QoS aware admission and power control for cognitive radio cellular networks

WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2009; 9:1520–1531Published online 26 March 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/wcm.765

QoS aware admission and power control for cognitive radiocellular networks

Jie Xiang1∗,†, Yan Zhang1, Tor Skeie1,2 and Jianhua He3

1Simula Research Laboratory, Norway2Department of Informatics, University of Oslo, Norway3Institute of Advanced Telecommunications, Swansea University, UK

Summary

In cognitive radio cellular networks (CogCell), the secondary users (SUs) are allowed to access the channelslicensed to the primary users (PUs) including Primary Transmitters (PTs) and Primary Receivers (PRs), only ifthe interference to the PRs is less than the predefined threshold, and the quality of service (QoS) requirements ofPTs are guaranteed. In addition, different SUs may require different levels of QoS, and pay differently dependingon the provided QoS. The network operator achieves different secondary revenues by admitting SUs in differentQoS levels. The problem we address in this paper is to maximize the total secondary revenue relative to theinterference constraints on PRs, and QoS requirements for both PTs and SUs. We formulate this optimizationproblem, and propose a power control scheme for both PTs and SUs. Then, we introduce three solutions includingan exact solution using dynamic programming, a greedy heuristic algorithm, and a minimal signal-interference-plus-noise-ratio (SINR) removal algorithm. Based on these algorithms, we propose three QoS aware admission andpower control (QAPC) schemes, one optimal solution called QAPC-dynamic, and two approximate solutions calledQAPC-greedy and QAPC-minimal SINR removal algorithm (MSRA) , respectively. Numerical results show thatQAPC-dynamic always achieves the highest secondary revenue while QAPC-MSRA gives the lowest secondaryrevenue. Since the time complexity of QAPC-dynamic is much higher than the other two schemes, QAPC-greedyis recommended considering the trade-off between the computation complexity and performance gain. Copyright© 2009 John Wiley & Sons, Ltd.

KEY WORDS: cognitive radio cellular networks; admission control; power control

1. Introduction

Spectrum is traditionally assigned via a fixed frequencyallocation policy. A portion of spectrum is exclusivelyused by a specific wireless system, and all subscribersto a wireless system should be granted to access

∗Correspondence to: Jie Xiang, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway.†E-mail: [email protected]

the exclusive spectrum. Following this approach, thespectrum resource is in danger of being exhausted.However, recent measurements have shown that thelicensed spectrum utilization is highly dependent onthe location and time [1,2]. For instance, in a certaingeographic area, the allocated spectrum bands are

Copyright © 2009 John Wiley & Sons, Ltd.

QOS AWARE ADMISSION AND POWER CONTROL FOR COGCELL 1521

not efficiently utilized. In mid-night, the spectrum isseldom used. To exploit the unused licensed spectrum,which is called spectrum hole, the concept of cognitiveradio (CR) has been proposed [3]. Enabled by CR,the unlicensed secondary users (SUs) can access thespectrum holes in an opportunistic way. The future-generation wireless system is characterized by self-x properties, i.e. self-configuration, self-management,and self-healing. With CR, cognitive radio cellularnetworks (CogCell) will play a significant role todevelop such kind of future-generation system. InCogCell, the CR-enabled SUs are able to sense theavailable spectrum holes, self-configure themselvesto best fit with the specific frequency, share thespectrum with the licensed primary users (PUs)efficiently, and opportunistically access the spectrumholes. In such a way, the spectrum utilization ofthe base station (BS) is able to be significantlyimproved.

