperative sensing can increase the reliability flexibilityspeed and coverage area of the sensing network In a cogni-tive radio with large number of sensing nodes cooperativespectrum sensing can increase the detection probabilityof primary users and the channel utilization Cooperativespectrum sensing can enhance the sensing performance byexploiting the spatial diversity in the observations of spatiallylocated secondary users which transmit their sensing infor-mation to a fusion center for final decision It has been shownthat increasing the number of cooperative users can decreasethe required detector sensitivity and sensing time Moreovera cooperative approach needs lower communication band-width and is more robust to channel fading [14ndash16]
The drawback of the feedback overhead of spectrumsensing is overcome in [14] by using a fixed number ofcommon feedback channels so that each node compares thesensing result with a threshold and selects the appropriatedata to be sent to the fusion center In [15] a sensor selectionstrategy is proposed to minimize the energy consumptionfor cooperative spectrum sensing under satisfactory pri-mary user detection performance A decentralized spectrumsensing approach is proposed in [16] to reduce the overalloverhead and power consumption of the network by elim-inating the need for fusion center node In this schemeeach secondary user communicates only with its adjacentnodes via one-hop transmissions within several rounds toreach global convergence The performance of cooperativespectrum sensing over Rayleigh fading channel is improvedin [17] using an adaptive linear combiner with weights tosecondary user decisions
In this paper a cooperative spectrum sensing is deployedfor cognitive heterogeneous network with a parallel approachinstead of centralized topology that needs wideband chan-nels With correlated local sensing observations a numericalalgorithm is proposed to optimize the local decisions oflocal cognitive users (LCUs) and send the information to acommon cognitive user (CCU) as fusion center The designof parallel topology increases the reliability flexibility speedand coverage area of the sensing network Based on Bayesianoptimality criteria with independent observations the opti-mized rule for decision making of each LCU is likelihoodratio test (LRT) [18ndash20] Since the prior probabilities ofhypotheses and accurate illustration of cost coefficients arenot available in real systems common Bayesian method formaximizing LRT is not practicalThereforeNeyman-Pearsoncriterion is adopted for optimum local decision rule (OLDR)so that the probability of false alarm is limited to a desiredvalue while the probability of missed detection is minimized[21]
The rest of this paper is organized as follows Section 2describes cooperative sensing schemes and Section 3 illus-trates the systemmodelThe proposed iterative algorithm fordecision making at LCUs is described in Section 4Then thismethod is simulated and the results are analyzed in Section 5The paper is concluded in Section 6 and the open issues forfuture researches are addressed
2 Cooperative Sensing Schemes
Various cooperative sensing schemes by LCUs depending onthe decision making methods of the fusion center can beused to carry out PU detection In a centralized networkapproach local sensors send the raw sensing information to afusion center which decides on the presence or absence of thePUHowever the transmission of these unprocessed observa-tions does not efficiently utilize the bandwidth Cooperativesensing methods perform some preliminary data processingat each sensor to condense the information [21] The majorcooperative configurations include parallel serial and treetopologies as shown in Figure 1
In a parallel sensing model each LCU can decide inde-pendently based on its sensed information and pass thequantized local decision to a CCU whose role as a fusioncenter is to make a final decision on PU existence accordingto the spatially collected results Even though extensive inves-tigations have been done for cooperative sensing schemes toincrease the sensing accuracy most of the research assumedthat the sensed information is independent and identicallydistributed within the local sensors [22] This assumption ispractically unrealistic as shadowing is highly correlated whenseveral cognitive users are geographically proximate withsimilar shadowing effects Spatially correlated shadowingwhich exponentially depends on the distance can bound theachievable gain of cooperative sensing [23]
For optimal PU detection Bayesian criterion with maxi-mizing LRT is the most common method in signal detectiontheory For a given set of observations119884 = [119910
1 119910
119873] it has
been shown that when the prior information of probabilitiesis known LRT is the optimized detection method in whichthe likelihood ratio is calculated for the received signals andcompared to a threshold 120579 as Λ(119884) = 119875(119884 | 119867
1)119875(119884 |
1198670) lt 120579 where 120579 is a function of prior probabilities of 119901
0
and 1199011and the cost function 119888
119894119895of 119867119894decision while 119867
119895has
been true so we have 120579 = (11988810
minus 11988800
)1199010(11988801
minus 11988811
)1199011 In
many cases it is difficult to know these cost coefficients andprior probabilities Instead Neyman-Pearson cost function 119865
is replaced under a condition that false alarmprobability119875119891is
less than a certain value 120572 as119865 = 120582(119875119891
minus120572)+119875119898 where 120582 is the
Lagrange multiplier 119875119891is the probability of false alarm and
119875119898is the probability of detection respectively To provide the
final relations for119875119889and119875119891 note that119875
119889= 1minusint
Ω119875(119884 | 119867
1)119889119884
and 119875119891
= 1 minus intΩ
119875(119884 | 1198670)119889119884 where Ω is decision region
of 1198670determined due to the type of local decision rules and
fusion rulesIn the case of Bayesian criterion for centralized network
as shown in Figure 1(a) there are 119873 sensors that send theirobservations directly to one fusion center before processingand the final decision 119880
119891is made based on a fusion rule as
119866(119884) while
119880119891
=
0 1198670decision if 119866 (119884) le 0
1 1198670decision if 119866 (119884) gt 0
(1)
The region of final decision based on 1198670is ΩCN = 119884
119866(119884) le 0 The fusion rule 119866(119884) is defined while minimizing
International Journal of Distributed Sensor Networks 3
Observations
Final decision
FC
middot middot middot
(a) Centralized topology
Observations
Final decision
FC
middot middot middotS1 S2SN
(b) Parallel topology
Observations
Final decisionmiddot middot middot SNS1 S2
(c) Serial topology
Observations
Obs
erva
tions
Final decision
S2 S3 S4
S1
S0
(d) Tree topology
Figure 1 Major topologies of cooperative sensing networks
the cost function of 119865 = 119888 + intΩCN
119891(119884)119889119884 where 119888 = (119901011988810
+
119901111988811
) 119891(119884) = 1198861119875(119884 | 119867
1) minus 1198860119875(119884 | 119867
0) with 119886
1= (11988801
minus
11988811
)1199011 and 119886
0= (11988810
minus11988800
)1199010Therefore the optimumdecision
region of centralized network is ΩCN = 119910119894
Λ(119884) lt 120579CN 119894 =
1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867
0) 120579CN is the
threshold of decision making for centralized network and 119873
is the number of sensorsIn parallel topology with distributed local observations
as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910
119894 Λ(119910
119894) le
120579119894 119894 = 1 119873 where 120579
119894is the threshold for the 119894th receiver
Meanwhile for AND fusion rule it is given that ΩLRTAND =
119878 minus 119910119894
Λ(119910119894) gt 120579
119894 119894 = 1 119873 where 119878 is the whole
decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579
119894can be achieved byminimizing the cost
function of 119865 which in the case of OR fusion rule is
119865LRTOR = 120574 + intΩLRTOR
119891 (119884) 119889119884 (2)
and for AND fusion rule is
119865LRTAND = 120574 + intΩLRTAND
119891 (119884) 119889119884 (3)
where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867
0)
The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion
3 System Model
In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in
4 International Journal of Distributed Sensor Networks
Primarynetwork
PU
PU
Tx
Rx
Heterogeneous network
Macro-eNB
H-UE
H-UEH-UE
H-eNB(CCU)
M-UE
(LCU1)
(LCU3)
(LCU2)
Figure 2 A heterogeneous network overlapping with primarynetwork
CCU (fusion center)
PU
Sensing channels
Reporting channels
LCU1 LCU2LCUN
middot middot middot
Figure 3 Parallel cooperative spectrum sensing
this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem
