Spectrum Sensing in Cognitive RadioSushobhan Nayak Y7027460

Deekshith Rao Juvvadi Y7027128Department of Electrical EngineeringIndian Institute of Technology Kanpur

Abstract—After its introduction in 1999, cognitive radio isbeing touted as the next Big Bang in wireless communication.A large part of the usability of cognitive radio rests upon itsability to detect white spaces in the spectrum, i.e. to detect thepresence of the primary or licensed user. As such, spectrumsensing occupies most of the research potential as far as cognitiveradio is concerned, and in this paper, a few of the spectrumsensing techniques will be looked upon. After looking at howthe Neyman-Pearson optimal detector for spectrum sensing canbe reduced to other well-known detectors, a detailed discussionof three signal processing techniques, viz. matched-filter, energydetection and cyclostationarity detection, is provided. Of specialinterest is the topic of cooperative sensing, where a number ofcognitive nodes can interact with each other or a master node toefficiently carry out the spectrum sensing, often more effectively.We look at a few of such techniques, varying from narrowbandto wideband detection, with special emphasis on optimal dataand decision fusion. Finally, we also consider one blind detectiontechnique, which can be applied even when no information aboutthe channel or the primary signal is available.

I. INTRODUCTION

After initially being proposed in [1], cognitive radio isbeing tauted as the next Big Bang in wireless communications.As [2] asserts, conventional fixed spectrum allocation resultsin a large part of frequency band remaining underutilized.Channels dedicated to licensed(primary) users are out ofreach of unlicensed users, while the licensed users hardlyoccupy the channel completely, at all times. Cognitive radiorevolution hopes to tap into this inconsistency and attemptsto utilize the channel in its full capacity. In this paradigm,“either a network or a wireless node changes its transmissionor reception parameters to communicate efficiently avoidinginterference with licensed or unlicensed users. This alterationof parameters is based on the active monitoring of severalfactors in the external and internal radio environment, suchas radio frequency spectrum, user behaviour and networkstate.”[3]. While the above description is essentially that offull cognitive radio, the present work will be primarily focusedon spectrum sensing cognitive radio. In this paradigm, thesecondary unlicensed users keep sensing the spectrum todetermine if a primary user is transmitting or not; and thenthey occupy the idle band and leave it as soon as the primaryuser kicks in. So it is extremely important that we employefficient and robust spectrum sensing techniques to determinethe presense of the signal from the primary user, and a reviewof those techniques is the basis of this term paper.

In the description that follows, the following system modelhas been used. Assuming there are M > 1 antennas at the

receiver, there are two hypotheses based on whether signalfrom primary user is present or absent – H0 and H1. Let thereceived signal, transmitted signal and noise vector for the Mantennas be

x(k) = [x1(k) . . . xM (k)]T,

s(k) = [s1(k) . . . sM (k)]T,

n(k) = [n1(k) . . . nM (k)]T.

respectively. The hypothesis problem on N such samples canthen be formulated as

H0 : x(k) = n(k),

H1 : x(k) = s(k) + n(k), k = 0, . . . , N − 1.

For a given probability of false alarm Pfa, i.e. the proba-bility of mistaking the presence of the primary signal when itactually isn’t, we need to choose the hypothesis that maximizesthe probability of detection Pd, i.e. the probability of correctlydetermining the presence of the primary signal, for a givennumber of samples. In the description that follows, following[4] it would be shown that the optimal receiver derived fromNeyman-Pearson theorem reduces to many known estimators.Special emphasis will be given to a few latest techniques incooperative sensing, and one blind sensing algorithm will alsobe evaluated.

II. NEYMAN-PEARSON MODEL

For a given Pfa, the Neyman-Pearson theorem asserts thatPd will be maximized for the following decision statistic,which is essentially the likelihood ratio test (LRT):

TLRT (x) =p(x|H1)

p(x|H0),

where x is the aggregation of x(k), k = 0, . . . , N−1 [4]. Themodel assumes that the distributions of signal and noise areknown, which is hardly the case. Under the assumption thatwe are dealing with a flat fading channel, and the si(k)’s areindependent over k, we have the following PDFs

p(x|Hi) =

N−1∏k=0

p(x(k)|Hi).

Fig. 1. Energy Detector (Source: [5])

Assuming Gaussian distributions for noise and signal samples,i.e., n(k) ∼ N (0, σ2

nI) and s(k) ∼ N (0,Rs), the LRTreduces to estimator-correlator(EC) detector

TEC(x) =

N−1∑k=0

xT (k)Rs(Rs + σ2nI)−1

x(k).