However, spectrum sharing brings us into agreat challenge that the SUs activity may causesevere interference with the PUs including primarytransmitters (PTs) and primary receivers (PRs).For the uplink of PTs, admitting SUs will causeinterference with the BS and decrease the uplink signal-interference-plus-noise-ratio (SINR) of PTs. On theother hand, admitting SUs will increase the interferencepower received by PRs. In order to minimize theinterference with PTs and PRs, admission controlscheme at the BS plays an indispensable role inCogCell. The issue of admission control schemehas been extensively investigated in conventionalcellular systems [4]. As indicated, conventional cellularnetworks are considerable different from CogCell.In CogCell, more constraints have to be consideredwith respect to the admission control problem dueto the presence of PUs. Let’s consider a generalscenario in CogCell that consists of one BS, severalSUs and PUs. SUs can be admitted by the BSprovided that the interference with PRs is less thanthe predefined threshold, and the quality of service(QoS) requirements of PTs are guaranteed. On theother hand, SUs have to adapt their transmissionpower to achieve their own QoS demands. Howto select a set of SUs and efficiently control thetransmission power of these SUs is a very challengingproblem.

In the literature, only few attempts have beenmade on the admission and power control problemin CogCell. In Reference [5], M.H. Islam et al.investigated the distributed power allocation andadmission control problem in the scenario of one BS

with multiple antennas, several SUs, one PT and onePR. In References [6,7], Y. Xing et al. consideredthe scenario with one PR, and several SUs withseparative secondary receivers. The study proposeda distribute constrained power control algorithm andfound the optimal link subset to achieve the maximumrevenue with the help of a potential game. In Reference[8], L. Zhang et al. modeled a smooth optimizationproblem, and proposed a minimal SINR removalalgorithm (MSRA) in order to find the optimal setof SUs to achieve maximum revenue. The results inReference [8] showed that MSRA outperforms thegame theory approach in Reference [6]. However,all of these studies assumed only a single PR ora single PT in the system. This assumption is notvalid since normally there are a number of PUssharing spectrum with SUs. In References [9,10],the authors explored the scenario with multiple PUs.However, in Reference [9], PTs are not considered inthe scenario, and no optimal solution is given. Theproblems formulated in Reference [10] are based onthe assumption that all SUs are admitted to the BS. Thisassumption is invalid for the scenario of large numberof SUs.

In this paper, we take the perspective of thenetwork operator at the BS and address the jointadmission and power control in CogCell. In particular,our contributions include three folds to advancethe state-of-the-art. These aspects also indicate themajor difference from the previous studies. Firstly,we formulate an optimization problem to maximizethe secondary revenue subjected to the interferenceconstraints on PRs, and QoS requirements of bothPTs and SUs. Data transmission rate (DTR) are usedas the major QoS metrics. Secondly, we analyze theQoS and power constraints of both PTs and SUs, andpropose a power control scheme for both PTs and SUs,then we model the admission control problem into aninstance of the classical multidimensional knapsack (d-KP) problem. We explore three methods, i.e., dynamicprogramming, greedy heuristic algorithm, and MSRA(used in Reference [8]), to solve this problem. Thirdly,simulation results are presented to demonstrate theperformance of the proposed schemes. We evaluatedthese schemes by observing the secondary revenue inthe case of changing the following parameters: thenumber of SUs, the number of PRs, and the interferencethresholds of PRs. Numerical results show that QAPC-dynamic always achieves the most secondary revenue,while QAPC-MSRA achieves the least secondaryrevenue. However, since the time complexity ofQAPC-dynamic is much higher than the other two

Copyright © 2009 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2009; 9:1520–1531

DOI: 10.1002/wcm

1522 J. XIANG ET AL.

Fig. 1. System model.

schemes, QAPC-greedy is recommended consider-ing both time complexity and secondary revenueoutput.

The rest of the paper is organized as follows. InSection 2, we introduce the CogCell system model, andformulate the network operator problem. In Section 3,we propose a power control scheme for both PTsand SUs. In Section 4, we transfer the originaloptimization problem into an instance of the classical d-KP problem, and introduce several algorithms to solveit. In Section 5, we explain our proposed QoS awareadmission and power control schemes. In Section 6, theperformance of our proposed schemes are evaluated.Finally, we draw the conclusions in Section 7.

2. System Model and Definitions

In this section, we will describe the system model,introduce the definitions of the interference caused bySUs, uplink SINR, and QoS requirements. Finally, wewill formulate the operator problem.