The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution
Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU
119894that receives the observation signals 119910
119894 from the
PU through the sensing channels Each LCU119894sends its local
binary decision 119906119894 to the fusion center the CCU tomake the
final decision using the fusion ruleThemetrics of probabilityof detection 119875
119889119894 and probability of false alarm 119875
119891119894 for
local decision at the 119894th LCU119894are derived to be employed
for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as
119884 = 119867 sdot 119878119901
+ 119881 (4)
where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ
1
ℎ119894 ℎ
119873] states the sensing channel gain vector and 119884 =
[1199101 119910
119894 119910
119873] shows the observation vector in which
119910119894denotes the received signal at LCU
119894 The vector of addi-
tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V
1 V
119894 V
119873] The observations of PUrsquos signal
are received through the sensing channels at LCU119894 In this
scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867
0and 119867
1are the binary
hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is
1198671
1199101
= ℎ1
sdot 119878119901
+ V1 119910
119873
= ℎ119873
sdot 119878119901
+ V119873
1198670
1199101
= V1 119910
119873= V119873
(5)
Given that 119910119894denotes the available observation of PU
signal at LCU119894receiver the local decision rule 119892
119894(119910119894) is
employed by LCU119894to make a binary decision 119906
119894about the
existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892
1(1199101) 119892
119894(119910119894) 119892
119873(119910119873
)] the fusion centerCCU receives the local decision as
119906119894
= 0 119892
119894(119910119894) le 0
1 119892119894(119910119894) gt 0
(6)
TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867
1 The local decision rule maps the
observation set 119884 = 1199101 119910
119873to a local decision set 119880 =
1199061 119906
119894 119906
119873 where 119906
119894isin 0 1 119894 = 1 119873 The
combination of local binary decisions 119906119894results in 2
119873 statesThus the 2
2119873
is the total number of states for final decision119906119891
= 119876(119880) and
119876 (119880) = 119876119899 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 1
le 119899 le 2119873
(7)
International Journal of Distributed Sensor Networks 5
where mod(119860 2) is the division remaining of 1198602 and 119906119894
=
mod((119899 minus 1)2(119894minus1)
2) is the 119894th bit of 119899 Hence 119876(119880) =
119876119899 119899 = sum
119873
119894=11199061198942119894minus1
+ 1 Consider two different sets as1198780
= 119899 119876119899
= 0 and 1198781
= 119899 119876119899
= 1 such that1198780
cup 1198781
= 1 2 2119873
then ΩOLDR = 119910119894
119876119899
= 0 119899 isin 1198780
where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867
0 With a given set of 119878
0 the fusion rule
119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867
0 For
a fixed fusion rule the region of final decision is ΩOLDR =
⋃119899isin1198780
Ω119899 where Ω
119899denotes the region of 119899th combination of
119876 as
Ω119899
= 119884 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 119876
= 119876119899
(8)
In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions
4 OLDR Algorithm with Gauss-Seidel Process
Each distributedH-UELCU119894performs the spectrum sensing
by energy detection to detect the initial PU signal obser-vation 119910
119894 This distributed information from all LCUs is
used by the OLDR algorithm to cooperatively optimize localdecision rules 119892
119894 according to the fix central fusion rule at
H-eNBCCU ANDOR and achieve the final minimized 119875119891
with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865
119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR
119891 (119884) 119889119884 (9)
where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867
1) minus 120582119875(119884 | 119867
0) Given
that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that
119865 (119866 119876) = 120574 + int119884isinΩOLDR
119891 (119884) 119889119884 = 120574
+ (int119892119894(119910119894)le0
(int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
) + int119910119894
int⋃119899isin11987802119894
Ω119899119894
)
sdot 119891 (119884) 119889119884
(10)
where Ω119899119894
is Ω119899excluding 119910
119894 11987801119894
11987802119894
are two subsetsof 1198780such that 119878
01119894cup 11987802119894
= 1198780 11987801119894
is a subset of 119899
belonging to 1198780with 119906
119894= 0 119878
01119894= 119899 119876
119899=
0 119906119894
= 0 and similarly 11987802119894
is a subset of 119899 belongingto 1198780with 119906
119894= 1 119878
02119894= 119899 119876
119899= 0 119906
119894= 1
The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892
1 119892
119873)
[26]
119892119894(119910119894) = (int
⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(11)
where Ω119899119894
= (1199101 119910
119894minus1 119910119894+1
119910119873
) 120601(119892119894 119906119894) le 0
and 120601(119892119894 119906119894) = (12 minus 119906
119894)119892119894 Consequently each set of
optimum local decisions is derived by solving several fixedpoint integral equations as
Γ119876
(119866) =
[[[[[[[[[[[[[[[[[[[[
[
(intcup119899isin119878011
Ω1198991
minus intcup119899isin119878021
Ω1198991
)119891 (119884) 119889119884
1198891199101
(intcup119899isin11987801119894
Ω119899119894
minus intcup119899isin11987802119894
Ω119899119894
)119891 (119884) 119889119884
119889119910119894
(intcup119899isin11987801119873
Ω119899119873
minus intcup119899isin11987802119873
Ω119899119873
)119891 (119884) 119889119884
119889119910119873
]]]]]]]]]]]]]]]]]]]]
]
(12)
Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892
1 119892
119873)
that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866
(119895) and the initial set as 119866(0) Gauss-Seidel
process for optimum local decision rules can be definedas
119866(119895+1)
= Γ119876
(119866(119895)
) forall119895 = 0 1 2 (13)
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
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Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
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RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
2 International Journal of Distributed Sensor Networks
Cooperative sensing can be used to acquire informationof an intelligent wireless network with various applicationsincluding radar and sensor networks [12 13] The designof cooperative sensing can increase the reliability flexibilityspeed and coverage area of the sensing network In a cogni-tive radio with large number of sensing nodes cooperativespectrum sensing can increase the detection probabilityof primary users and the channel utilization Cooperativespectrum sensing can enhance the sensing performance byexploiting the spatial diversity in the observations of spatiallylocated secondary users which transmit their sensing infor-mation to a fusion center for final decision It has been shownthat increasing the number of cooperative users can decreasethe required detector sensitivity and sensing time Moreovera cooperative approach needs lower communication band-width and is more robust to channel fading [14ndash16]
The drawback of the feedback overhead of spectrumsensing is overcome in [14] by using a fixed number ofcommon feedback channels so that each node compares thesensing result with a threshold and selects the appropriatedata to be sent to the fusion center In [15] a sensor selectionstrategy is proposed to minimize the energy consumptionfor cooperative spectrum sensing under satisfactory pri-mary user detection performance A decentralized spectrumsensing approach is proposed in [16] to reduce the overalloverhead and power consumption of the network by elim-inating the need for fusion center node In this schemeeach secondary user communicates only with its adjacentnodes via one-hop transmissions within several rounds toreach global convergence The performance of cooperativespectrum sensing over Rayleigh fading channel is improvedin [17] using an adaptive linear combiner with weights tosecondary user decisions
In this paper a cooperative spectrum sensing is deployedfor cognitive heterogeneous network with a parallel approachinstead of centralized topology that needs wideband chan-nels With correlated local sensing observations a numericalalgorithm is proposed to optimize the local decisions oflocal cognitive users (LCUs) and send the information to acommon cognitive user (CCU) as fusion center The designof parallel topology increases the reliability flexibility speedand coverage area of the sensing network Based on Bayesianoptimality criteria with independent observations the opti-mized rule for decision making of each LCU is likelihoodratio test (LRT) [18ndash20] Since the prior probabilities ofhypotheses and accurate illustration of cost coefficients arenot available in real systems common Bayesian method formaximizing LRT is not practicalThereforeNeyman-Pearsoncriterion is adopted for optimum local decision rule (OLDR)so that the probability of false alarm is limited to a desiredvalue while the probability of missed detection is minimized[21]