It can further be noticed that Rs(Rs + σ2nI)−1

x(k) is theMMSE estimation of s(k), so that TEC is actually the cor-relation of the observed signal x(k) with MMSE estimationof s(k). The assumption that Rs = σ2

sI reduces TEC to theenergy-detector (ED) given by

TED(x) =

N−1∑k=0

xT (k)x(k).

Furthermore, under the assumption that s(k) is deterministicand known to the receiver, LRT reduces to the matched-filterdetector given by

TMF (x) =

N−1∑k=0

sT (k)x(k).

So, we notice that the LRT reduces to different known detec-tors under given constraints.

III. SIGNAL PROCESSING TECHNIQUES FORTRANSMITTER DETECTION

Mainly three techniques are in vogue for transmitter detec-tion, which are described below.

A. Matched-Filter

Matched filter optimizes detection by maximizing receivedSNR. Given that it has a priori knowledge of the primarysignal, coherency makes sure that only O(1/SNR) samplesare needed for effective detection, thereby making detectionfaster so that an idle channel can be quickly occupied withoutdelay. On the bleak side, knowledge of the primary signalmight not be available. Furthermore, in case there are a lotof primary users, the radio receiver would have to have adedicated matched filter for each different one of them.

B. Energy Detector

To counter the above problem, non-coherent detection canbe done through energy-detectors ([5]). Consider Figure 1.The basic idea is to compare the enrgy of the received signalto a threshold to determine the presence of the primary signal.It can also be implemented by averaging the FFT of thesignal over frequency bins and comparing with a threshold.

Mathemetically, if the test statistic be (in case of a singlereceive antenna)

T (x) =1

N

N−1∑k=0

|x(k)|2,

under H0, T (x) is Chi-square distributed with 2N degreesof freedom, the PDF of which can be approximated by CLTas a Gaussian with mean µ0 = σ2

n and variance σ20 =

1N [E|n(k)|4 − σ4

n]. For n(k) ∼ CN (0, σ2n), E|n(k)|4 = 2σ4

n,and σ2

0 = 1N σ

4n. Therefore, for a given threshold ε, false alarm

probability is

Pfa(ε) = Pr(T (x) > ε|H0)

=1√

2πσ20

∫ ∞ε

e−(T (x)−µ0)2/2σ20

= Q((

ε

σ2n

− 1

)√N

).

Similarly, for H1, T (x) has a Gaussian distribution with µ1 =

σ2s + σ2

n and σ21 = 1

N [E|s(k)|4 + E|n(k)|4 − (σ2s − σ2

n)2].

Assuming s(k) to be a complex PSK modulated signal withE|s(k)|4 = σ4

s , we have σ21 = 1

N (2γ + 1)σ4n, where γ =

σ2s/σ

2n. Then, for threshold ε, probability of detection is

Pd(ε) = Pr(T (x) > ε|H1)

= Q

((ε

σ2n

− γ − 1

)√N

2γ + 1

).

Hence, for a target false alarm of Pfa, probability of detection

Pd = Q(

1√2γ + 1

(Q−1(Pfa)−

√Nγ))

.

Non-coherent detection requires more number of samples(O(1/SNR2)) to give the same performance as the coher-ent detector. [6] presents many more disadvantages of thistechnique. The threshold is ambiguous as it is susceptible tovarying noise levels. In-band interference can give erroneousresults even if adaptive thresholding is followed. Also, thedetector’s failure to recognize interference rules out the use ofany adaptive signal processing for interference cancellation.

C. Cyclostationary Detection

Digital modulated signals usually exhibit cyclostationar-ity, i.e. their statistical parameters vary periodically in time.Since different types of signals have diffrent non-zero cyclicfrequencies, they can be identified from their signature. [7]elaborates a few statistical tests to detect cyclostationarity.One of the useful techniques is determination on the basis ofspectral-correlation density(SCD). For a source signal x(t),the received signal after wireless transmission can be writtenas

y(t) = x(t)⊗ h(t)

where h(t) is the channel response. The SCD of y(t) is

Sy(f) = H(f +α

2)H∗(f − α

2)Sx(f)

with α being the cyclic frequency of x(t), and other symbolshave their usual meaning. While a signal takes nonzero val-ues at a few nonzero cyclic frquencies, noise is devoid ofcyclostationarity, so that noise SCD is zero at all nonzerocyclic frequencies, there by making analysis of SCD a validand effective technique. The advantages of the process includerobustness against noise and channel fluctuations. On the flipside, it requires a high sampling rate, many samples for com-plex SCD computation and the possibility that sampling timeerror and frequency offset could affect the cyclic frequencies.