The rest of this paper is organized as follows Section 2describes cooperative sensing schemes and Section 3 illus-trates the systemmodelThe proposed iterative algorithm fordecision making at LCUs is described in Section 4Then thismethod is simulated and the results are analyzed in Section 5The paper is concluded in Section 6 and the open issues forfuture researches are addressed
2 Cooperative Sensing Schemes
Various cooperative sensing schemes by LCUs depending onthe decision making methods of the fusion center can beused to carry out PU detection In a centralized networkapproach local sensors send the raw sensing information to afusion center which decides on the presence or absence of thePUHowever the transmission of these unprocessed observa-tions does not efficiently utilize the bandwidth Cooperativesensing methods perform some preliminary data processingat each sensor to condense the information [21] The majorcooperative configurations include parallel serial and treetopologies as shown in Figure 1
In a parallel sensing model each LCU can decide inde-pendently based on its sensed information and pass thequantized local decision to a CCU whose role as a fusioncenter is to make a final decision on PU existence accordingto the spatially collected results Even though extensive inves-tigations have been done for cooperative sensing schemes toincrease the sensing accuracy most of the research assumedthat the sensed information is independent and identicallydistributed within the local sensors [22] This assumption ispractically unrealistic as shadowing is highly correlated whenseveral cognitive users are geographically proximate withsimilar shadowing effects Spatially correlated shadowingwhich exponentially depends on the distance can bound theachievable gain of cooperative sensing [23]
For optimal PU detection Bayesian criterion with maxi-mizing LRT is the most common method in signal detectiontheory For a given set of observations119884 = [119910
1 119910
119873] it has
been shown that when the prior information of probabilitiesis known LRT is the optimized detection method in whichthe likelihood ratio is calculated for the received signals andcompared to a threshold 120579 as Λ(119884) = 119875(119884 | 119867
1)119875(119884 |
1198670) lt 120579 where 120579 is a function of prior probabilities of 119901
0
and 1199011and the cost function 119888
119894119895of 119867119894decision while 119867
119895has
been true so we have 120579 = (11988810
minus 11988800
)1199010(11988801
minus 11988811
)1199011 In
many cases it is difficult to know these cost coefficients andprior probabilities Instead Neyman-Pearson cost function 119865
is replaced under a condition that false alarmprobability119875119891is
less than a certain value 120572 as119865 = 120582(119875119891
minus120572)+119875119898 where 120582 is the
Lagrange multiplier 119875119891is the probability of false alarm and
119875119898is the probability of detection respectively To provide the
final relations for119875119889and119875119891 note that119875
119889= 1minusint
Ω119875(119884 | 119867
1)119889119884
and 119875119891
= 1 minus intΩ
119875(119884 | 1198670)119889119884 where Ω is decision region
of 1198670determined due to the type of local decision rules and
fusion rulesIn the case of Bayesian criterion for centralized network
as shown in Figure 1(a) there are 119873 sensors that send theirobservations directly to one fusion center before processingand the final decision 119880
119891is made based on a fusion rule as
119866(119884) while
119880119891
=
0 1198670decision if 119866 (119884) le 0
1 1198670decision if 119866 (119884) gt 0
(1)
The region of final decision based on 1198670is ΩCN = 119884
119866(119884) le 0 The fusion rule 119866(119884) is defined while minimizing
International Journal of Distributed Sensor Networks 3
Observations
Final decision
FC
middot middot middot
(a) Centralized topology
Observations
Final decision
FC
middot middot middotS1 S2SN
(b) Parallel topology
Observations
Final decisionmiddot middot middot SNS1 S2
(c) Serial topology
Observations
Obs
erva
tions
Final decision
S2 S3 S4
S1
S0
(d) Tree topology
Figure 1 Major topologies of cooperative sensing networks
the cost function of 119865 = 119888 + intΩCN
119891(119884)119889119884 where 119888 = (119901011988810
+
119901111988811
) 119891(119884) = 1198861119875(119884 | 119867
1) minus 1198860119875(119884 | 119867
0) with 119886
1= (11988801
minus
11988811
)1199011 and 119886
0= (11988810
minus11988800
)1199010Therefore the optimumdecision
region of centralized network is ΩCN = 119910119894
Λ(119884) lt 120579CN 119894 =
1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867
0) 120579CN is the
threshold of decision making for centralized network and 119873
is the number of sensorsIn parallel topology with distributed local observations
as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910
119894 Λ(119910
119894) le
120579119894 119894 = 1 119873 where 120579
119894is the threshold for the 119894th receiver
Meanwhile for AND fusion rule it is given that ΩLRTAND =
119878 minus 119910119894
Λ(119910119894) gt 120579
119894 119894 = 1 119873 where 119878 is the whole
decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579
119894can be achieved byminimizing the cost
function of 119865 which in the case of OR fusion rule is
119865LRTOR = 120574 + intΩLRTOR
119891 (119884) 119889119884 (2)
and for AND fusion rule is
119865LRTAND = 120574 + intΩLRTAND
119891 (119884) 119889119884 (3)
where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867
0)
The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion
3 System Model
In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in
4 International Journal of Distributed Sensor Networks
Primarynetwork
PU
PU
Tx
Rx
Heterogeneous network
Macro-eNB
H-UE
H-UEH-UE
H-eNB(CCU)
M-UE
(LCU1)
(LCU3)
(LCU2)
Figure 2 A heterogeneous network overlapping with primarynetwork
CCU (fusion center)
PU
Sensing channels
Reporting channels
LCU1 LCU2LCUN
middot middot middot
Figure 3 Parallel cooperative spectrum sensing
this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem
The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution
Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU
119894that receives the observation signals 119910
119894 from the
PU through the sensing channels Each LCU119894sends its local
binary decision 119906119894 to the fusion center the CCU tomake the
final decision using the fusion ruleThemetrics of probabilityof detection 119875
119889119894 and probability of false alarm 119875
119891119894 for
local decision at the 119894th LCU119894are derived to be employed
for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as
119884 = 119867 sdot 119878119901
+ 119881 (4)
where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ
1
ℎ119894 ℎ
119873] states the sensing channel gain vector and 119884 =
[1199101 119910
119894 119910
119873] shows the observation vector in which
119910119894denotes the received signal at LCU
119894 The vector of addi-
tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V
1 V
119894 V
119873] The observations of PUrsquos signal
are received through the sensing channels at LCU119894 In this
scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867
0and 119867
1are the binary
hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is
1198671
1199101
= ℎ1
sdot 119878119901
+ V1 119910
119873
= ℎ119873
sdot 119878119901
+ V119873
1198670
1199101
= V1 119910
119873= V119873
(5)
Given that 119910119894denotes the available observation of PU
signal at LCU119894receiver the local decision rule 119892
119894(119910119894) is
employed by LCU119894to make a binary decision 119906
119894about the
existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892
1(1199101) 119892
119894(119910119894) 119892
119873(119910119873
)] the fusion centerCCU receives the local decision as
119906119894
= 0 119892
119894(119910119894) le 0
1 119892119894(119910119894) gt 0
(6)
TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867
1 The local decision rule maps the
observation set 119884 = 1199101 119910
119873to a local decision set 119880 =
1199061 119906
119894 119906
119873 where 119906
119894isin 0 1 119894 = 1 119873 The
combination of local binary decisions 119906119894results in 2
119873 statesThus the 2
2119873
is the total number of states for final decision119906119891
= 119876(119880) and
119876 (119880) = 119876119899 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 1
le 119899 le 2119873
(7)
International Journal of Distributed Sensor Networks 5
where mod(119860 2) is the division remaining of 1198602 and 119906119894
=
mod((119899 minus 1)2(119894minus1)
2) is the 119894th bit of 119899 Hence 119876(119880) =
119876119899 119899 = sum
119873
119894=11199061198942119894minus1
+ 1 Consider two different sets as1198780
= 119899 119876119899
= 0 and 1198781
= 119899 119876119899
= 1 such that1198780
cup 1198781
= 1 2 2119873
then ΩOLDR = 119910119894
119876119899
= 0 119899 isin 1198780
where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867
0 With a given set of 119878
0 the fusion rule
119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867
0 For
a fixed fusion rule the region of final decision is ΩOLDR =
⋃119899isin1198780
Ω119899 where Ω
119899denotes the region of 119899th combination of
119876 as
Ω119899
= 119884 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 119876
= 119876119899
(8)
In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions
4 OLDR Algorithm with Gauss-Seidel Process
Each distributedH-UELCU119894performs the spectrum sensing
by energy detection to detect the initial PU signal obser-vation 119910
119894 This distributed information from all LCUs is
used by the OLDR algorithm to cooperatively optimize localdecision rules 119892
119894 according to the fix central fusion rule at
H-eNBCCU ANDOR and achieve the final minimized 119875119891
with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865
119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR
119891 (119884) 119889119884 (9)
where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867
1) minus 120582119875(119884 | 119867
0) Given
that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that
119865 (119866 119876) = 120574 + int119884isinΩOLDR
119891 (119884) 119889119884 = 120574
+ (int119892119894(119910119894)le0
(int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
) + int119910119894
int⋃119899isin11987802119894
Ω119899119894
)
sdot 119891 (119884) 119889119884
(10)
where Ω119899119894
is Ω119899excluding 119910
119894 11987801119894
11987802119894
are two subsetsof 1198780such that 119878
01119894cup 11987802119894
= 1198780 11987801119894
is a subset of 119899
belonging to 1198780with 119906
119894= 0 119878
01119894= 119899 119876
119899=
0 119906119894
= 0 and similarly 11987802119894
is a subset of 119899 belongingto 1198780with 119906
119894= 1 119878
02119894= 119899 119876
119899= 0 119906
119894= 1
The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892
1 119892
119873)
[26]
119892119894(119910119894) = (int
⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(11)
where Ω119899119894
= (1199101 119910
119894minus1 119910119894+1
119910119873
) 120601(119892119894 119906119894) le 0
and 120601(119892119894 119906119894) = (12 minus 119906
119894)119892119894 Consequently each set of
optimum local decisions is derived by solving several fixedpoint integral equations as
Γ119876
(119866) =
[[[[[[[[[[[[[[[[[[[[
[
(intcup119899isin119878011
Ω1198991
minus intcup119899isin119878021
Ω1198991
)119891 (119884) 119889119884
1198891199101
(intcup119899isin11987801119894
Ω119899119894
minus intcup119899isin11987802119894
Ω119899119894
)119891 (119884) 119889119884
119889119910119894
(intcup119899isin11987801119873
Ω119899119873
minus intcup119899isin11987802119873
Ω119899119873
)119891 (119884) 119889119884
119889119910119873
]]]]]]]]]]]]]]]]]]]]
]
(12)
Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892
1 119892
119873)
that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866
(119895) and the initial set as 119866(0) Gauss-Seidel
process for optimum local decision rules can be definedas
119866(119895+1)
= Γ119876
(119866(119895)
) forall119895 = 0 1 2 (13)
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
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DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 3
Observations
Final decision
FC
middot middot middot
(a) Centralized topology
Observations
Final decision
FC
middot middot middotS1 S2SN
(b) Parallel topology
Observations
Final decisionmiddot middot middot SNS1 S2
(c) Serial topology
Observations
Obs
erva
tions
Final decision
S2 S3 S4
S1
S0
(d) Tree topology
Figure 1 Major topologies of cooperative sensing networks
the cost function of 119865 = 119888 + intΩCN
119891(119884)119889119884 where 119888 = (119901011988810
+
119901111988811
) 119891(119884) = 1198861119875(119884 | 119867
1) minus 1198860119875(119884 | 119867
0) with 119886
1= (11988801
minus
11988811
)1199011 and 119886
0= (11988810
minus11988800
)1199010Therefore the optimumdecision
region of centralized network is ΩCN = 119910119894
Λ(119884) lt 120579CN 119894 =
1 119873 where Λ(119884) = 119875(119884 | 1198671)119875(119884 | 119867
0) 120579CN is the
threshold of decision making for centralized network and 119873
is the number of sensorsIn parallel topology with distributed local observations
as shown in Figure 1(b) Bayesian criterion leads to LRT forlocal decision rule For a network with 119873 receivers and ORfusion rule it can be written that ΩLRTOR = 119910
119894 Λ(119910
119894) le
120579119894 119894 = 1 119873 where 120579
119894is the threshold for the 119894th receiver
Meanwhile for AND fusion rule it is given that ΩLRTAND =
119878 minus 119910119894
Λ(119910119894) gt 120579
119894 119894 = 1 119873 where 119878 is the whole
decision region Based on Neyman-Pearson criterion thevalues of thresholds 120579
119894can be achieved byminimizing the cost
function of 119865 which in the case of OR fusion rule is
119865LRTOR = 120574 + intΩLRTOR
119891 (119884) 119889119884 (2)
and for AND fusion rule is
119865LRTAND = 120574 + intΩLRTAND
119891 (119884) 119889119884 (3)
where 120574 = 120582(1 minus 120572) 119891(119884) = 119875(119884 | 1198671) minus 120582119875(119884 | 119867
0)
The region of decision making for parallel sensingapproach under cognitive radio channels is discussed in thenext section The local decision rules of local cognitive usersand fusion rule are formulated to design an optimal algorithmwith Neyman-Pearson criterion
3 System Model
In this work a cellular network scenario so called as hetero-geneous network is considered for densely populated areassuch that macrocells are mixed with low power cells Thesmall cells of heterogeneous networks can increase the signalcoverage for the areas that are not accessible by macrobasestations to optimize the reliability and data rate However in
4 International Journal of Distributed Sensor Networks
Primarynetwork
PU
PU
Tx
Rx
Heterogeneous network
Macro-eNB
H-UE
H-UEH-UE
H-eNB(CCU)
M-UE
(LCU1)
(LCU3)
(LCU2)
Figure 2 A heterogeneous network overlapping with primarynetwork
CCU (fusion center)
PU
Sensing channels
Reporting channels
LCU1 LCU2LCUN
middot middot middot
Figure 3 Parallel cooperative spectrum sensing
this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem
The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution
Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU
119894that receives the observation signals 119910
119894 from the
PU through the sensing channels Each LCU119894sends its local
binary decision 119906119894 to the fusion center the CCU tomake the
final decision using the fusion ruleThemetrics of probabilityof detection 119875
119889119894 and probability of false alarm 119875
119891119894 for
local decision at the 119894th LCU119894are derived to be employed
for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as
119884 = 119867 sdot 119878119901
+ 119881 (4)
where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ
1
ℎ119894 ℎ
119873] states the sensing channel gain vector and 119884 =
[1199101 119910
119894 119910
119873] shows the observation vector in which
119910119894denotes the received signal at LCU
119894 The vector of addi-
tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V
1 V
119894 V
119873] The observations of PUrsquos signal
are received through the sensing channels at LCU119894 In this
scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867
0and 119867
1are the binary
hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is
1198671
1199101
= ℎ1
sdot 119878119901
+ V1 119910
119873
= ℎ119873
sdot 119878119901
+ V119873
1198670
1199101
= V1 119910
119873= V119873
(5)
Given that 119910119894denotes the available observation of PU
signal at LCU119894receiver the local decision rule 119892
119894(119910119894) is
employed by LCU119894to make a binary decision 119906
119894about the
existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892
1(1199101) 119892
119894(119910119894) 119892
119873(119910119873
)] the fusion centerCCU receives the local decision as
119906119894
= 0 119892