IV. COOPERATIVE SENSING

Given a master node, many cognitive nodes can interactamongst each other to detect the presence of primary signal,leading to increased sensitivity due to their dispersed nature.They can either send their collected data to the master, lettingthe master do data fusion to decide on the presence ofthe primary signal; or they could each send their individualdecisions and the master conducts decision fusion to take adecision.

A. Data Fusion

Let each user employ energy detection and compute re-ceived source signal as

Ti(x) =1

N

N−1∑k=0

|xi(k)|2,

which is sent to the master who linearly combines them to getdecision statistic

T (x) =

M∑i=1

giTi,

with gi ≥ 0 and∑Mi=1 gi = 1 (As one might notice, the

notations of the previous section have been modified a bitfor simplicity– the M antennas are now being treated as Mcognitive nodes, without any implication on the validity of thediscussion). gi’s are decided using a priori knowledge, if it isavailable. [8] asserts that for low-SNR, optimal gi’s are givenby

gi =σ2i∑M

k=1 σ2k

, i = 1, . . . ,M,

with σ2i being the received source signal power of user i. The

decision statistic is then compared to a threshold to decide onthe presence of the primary user, just as in a general energydetector case.

B. Decision Fusion

While [9] asserts that the Chair-Varshney rule based on alog likelihood ratio test is the optimal decision fusion rule,it also describes two other simplistic rules. OR fusion rulepredicts the presence of the primary signal if at least one of

the received decision from the users is 1 (indicating presence).The probabilities in this case are

Pd = 1−M∏i=1

(1− Pd,i),

Pfa = 1−M∏i=1

(1− Pfa,i),

where Pd,i and Pfa,i are individual probabilities of the ithuser. AND rule, as the name suggests, outputs 1 only if allthe individual decisions are 1, the probabilities in this casebeing

Pd =

M∏i=1

Pd,i,

Pfa =

M∏i=1

Pfa,i.

The majority rule asserts that if more than half of the receiveddecisions are 1’s, then the master rules in favor of the presenceof the primary signal. In general, if the master decides 1 whenK out of the M decisions are 1, then the probabilities become

Pd =

M−K∑i=0

(M

K + i

)(1− Pd,i)M−K−i × (1− Pd,i)K+i

,

Pfa =

M−K∑i=0

(M

K + i

)(1− Pfa,i)M−K−i × (1− Pfa,i)K+i

.

The fusion decisions described above are known as countingrules, as the master essentially counts the number of decisionsin favor of primary. [10] however propose a linear quadraticdetector that can provide better results. Let the decision takenat the ith node be Ui. Then the paper suggests a sub-optimalsolution to the fusion problem that uses partial statisticalknowledge. It “makes use of up to the second order statistics ofthe local decisions {Ui}M1 under H1 and up to the fourth orderstatistics under H0, in the form of moments.” Independentobservations under H0 lead to easy calculation of momentsunder H0. The pairwise statistics under H1 lead to determi-nation of second order moments under H1. This is usuallymuch easier than obtaining entire statistics of all the signalswhen a large number of cooperating nodes are concerned.The detectors are the linear-quadratic (LQ) detectors, i.e. theycompare a linear-quadratic function of {Ui}M1 with a thresholdto make their decision. The inclusion of quadratic termsmotivates the improvement over the linear counting rule. Theuse of moments only helps adapt the method for all classes ofdistribution. The deflection criterion is used to optimize over aclass of LQ detectors. The deflection or the generalised signal-to-noise ratio of a detection rule that compares a function T (x)of observation x is given by:

DT =[E0(T (X))− E1(T (X))]

2

Var0(T (X)).

Higher deflection is an indication of better error-probabilityperformance. It is to be noted that the decisions {Ui}M1contribute to the decision fusion hypothesis only throughtheir probabilities under the two hypotheses. So, an intelligentdecision variable will be the log-likelihood ratios of the bitsthemselves. The metric is:

T (X) = hTX + XTAX

with X being the vector of log-likelihood ratios of the receivedbits with means under H0 subtracted:

Xi = log

(p1(Ui)

p0(Ui)

)− E0

[log

(p1(Ui)

p0(Ui)

)]where h is a vector of length M and A is an M ×M squarematrix. We need to find a LQ detector of the above form whileminimizing the deflection. This requires the knowledge of upto the second order statistics of the bits under H1 and up tothe fourth order statistics of the bits under H0 since theseterms explicitly appear in the expression for the deflection.Let’s define the matrix C = E0[XXT ]. Adding a constantdoesn’t change the decision metric, so that we might as welllook upon

S(Z) = pTZ

where p and Z are (M2 +M)× 1 vectors, and

Z =

X1 . . . XM

X21 − C11 . . . X1XM − C1M

X2X1 − C21 . . . X2XM − C2M

. . .XMX1 − CM1 . . . X

2M − CMM

So, Z is formed by appending X with raster scanned form ofXXT − C. Thus the first M elements of Z are the elementsof X, the next M are the first row of XXT −C etc. p is thevector formed by appending h with A in raster scanned form.So, we essentially have to solve for optimal p that maximizesdeflection.