119894(119910119894) le 0
1 119892119894(119910119894) gt 0
(6)
TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867
1 The local decision rule maps the
observation set 119884 = 1199101 119910
119873to a local decision set 119880 =
1199061 119906
119894 119906
119873 where 119906
119894isin 0 1 119894 = 1 119873 The
combination of local binary decisions 119906119894results in 2
119873 statesThus the 2
2119873
is the total number of states for final decision119906119891
= 119876(119880) and
119876 (119880) = 119876119899 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 1
le 119899 le 2119873
(7)
International Journal of Distributed Sensor Networks 5
where mod(119860 2) is the division remaining of 1198602 and 119906119894
=
mod((119899 minus 1)2(119894minus1)
2) is the 119894th bit of 119899 Hence 119876(119880) =
119876119899 119899 = sum
119873
119894=11199061198942119894minus1
+ 1 Consider two different sets as1198780
= 119899 119876119899
= 0 and 1198781
= 119899 119876119899
= 1 such that1198780
cup 1198781
= 1 2 2119873
then ΩOLDR = 119910119894
119876119899
= 0 119899 isin 1198780
where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867
0 With a given set of 119878
0 the fusion rule
119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867
0 For
a fixed fusion rule the region of final decision is ΩOLDR =
⋃119899isin1198780
Ω119899 where Ω
119899denotes the region of 119899th combination of
119876 as
Ω119899
= 119884 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 119876
= 119876119899
(8)
In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions
4 OLDR Algorithm with Gauss-Seidel Process
Each distributedH-UELCU119894performs the spectrum sensing
by energy detection to detect the initial PU signal obser-vation 119910
119894 This distributed information from all LCUs is
used by the OLDR algorithm to cooperatively optimize localdecision rules 119892
119894 according to the fix central fusion rule at
H-eNBCCU ANDOR and achieve the final minimized 119875119891
with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865
119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR
119891 (119884) 119889119884 (9)
where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867
1) minus 120582119875(119884 | 119867
0) Given
that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that
119865 (119866 119876) = 120574 + int119884isinΩOLDR
119891 (119884) 119889119884 = 120574
+ (int119892119894(119910119894)le0
(int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
) + int119910119894
int⋃119899isin11987802119894
Ω119899119894
)
sdot 119891 (119884) 119889119884
(10)
where Ω119899119894
is Ω119899excluding 119910
119894 11987801119894
11987802119894
are two subsetsof 1198780such that 119878
01119894cup 11987802119894
= 1198780 11987801119894
is a subset of 119899
belonging to 1198780with 119906
119894= 0 119878
01119894= 119899 119876
119899=
0 119906119894
= 0 and similarly 11987802119894
is a subset of 119899 belongingto 1198780with 119906
119894= 1 119878
02119894= 119899 119876
119899= 0 119906
119894= 1
The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892
1 119892
119873)
[26]
119892119894(119910119894) = (int
⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(11)
where Ω119899119894
= (1199101 119910
119894minus1 119910119894+1
119910119873
) 120601(119892119894 119906119894) le 0
and 120601(119892119894 119906119894) = (12 minus 119906
119894)119892119894 Consequently each set of
optimum local decisions is derived by solving several fixedpoint integral equations as
Γ119876
(119866) =
[[[[[[[[[[[[[[[[[[[[
[
(intcup119899isin119878011
Ω1198991
minus intcup119899isin119878021
Ω1198991
)119891 (119884) 119889119884
1198891199101
(intcup119899isin11987801119894
Ω119899119894
minus intcup119899isin11987802119894
Ω119899119894
)119891 (119884) 119889119884
119889119910119894
(intcup119899isin11987801119873
Ω119899119873
minus intcup119899isin11987802119873
Ω119899119873
)119891 (119884) 119889119884
119889119910119873
]]]]]]]]]]]]]]]]]]]]
]
(12)
Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892
1 119892
119873)
that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866
(119895) and the initial set as 119866(0) Gauss-Seidel
process for optimum local decision rules can be definedas
119866(119895+1)
= Γ119876
(119866(119895)
) forall119895 = 0 1 2 (13)
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
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DistributedSensor Networks
International Journal of
4 International Journal of Distributed Sensor Networks
Primarynetwork
PU
PU
Tx
Rx
Heterogeneous network
Macro-eNB
H-UE
H-UEH-UE
H-eNB(CCU)
M-UE
(LCU1)
(LCU3)
(LCU2)
Figure 2 A heterogeneous network overlapping with primarynetwork
CCU (fusion center)
PU
Sensing channels
Reporting channels
LCU1 LCU2LCUN
middot middot middot
Figure 3 Parallel cooperative spectrum sensing
this network the coverage areas of small cells and primarysystems can be overlapped This mutual interference occurswhen they are using the same time-frequency resources whilespatially located in a certain distance apart from each otheras shown in Figure 2 The frequency reusing of adjacentmacrocell user equipment (M-UE) or other primary systemsby small cells can create interferences to heterogeneoususer equipment (H-UE) Hence H-UE which operates assecondary users needs to transmit under a certain powerlevel which is acceptable by the licensed users PUs and atthe same time mitigates the interference from the primarysystem
The decision making on the presence or absence of PUsignals is a critical part of spectrum sensing procedure atcognitive H-UE In practice each cognitive piece of H-UEplays a role same as distributed LCUs that is equipped withspectrum sensing by energy detection to locally measurethe PU signal transmission power and frequencies Thelocal decisions are the output of certain local rules at thesedistributed pieces of H-UEs that will be sent to H-eNB withthe capability of a CCU to process the received informationand produce the final decision based on the embedded fusionrule Then in the presence of PU signals pieces of H-UEadapt their configurations to avoid mutual interferences withprimary network Since the channel impairments affect theinput observations of each energy detector at H-UE theassumption of independency is not correct any more anda cooperative decision making is required as the solution
Cognitive features enable the secondary users to analyzeinterference using the spectrum sensing mechanism that ismainly performed in LCUs whereas the decision is made forthe cooperative network Let us consider 119873 distributed LCUsas shown in Figure 3 In this figure the 119894th LCU is shownas LCU
119894that receives the observation signals 119910
119894 from the
PU through the sensing channels Each LCU119894sends its local
binary decision 119906119894 to the fusion center the CCU tomake the
final decision using the fusion ruleThemetrics of probabilityof detection 119875
119889119894 and probability of false alarm 119875
119891119894 for
local decision at the 119894th LCU119894are derived to be employed
for the performance evaluation Assuming that during thesensing time CUs do not broadcast and there is no mutualinterference between them the vector of the received signalthrough the sensing channels is defined as
119884 = 119867 sdot 119878119901
+ 119881 (4)
where 119878119901denotes PUrsquos transmitted signal 119867 = [ℎ
1
ℎ119894 ℎ
119873] states the sensing channel gain vector and 119884 =
[1199101 119910
119894 119910
119873] shows the observation vector in which
119910119894denotes the received signal at LCU
119894 The vector of addi-
tive white Gaussian noise (AWGN) at LCU receivers is119881 = [V
1 V
119894 V
119873] The observations of PUrsquos signal
are received through the sensing channels at LCU119894 In this
scenario the correlated channels lead to correlated sensingobservations at the LCU receivers that analyze the data asa binary hypothesis testing form 119867
0and 119867
1are the binary
hypotheses which define the absence and presence of PUrespectively Then the general form of the received signal atthe spectrum sensing part of LCU is
1198671
1199101
= ℎ1
sdot 119878119901
+ V1 119910
119873
= ℎ119873
sdot 119878119901
+ V119873
1198670
1199101
= V1 119910
119873= V119873
(5)
Given that 119910119894denotes the available observation of PU
signal at LCU119894receiver the local decision rule 119892
119894(119910119894) is
employed by LCU119894to make a binary decision 119906
119894about the
existence of PU signal Based on a set of local decision rulesas 119866(119884) = [119892
1(1199101) 119892
119894(119910119894) 119892
119873(119910119873
)] the fusion centerCCU receives the local decision as
119906119894
= 0 119892
119894(119910119894) le 0
1 119892119894(119910119894) gt 0
(6)