Now Z has zero mean under H0. So, the deflection of S(Z)is given by

DS =pTµ

2

pTKp

with µ = E1(Z) and K = E0(XXT ). The problem nowessentially is to optimize over p’s that are not in the singularspace of K.

C. 2-Node Cooperation

In the previous subsection, the basic paradigm was commu-nication of data or decision to a master node which has theauthority to take the final decision. [11] describes a 2-nodecognitive user model, where decision is taken by cooperationbetween the nodes without the involvement of the master. Fornotational convenience, let’s define the system model for thissection as follows:

y = fx+ w

where x is the sent signal, y is the received signal, f and w arefading coefficient and noise respectively, modelled as complex

Fig. 2. Cooperation between U1 and U2 (Source: [11])

Fig. 3. Timeslot distribution (Source: [11])

Gaussian random variables. Now consider, for simplicity, a 2-user netwrok. Let the radios be U1 and U2. The two need tovacate the band dedicated to a primary user as soon as theprimary signal is transmitted. However, if a user is situated atthe decodability boundary (U1 in Figure 2), the time to detectthe primary signal is too large (more samples needed as SNRis too low) for comfort. But intuitively, we notice that U2 canget a better detection time and can relay that to U1, therebyreducing the total time of detection by U1.

Assuming that both the users communicate with a singlebase station, we can assign U2 the role of relaying U1’s signal.By the use of slotted transmission, U1 and U2 can transmitin successive slots. From Figure 3, U1 transmits in timeslot T1, while U2 listens. In T2, U2 relays the previous slotinformation. Incorporating the possibility that the primary useris transmitting, we have the following expression for the signalreceived by U2 from U1 in slot T1,

y = θhp2 + ah12 + w,

where hpi denotes the instantaneous channel gain between theprimary user and Ui, h12 denotes the instantaneous channelgain between U1 and U2, and w is the additive Gaussian noise.It is also assumed that hp2, h12, w are zero-mean complexGaussian distributed, and are pairwise independent. Reciprocalchannels assure that h12 = h21. θ is the variable that representsthe presence or absence of the primary signal, i.e., θ = 1implies primary is transmitting. θ = 0 otherwise. a is thesignal from U1 such that Ea = 0. By putting the transmitpower constraint of U1 as P , we have

E[|ah12|2] = PG12,

with G12 = E[|h12|2] refering to the channel gain betweenU1 and U2. The pairwise independence between hp2, h12, w

assures thatE[|y|2] = θ2P2 + PG12 + 1

where P2 = E[|hp2|2] is the received power at U2 due to theprimary signal. When timeslot T2 comes, U2 starts relayingsignal received from U1. Assuming U2 has maximum powerconstraint P , U2 appropriately scales down the received signalto meet this power constraint. The new relayed signal (that wasoriginally sent by U1) is received by U1, which is given by

y =√βyh12 + θhp1 + w

=√βh12(θhp2 + ah12 + w) + θhp1 + w,

where hp1 is the instantaneous channel gain between primaryuser and U1, w is additive Gaussian noise, and β is the scalingfactor employed by U2 to match the power constraint,

β =P

E[|y|2]=

P

θ2P2 + PG12 + 1.

Cancelling the message signal, U1 now has

Y = θH +W

with H = hp1 +√βh12hp2 and W = w +

√βh12w.

The detection problem now simply reduces to the hypothesistesting problem that given the observation

Y = θH +W

which of the following holds

H1 : θ = 1

H0 : θ = 0.

Now, a simple energy detector can be used to detect thepresence of the primary signal. The model can be furtherextended for more than 2 nodes– a detailed discussion ofwhich can be found in [11].

D. Wideband Detection

The methods discussed above usually pertain to detectionof primary user in a narrow fixed band. Wideband spectrumsensing would require much more resourses, and as suchusing only one cognitive node for sensing the whole band iscounter-intuitive. [12] propose a cooperative shared spectrumsensing model for wideband detection in a noisy channel. Theidea is essentially to form a number of groups of cognitiveradios, each group dedicated towards detecting a particularband in the whole of frequency spectrum. The nodes in asingle group cooperate amongst themselves, taking decisionstogether, thereby effectively allocating system resourses.