TheCCU follows a fusion rule as119876(119880)which is a Booleanfunction and whenever 119876(119880) = 0 the final decision is takenas 1198670 otherwise it is 119867
1 The local decision rule maps the
observation set 119884 = 1199101 119910
119873to a local decision set 119880 =
1199061 119906
119894 119906
119873 where 119906
119894isin 0 1 119894 = 1 119873 The
combination of local binary decisions 119906119894results in 2
119873 statesThus the 2
2119873
is the total number of states for final decision119906119891
= 119876(119880) and
119876 (119880) = 119876119899 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 1
le 119899 le 2119873
(7)
International Journal of Distributed Sensor Networks 5
where mod(119860 2) is the division remaining of 1198602 and 119906119894
=
mod((119899 minus 1)2(119894minus1)
2) is the 119894th bit of 119899 Hence 119876(119880) =
119876119899 119899 = sum
119873
119894=11199061198942119894minus1
+ 1 Consider two different sets as1198780
= 119899 119876119899
= 0 and 1198781
= 119899 119876119899
= 1 such that1198780
cup 1198781
= 1 2 2119873
then ΩOLDR = 119910119894
119876119899
= 0 119899 isin 1198780
where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867
0 With a given set of 119878
0 the fusion rule
119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867
0 For
a fixed fusion rule the region of final decision is ΩOLDR =
⋃119899isin1198780
Ω119899 where Ω
119899denotes the region of 119899th combination of
119876 as
Ω119899
= 119884 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 119876
= 119876119899
(8)
In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions
4 OLDR Algorithm with Gauss-Seidel Process
Each distributedH-UELCU119894performs the spectrum sensing
by energy detection to detect the initial PU signal obser-vation 119910
119894 This distributed information from all LCUs is
used by the OLDR algorithm to cooperatively optimize localdecision rules 119892
119894 according to the fix central fusion rule at
H-eNBCCU ANDOR and achieve the final minimized 119875119891
with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865
119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR
119891 (119884) 119889119884 (9)
where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867
1) minus 120582119875(119884 | 119867
0) Given
that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that
119865 (119866 119876) = 120574 + int119884isinΩOLDR
119891 (119884) 119889119884 = 120574
+ (int119892119894(119910119894)le0
(int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
) + int119910119894
int⋃119899isin11987802119894
Ω119899119894
)
sdot 119891 (119884) 119889119884
(10)
where Ω119899119894
is Ω119899excluding 119910
119894 11987801119894
11987802119894
are two subsetsof 1198780such that 119878
01119894cup 11987802119894
= 1198780 11987801119894
is a subset of 119899
belonging to 1198780with 119906
119894= 0 119878
01119894= 119899 119876
119899=
0 119906119894
= 0 and similarly 11987802119894
is a subset of 119899 belongingto 1198780with 119906
119894= 1 119878
02119894= 119899 119876
119899= 0 119906
119894= 1
The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892
1 119892
119873)
[26]
119892119894(119910119894) = (int
⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(11)
where Ω119899119894
= (1199101 119910
119894minus1 119910119894+1
119910119873
) 120601(119892119894 119906119894) le 0
and 120601(119892119894 119906119894) = (12 minus 119906
119894)119892119894 Consequently each set of
optimum local decisions is derived by solving several fixedpoint integral equations as
Γ119876
(119866) =
[[[[[[[[[[[[[[[[[[[[
[
(intcup119899isin119878011
Ω1198991
minus intcup119899isin119878021
Ω1198991
)119891 (119884) 119889119884
1198891199101
(intcup119899isin11987801119894
Ω119899119894
minus intcup119899isin11987802119894
Ω119899119894
)119891 (119884) 119889119884
119889119910119894
(intcup119899isin11987801119873
Ω119899119873
minus intcup119899isin11987802119873
Ω119899119873
)119891 (119884) 119889119884
119889119910119873
]]]]]]]]]]]]]]]]]]]]
]
(12)
Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892
1 119892
119873)
that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866
(119895) and the initial set as 119866(0) Gauss-Seidel
process for optimum local decision rules can be definedas
119866(119895+1)
= Γ119876
(119866(119895)
) forall119895 = 0 1 2 (13)
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
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DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 5
where mod(119860 2) is the division remaining of 1198602 and 119906119894
=
mod((119899 minus 1)2(119894minus1)
2) is the 119894th bit of 119899 Hence 119876(119880) =
119876119899 119899 = sum
119873
119894=11199061198942119894minus1
+ 1 Consider two different sets as1198780
= 119899 119876119899
= 0 and 1198781
= 119899 119876119899
= 1 such that1198780
cup 1198781
= 1 2 2119873
then ΩOLDR = 119910119894
119876119899
= 0 119899 isin 1198780
where ΩOLDR defines the region of optimal decision makingfor parallel cooperative cognitive network which leads to thefinal decision of 119867
0 With a given set of 119878
0 the fusion rule
119876(119880) is deterministic and constant and for every 119899 belongingto 1198780 119899th composition will result in a decision on 119867
0 For
a fixed fusion rule the region of final decision is ΩOLDR =
⋃119899isin1198780
Ω119899 where Ω
119899denotes the region of 119899th combination of
119876 as
Ω119899
= 119884 119906119894
= mod (119899 minus 1
2(119894minus1) 2) 119876
= 119876119899
(8)
In the next section the optimization problem for parallellocal decision rules is reduced to solve a set of fixed pointintegral equations that minimizes the Neyman-Pearson costfunction The decision rules are digitized for simplicity andGauss-Seidel algorithm [24] and Golden Section search [25]are applied to find the final solutions
4 OLDR Algorithm with Gauss-Seidel Process
Each distributedH-UELCU119894performs the spectrum sensing
by energy detection to detect the initial PU signal obser-vation 119910
119894 This distributed information from all LCUs is
used by the OLDR algorithm to cooperatively optimize localdecision rules 119892
119894 according to the fix central fusion rule at
H-eNBCCU ANDOR and achieve the final minimized 119875119891
with Gauss-Seidel process Based on the Neyman-Pearsoncriterion the optimum local decision rule is defined tominimize the corresponding cost function 119865
119865 (119866 119876) = 120582 (1 minus 120572) + intΩOLDR
119891 (119884) 119889119884 (9)
where 119876 is the Boolean fusion function 119884 denotes localobservations and 119891(119884) = 119875(119884 | 119867
1) minus 120582119875(119884 | 119867
0) Given
that 120574 = 120582(1 minus 120572) according to the above relations it can beconcluded that
119865 (119866 119876) = 120574 + int119884isinΩOLDR
119891 (119884) 119889119884 = 120574
+ (int119892119894(119910119894)le0
(int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
) + int119910119894
int⋃119899isin11987802119894
Ω119899119894
)
sdot 119891 (119884) 119889119884
(10)
where Ω119899119894
is Ω119899excluding 119910
119894 11987801119894
11987802119894
are two subsetsof 1198780such that 119878
01119894cup 11987802119894
= 1198780 11987801119894
is a subset of 119899
belonging to 1198780with 119906
119894= 0 119878
01119894= 119899 119876
119899=
0 119906119894
= 0 and similarly 11987802119894
is a subset of 119899 belongingto 1198780with 119906
119894= 1 119878
02119894= 119899 119876
119899= 0 119906
119894= 1
The set of optimum local decision rules that minimizes the119865 function in (10) can be defined as 119866 = (119892
1 119892
119873)
[26]
119892119894(119910119894) = (int
⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(11)
where Ω119899119894
= (1199101 119910
119894minus1 119910119894+1
119910119873
) 120601(119892119894 119906119894) le 0
and 120601(119892119894 119906119894) = (12 minus 119906
119894)119892119894 Consequently each set of
optimum local decisions is derived by solving several fixedpoint integral equations as
Γ119876
(119866) =
[[[[[[[[[[[[[[[[[[[[
[
(intcup119899isin119878011
Ω1198991
minus intcup119899isin119878021
Ω1198991
)119891 (119884) 119889119884
1198891199101
(intcup119899isin11987801119894
Ω119899119894
minus intcup119899isin11987802119894
Ω119899119894
)119891 (119884) 119889119884
119889119910119894
(intcup119899isin11987801119873
Ω119899119873
minus intcup119899isin11987802119873
Ω119899119873
)119891 (119884) 119889119884
119889119910119873
]]]]]]]]]]]]]]]]]]]]
]
(12)
Therefore the problem of optimum cooperative sensingis essentially reduced to optimizing a set of 119866 = (119892
1 119892
119873)