First, the wide bandwidth of f = [f1, fM+1) to be scannedis divided into M subbands, viz.

fm = [fm, fm+1), f =

M⋃m=1

fm.

A group of cognitive nodes is assigned for each fm, whichare denoted by Cm ε C = {1, 2, . . . , N} such that

Cm ∩ Cn = Φ, C =

M⋃m=1

Cm.

So, the set of {dm : m = 1, 2, . . . ,M} many nodes are sensingfrequency band fm. Considering a network with dm = |Cm|radios in each cluster, the binary hypothesis test at time tessentially reduces to (for each cluster):

Hm0 : xmj (t) = vmj (t)

Hm1 : xmj (t) = s(t) + vmj (t)

with j = 1, 2, . . . , dm, m = 1, 2, . . . ,M, t =1, 2, . . . , Ti. s(t), x

mj (t), vmj (t) are the primary signal and

received signal and the noise at j’th node in i’th cluster,respectively. Ti is determined from time-bandwidth product.It is assumed that s(t) and {vmj (t)} are independent of eachother for all m, j, t. Again, noise is assumed to be zero-meanwhite, may be non-Gaussian. The spectrum sensing SNR isdefined as

γs∆=

1

σ2v

1

T0

∫ T0

0

|s(t)|2

where T0, σ2v are signal duration and power of sensing noise.

Using the local decision function Γ : CT0+1×1 → {0, 1}, everynode makes a decision. The decision function can be any thing,ranging from energy detector, coherent detector, wavelet-baseddetector or cyclostationary detector. The local decision of eachradio is denoted by bmj such that

Γ({xmj (t)}T0

t=0) =⇒ Hi : bmj = i

where iε{0, 1}. A generic probabilistic model given by

Pij = Pr{bmj = Hi|Hj}, i, jε{0, 1}

is used to characterize the performance.The decisions bmj are sent to a cognitive base station(CBS),

and the received signal at the CBS is

ymj = Ahmj + wmj , hmj = {−1, 1} =⇒ bmj = {0, 1}

where A,wmj are attenuation factor and noise respectively (0 ismapped to -1 and 1 is self-mapped). The CBS, based on this,decides whether the primary signal is present or not. Whilethe optimal detector

L(ym) =f(ym|H0)

f(ym|H1)

is hard to implement as it requires the local performanceparameter, Pij , the authors propose a suboptimal detector thatworks in two stages: 1)detect the transmitted{bmj }

dmj=1

using a

MAP detector, and 2) fuse the detected {bmj }dm

j=1to predict the

presence of the primary signal. The fused decision is finallyrelayed to all the nodes.

V. BLIND SPECTRUM SENSING

Blind spectrum detection assumes no information on sourcesignal or noise power.[13] proposes one such method. It usesthe Akaike Information Criterion (AIC) to detect vacant sub-bands. The basic idea is the following: if we are approximatingan unknown pdf f by gθ, then the Kullback-Leibler discrep-ancy

−Eθ[∫

fX(x) log gθ(x)dx

]is an indication of how different they are from each other. Theabove expectation can be estimated through Akaike model.The AIC is an approximate unbiased estimator of this expec-tation and is given by

AIC = −2

N−1∑n=0

log gθ(xn) + 2U

The paper proposes that ambient noise be modelled usingGaussian distribution, and its norm as Rayleigh. So, thefrequency band of the spectrum is scanned using slidingwindows and Akaine weights are computed for the Gaussiandistribution. The first step involves choosing the size of theobserved window for an estimate of the parameters θ over thiswindow. The Akaike values are estimated there after, and thewindow is slid by a symbol. The maximum value of the Akaikeweights corresponds to the vacant sub-bands (as the estimatedmodel is Gaussian, it will have the highest Akaike weightsfor the frequencies which are spanned by pure Gaussian noisesignal), and similar subbands are found based on the referencesub-band. Finally, a threshold is set for the weights, based onwhich the prediction of the presence of primary signal is done.

VI. CONCLUSION

In this term paper, various issues in spectrum sensing forcognitive radio and available techniques to handle those issueshave been described. While traditional methods like matched-filtering, energy detection and cyclostationary detection weretouched upon, special emphasis was given to cooperativedecision methods, and a few of them were described in detail,each having their different strengths and weaknesses. Thispaper, however, is in no way a comprehensive discussion ofall the pertinent techniques, as due to lack of space, newtechniques like the multi-taper method of cyclostationarity [14]

and the wavelet based wideband spectrum sensing [15] havebeen left out. Nonetheless, it is expected that the discussedissues and techniques are adequate enough for a first exposureto the field.

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