that satisfies the integral equations An iterative algorithmbased on Gauss-Seidel process can approximate the solutionof the above equations [26] This method is used for solvinga matrix of linear equations when the number of systemparameters is too high to find a solution by common PLUtechniques The initial requirement is that the diagonalelements of the matrix of equations must be nonzero andconvergence is provided when this matrix is either diagonallydominant or symmetric and positive definite [24] Let usconsider the local decision rule in 119895th iteration stage of thealgorithm as 119866
(119895) and the initial set as 119866(0) Gauss-Seidel
process for optimum local decision rules can be definedas
119866(119895+1)
= Γ119876
(119866(119895)
) forall119895 = 0 1 2 (13)
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 International Journal of Distributed Sensor Networks
where
119892119894
(119895+1)(119910119894)
= (int⋃119899isin11987801119894
Ω119899119894
minus int⋃119899isin11987802119894
Ω119899119894
)
sdot119891 (119884) 119889119884
119889119910119894
(14)
To reduce the computation complexity the discrete vari-ables 119905
119894are extracted from 119910
119894as 119879 = 119905
1 119905
119894 119905
119873 and
(14) can be described as
119892119895+1
119894(119905119894)
= ( sum
⋃119899isin11987801119894
Ω119899119894
minus sum
⋃119899isin11987802119894
Ω119899119894
)119891 (119879) Δ119879
Δ119905119894
(15)
Hence the discrete local decision rules are defined as
119885119894(119905119894) = 119868 (119892
119894(119905119894))
119868 (119909) = 0 119909 le 0
1 119909 gt 0
(16)
Accordingly the cost function 119865 is approximated as
119865 (119885 119876) = 120574
+ sum
119899isin1198780
( sum
11990511198851=1199061
sum
119905119894119885119894=119906119894
sum
119905119873119885119873=119906119873
119891 (119879) Δ119879)
(17)
Therefore
119892119895+1
119894(119905119894) = ( sum
119899isin11987801119894
minus sum
119899isin11987802119894
)
sum
1199051
sdot sdot sdot sum
119905119894minus1
sum
119905119894+1
sdot sdot sdot sum
119905119873
119894minus1
prod
119871=1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895+1)(119905119871)
1003816100381610038161003816100381610038161003816)
119873
prod
119871=119894+1
(1 minus
1003816100381610038161003816100381610038161003816mod (
119899 minus 1
2(119871minus1) 2) minus 119885
119871
(119895)(119905119871)
1003816100381610038161003816100381610038161003816)
119891 (119879) Δ119879
Δ119910119894
(18)
For the simplicity of computations discrete local decisionrules 119885
119894(119905119894) are substituted instead of 119892
119894(119905119894) as both of them
have the same region of decision making Note that the iter-ative process converges when absolute relative approximateerror |(119885
119894
(119895+1)(119905119894) minus 119885
119894
(119895)(119905119894))119885119894
(119895+1)(119905119894)| times 100 ≪ 120576 where
120576 gt 0 is prespecified tolerance parameter For each positivevalue of Δ119905
119894and initial selection of 119885
0
119894 the algorithm is
converged after a certain number of iterations to a set of119885119895
119894that satisfies the convergence condition Figure 4 presents
the flowchart of the developed optimization algorithm basedon the golden section search method for Neyman-Pearsoncriterion Golden section ratio of golden section search isapplied with 120593 = 0618 or symmetrically (1 minus 0618) = 0382
to condense the width of the range in each step [25]
5 Simulation and Discussion
For the performance evaluation of the proposed OLDRalgorithm and compared to the other methods the receiveroperating characteristic (ROC) curve is depicted as a graph of119875119889versus 119875
119891 To depict ROC curves for the OLDR algorithm
in each iteration the values of 119875119889and 119875
119891are provided based
on the OLDR rules As a benchmark the simulation resultsare compared to centralized network and parallel networkwith LRT local decision rule
When normal pdf is assumed for the sensed signalsthe conditional pdf rsquos under both hypotheses 119867
0and
1198671are defined as 119901(119910
1 1199102 119910
119873| 1198670) = 119873(120583
0 1198620)
and 119901(1199101 1199102 119910
119873| 1198671) = 119873(120583
1 1198621) where 119862
0
and 1198621are the covariance matrices under 119867
0and 119867
1
respectively With correlation coefficient minus1 le 120588 le 1the covariance matrix is written as 119862(119910
1 1199102 119910
119873) =
[1205902
1 12058812
12059011205902 120588
11198731205901120590119873
1205881198731
120590119873
1205901 1205881198732
120590119873
1205902 120590
2
119873]
The performance of OLDR algorithm for cooperativespectrum sensing is shown in this section Centralizednetwork (CN) with a fusion center is considered as theoptimum benchmark for the evaluation of the proposedmethod Numerical results are analyzed for both OLDRand LRT local decision rules with ANDOR fusion rulesThen the effect of various correlation coefficients (120588)on ROC curves is investigated with correlated sensedsignals
In the first case a cooperative spectrum sensing with twolocal cognitive users is considered Given that the receivedobservations from PU are random Gaussian signal 119867 sdot 119878
119901
with mean 120583119867sdot119878119901
= 2 and variance 1205902
119867sdot119878119901
= 1 added to 1198991
and 1198992as independent zero mean Gaussian noises such that
1205902
1198991
= 2 and 1205902
1198992
= 1 then the conditional pdf rsquos under bothhypotheses 119867
0and 119867
1 are 119901(119910
1 1199102
| 1198670) = 119873(120583
0 1198620) and
119901(1199101 1199102
| 1198671) = 119873(120583
1 1198621) Therefore 120583
0= [0 0] 119862
0= [2 0
0 1] 1205831
= [2 2] 1198621
= [3 1 1 2]Figure 5 compares the performance of OLDR and LRT
with centralized network As illustrated in this figure OLDRwithAND fusion rule outperforms the other techniques since
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 7
Start
Yes NoYesNo
Yes
No
End
Initializing of 120582(j) and Δ120582 j = 0
P(j)
flt 120572 P
(j)
fgt 120572
P(j)
flt 120572 P
(j)
fgt 120572
120582(j+1) = 120582(j) minus Δ120582j = j + 1 j = j + 1
j = j + 1
120582(j+1) = 120582(j) + Δ120582
120582(j+1) = 120582(j) + Δ120582
Δ120582 =
120593 times Δ120582 if P(j)
fgt 120572
minus120593 times Δ120582 otherwise
Pf(120582(j)) minus 120572 le 120576
P(j)
f(120582(j)) = 1 minusint
ΩOLDR(g1g119873)P(y1 yN |H0)dy1middot middot middot dyN
Figure 4 The proposed optimization algorithm (OLDR)
it is closer to the CN curve Meanwhile OLDR performsbetter than LRT with the same fusion rules for example at119875119891
= 002 OLDR shows 4 improvement in 119875119889compared to
the LRT with the same fusion rulesIn the second case parallel spectrum sensing with two
local cognitive users are considered with correlated receivedsignals as 120583
0= [0 0] 120583
1= [2 2] 119862
0= 1198621
= [1205902
1 12058812059011205902
12058812059011205902 1205902
2] The results of simulations with 120588 = 01 are
presented in Figure 6 which illustrates that the OLDR withAND fusion rule is more proximate to the CN curve andachieves a better performance than OR fusion rule forinstance at 119875
119891= 002 the improvement is about 4
The performance of the same network for various valuesof correlation coefficient (120588) is shown in Figure 7 Accordingto these results the performance is enhanced by the reductionof the correlation coefficient (120588)
Now a network of three local cognitive users with Gaus-sian signal observations is considered with mean 120583
119867sdot119878119901
= 2
and variance 1205902
119867sdot119878119901
= 1 added to zero mean independentnoises with 120590
2
1198991
= 3 12059021198992
= 2 and 1205902
1198993
= 1Thus the covariance
0 002 004 006 008 01 012 014 016 018 0203
04
05
06
07
08
09
1
CN-2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 CU
Pf
Pd
Figure 5 ROC comparison forGaussian received signal in indepen-dent Gaussian noise with two LCUs
03
04
05
06
07
08
09
1
CN 2 LCUOLDR-AND 2 LCUOLDR-OR 2 LCU
LRT-AND 2 LCULRT-OR 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
Figure 6 ROC comparison for deterministic received signal incorrelated Gaussian noises with two LCUs
matrices under 1198670and 119867
1are described as 119862
0= [3 0 0
0 2 0 0 0 1] and 1198621
= [4 1 1 1 3 1 1 1 2]Figures 8 and 9 show that increasing the number of local
cognitive users enhances the performance of the network ForGaussian received signals with independentGaussian noise at119875119891
= 002 the 119875119889is enhanced about 3 for OLDR with three
LCUs comparing to OLDR with two LCUsFrom these results it is concluded that for a fixed fusion
rule OLDR algorithm shows a superior performance oflocal decision rules to detect primary users compared toLRT method Apparently the probability of primary userdetection is increased with the number of cooperative localcognitive users equipped with spectrum sensing When thesensing channels are correlated results show performancedegradation in higher correlation coefficients
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 International Journal of Distributed Sensor Networks
03
04
05
06
07
08
09
1
0 002 004 006 008 01 012 014 016 018 02Pf
Pd
OLDR-AND 120588 = minus03
OLDR-AND 120588 = minus01
OLDR-AND 120588 = 0
OLDR-AND 120588 = 01
OLDR-AND 120588 = 03
Figure 7 ROC comparison for deterministic received signal incorrelated Gaussian noise with different correlation coefficients (120588)
CN 3 LCUOLDR-AND 3 LCU
OLDR-AND 2 LCUCN 2 LCU
0 002 004 006 008 01 012 014 016 018 02Pf
03
04
05
06
07
08
09
1
Pd
Figure 8 ROC comparison for Gaussian received signal in inde-pendent Gaussian noises with different numbers of LCUs
OLDR method is a low complexity solution for theproblem of (11) which is reduced to optimizing a set of localdecision rules 119866 = (119892
1 119892
119873) that satisfies the integral
equations (12) In addition the computation complexity of(14) has been reduced by considering discrete variables forthe observations 119910
119894 as well as local decision rules 119892
119894 to 119905119894
and 119885119894 respectively For the centralized network there is
no local decision rule and the local decision rule of LRTmethod is defined as Λ(119910
119894) le 120579
119894 where 120579
119894is the threshold
for the 119894th receiver In each iteration of the algorithm withLRTΛ(119884
119894) is calculated for all observations119910
119894 and compared
with threshold 120579119894 For the initial threshold within a range
of 119872 levels the time complexity of each local decision rulecan be written as 119874(119872) According to (18) the local decision
CN 3 LCUOLDR-AND 3 LCU
CN 2 LCUOLDR-AND 2 LCU
03
04
05
06
07
08
09
1
Pd
004 018 02008 01 012 014 016002 0060Pf
Figure 9 ROC comparison for deterministic signal in correlatedGaussian noises with different numbers of LCUs
Number of LCUs1 2 3 4 5 6 7 8
CNOLDRLRT
0
10
20
30
40
50
60
70Ti
me c
ompl
exity
Figure 10 Time complexity comparison of local decision rules
rule of OLDR algorithm 119892119895+1
119894 has to be updated at each
iteration with the time complexity of 119874(1198732) compared to the
other local decision rulesThe time complexity comparison oflocal decision rules for 119872 = 20 is shown in Figure 10 whichdescribes the increase of the calculations number propor-tional to the number of the receivers 119873 However since CNmethod consumes too large bandwidths for sending the datato the fusion center and LRT method assumes independentobservations they cannot be considered as optimum solutionfor cooperative cognitive users with correlated sensed signals
6 Conclusion
In this paper the cooperative spectrum sensing for cognitiveheterogeneous network has been designed with a parallelconfiguration An optimum algorithm for local decision
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Distributed Sensor Networks 9
rule based on Neyman-Pearson criterion with correlatedobservations from PUs has been proposed This schemebased on a discrete Gauss-Seidel iterative algorithm leads toa low complexity method of finding an optimum solution forLCUrsquos decision rules The performance evaluation shows theefficiency of this algorithm with fixed fusion rules in whichAND rule outperforms the OR fusion rule Furthermorewith lower correlation coefficients a better performance isachieved The experimental measurements and implemen-tation of OLDR algorithm for a distributed heterogeneouscognitive network are a challenging open area for the futurework Meanwhile optimizing the fusion rule simultaneouslywith the local decision rules study of different topologiesof cooperative cognitive networks the performance analysisof multilevel decision rules and shadowing in reportingchannels are among the other suggestions for the futureexploration
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] Federal Communications Commission ldquoSpectrum policy taskforcerdquo Report ET Docket 02-135 2002
[2] O B Akan O B Karli and O Ergul ldquoCognitive radio sensornetworksrdquo IEEE Network vol 23 no 4 pp 34ndash40 2009
[3] J Mitola III and G Q Maguire Jr ldquoCognitive radio makingsoftware radios more personalrdquo IEEE Personal Communica-tions vol 6 no 4 pp 13ndash18 1999
[4] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005
[5] H Arslan and M E Shin ldquoUWB cognitive radiordquo in CognitiveRadio Software Defined Radio and Adaptive Wireless Systemschapter 6 pp 355ndash381 Springer Dordrecht The Netherlands2007
[6] A A El-Saleh M Ismail M A M Ali and A N H AlnuaimyldquoCapacity optimization for local and cooperative spectrumsensing in cognitive radio networksrdquoWorld Academy of ScienceEngineering and Technology vol 4 no 11 pp 679ndash685 2009
[7] H Hosseini N Fisal and S K Syed-Yusof ldquoEnhanced FCMEthresholding for wavelet-based cognitive UWB over fadingchannelsrdquo ETRI Journal vol 33 no 6 pp 961ndash964 2011
[8] I F Akyildiz B F Lo and R Balakrishnan ldquoCooperative spec-trum sensing in cognitive radio networks a surveyrdquo PhysicalCommunication vol 4 no 1 pp 40ndash62 2011
[9] H Du Z XWei YWang andD C Yang ldquoDetection reliabilityand throughput analysis for cooperative spectrum sensing incognitive radio networksrdquo Advanced Materials and EngineeringMaterials vol 457-458 pp 668ndash674 2012
[10] Q-T Vien G B Stewart H Tianfield and H X NguyenldquoEfficient cooperative spectrum sensing for three-hop cognitivewireless relay networksrdquo IET Communications vol 7 no 2 pp119ndash127 2013
[11] X Liu M Jia and X Tan ldquoThreshold optimization of coop-erative spectrum sensing in cognitive radio networksrdquo RadioScience vol 48 no 1 pp 23ndash32 2013
[12] H Chen S Ta and B Sun ldquoCooperative game approach topower allocation for target tracking in distributedMIMO radarsensor networksrdquo IEEE Sensors Journal vol 15 no 10 pp 5423ndash5432 2015
[13] R M Vaghefi and R M Buehrer ldquoCooperative joint synchro-nization and localization in wireless sensor networksrdquo IEEETransactions on Signal Processing vol 63 no 14 pp 3615ndash36272015
[14] S Jaewoo and R Srikant ldquoImproving channel utilization viacooperative spectrum sensing with opportunistic feedback incognitive radio networksrdquo IEEECommunications Letters vol 19no 6 pp 1065ndash1068 2015
[15] M Najimi A Ebrahimzadeh S M H Andargoli and AFallahi ldquoEnergy-efficient sensor selection for cooperative spec-trum sensing in the lack or partial informationrdquo IEEE SensorsJournal vol 15 no 7 pp 3807ndash3818 2015
[16] C G Tsinos and K Berberidis ldquoDecentralized adaptiveeigenvalue-based spectrum sensing for multiantenna cognitiveradio systemsrdquo IEEE Transactions onWireless Communicationsvol 14 no 3 pp 1703ndash1715 2015
[17] G Loganathan G Padmavathi and S Shanmugavel ldquoAn effi-cient adaptive fusion scheme for cooperative spectrum sensingin cognitive radios over fading channelsrdquo in Proceedings ofthe International Conference on Information Communicationand Embedded Systems (ICICES rsquo14) pp 1ndash5 Chennai IndiaFeburary 2014
[18] I Y Hoballah and P K Varshney ldquoDistributed Bayesian signaldetectionrdquo IEEETransactions on InformationTheory vol 35 no5 pp 995ndash1000 1989
[19] W A Hashlamoun and P K Varshney ldquoAn approach tothe design of distributed Bayesian detection structuresrdquo IEEETransactions on Systems Man and Cybernetics vol 21 no 5 pp1206ndash1211 1991
[20] W A Hashlamoun and P K Varshney ldquoFurther results ondistributed Bayesian signal detectionrdquo IEEE Transactions onInformation Theory vol 39 no 5 pp 1660ndash1661 1993
[21] R Viswanathan and P K Varshney ldquoDistributed detectionwithmultiple sensors Part Imdashfundamentalsrdquo Proceedings of theIEEE vol 85 no 1 pp 54ndash63 1997
[22] V R Kanchumarthy R Viswanathan and M MadishettyldquoImpact of channel errors on decentralized detection perfor-mance of wireless sensor networks a study of binary modu-lations Rayleigh-fading and nonfading channels and fusion-combinersrdquo IEEE Transactions on Signal Processing vol 56 no5 pp 1761ndash1769 2008
[23] S M Mishra A Sahai and R W Brodersen ldquoCooperativesensing among cognitive radiosrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo06) pp1658ndash1663 Istanbul Turkey July 2006
[24] A W Al-Khafaji and J R Tooley Numerical Methods inEngineering Practice Holt Rinehart and Winston New YorkNY USA 1986
[25] X Li J Cao Q Ji and Y Hei ldquoEnergy efficient techniques withsensing time optimization in cognitive radio networksrdquo in Pro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo13) pp 25ndash28 Shanghai China April 2013
[26] Y Zhu R S Blum Z-Q Luo and K M Wong ldquoUnex-pected properties and optimum-distributed sensor detectors fordependent observation casesrdquo IEEE Transactions on AutomaticControl vol 45 no 1 pp 62ndash72 2000
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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