2.1. System Model

There are two modes in CogCell for spectrum sharingbetween SUs and PUs. One mode is called overlay,wherein SUs should stop transmission on the channelonce PUs are detected. The other one is called underlay,

wherein SUs and PUs can coexist and share the samespectrum with each other in case the interferencecaused by SUs is under the predefined threshold[11,12]. In this paper, we focus on the underlay mode.The system model of CogCell used in this paper isillustrated in Figure 1, where there is one BS, severalPUs and SUs. We split the PUs into PTs and PRs.PTs transmit data on the channel. PRs are in thereceiving mode, and can receive data from PTs or otherprimary systems, etc. This CogCell scenario employscode division multiple access (CDMA). Therefore, thePTs and SUs can access the same channel to the BSsimultaneously.

Table I lists the notations used in this paper. Let Ns,N t

p, N rp denote the set of SUs, PTs, PRs, respectively.

The number of SUs, PTs, and PRs can be denotedas ns (ns = |Ns|), nt

p (ntp = |N t

p|), nrp (nr

p = |N rp |),

respectively. The operator of the BS receives thesecondary revenue from the accumulated payments byevery SU in service. Suppose that SU i (i ∈ Ns) willpay ri to the operator, with the QoS demand in termsof minimum DTR λ

sqi . On the other hand, SU i will

generate an interference τij to the PR j if SU i isallowed to access the BS. However, the interferenceto PR j from all the SUs cannot exceed the predefinedthreshold �j .

In order to maximize the secondary revenue, we needto select a subset of the SUs to access the channel tothe BS with limited interference to PRs and guaranteed


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Table I. Table of notations.

Symbol Meaning

B The channel bandwidthNs The set of SUsN t

p The set of PTsN r

p The set of PRsns The number of SUsnt

p The number of PTsnr

p The number of PRsP s

i The transmission power of SU i

Ppk

The transmission power of PT k

P smax The maximum transmission power at SUs

Ppmax The maximum transmission power at PTs

ri The revenue from SU i

τij The interference from SU i to PR j

�j The interference threshold at PR j

hsbi The power attenuation from SU i to the BS

hspij The power attenuation from SU i to PR j

hpbk

The power attenuation from PT k to the BSdsb

i The distance between SU i to the BSd

spij The distance between SU i to PR j

dpbk

The distance between PT k to the BSIs The interference received at BS from all the active SUsIp The interference received at BS caused by all the PTsξsi The SINR of SU i measured at BS

ξpk

The SINR of PT k measured at BSλ

sqi The minimum DTR required by SU i

λpqk

The minimum DTR required by PT k

ξsqi The minimum SINR required by SU i

ξpqk

The minimum SINR required by PT k

QoS requirements of PTs and SUs. In the following,we will express the definition of interference fromSUs to PRs, SINR and QoS requirements, and finallyformulate the optimization problem.

2.2. Interference Caused by SUs

If SUs transmit on the channel, PRs will receiveinterference power from these SUs. Let τij denote theinterference power received at PR j (j ∈ N r

p) causedby SU i (i ∈ Ns).

τij = hspij P s

i , ∀i ∈ Ns, j ∈ N rp (1)

where P si denotes the transmission power at SU i. h

spij

denotes the power attenuation from SU i to the PR j.In this paper, we only consider the large-scale fading.Therefore, h

spij can be calculated as follows:

hspij = Gs

iGprj

(dspij )n

, ∀i ∈ Ns, j ∈ N rp (2)

where Gsi and G

prj denote the antenna gains of SU i

and PR j, respectively. dspij denotes the distance from

the SU i to PR j. The exponent n is the path fadingfactor. For example, n = 2 in free space; n = 4 if weconsider the reflection from ground [13].

Let T Ij denote the interference power received by PR

j from all the admitted SUs.

T Ij =

ns∑i=1

τijxi

=ns∑

i=1

GsiG

prj P s

i xi

(dspij )n

, ∀j ∈ N rp (3)

where xi is a binary variable. It indicates that SU i

is admitted to transmit to the BS if xi is equal to 1,otherwise, SU i is not allowed to transmit. To obey thecoexistence rule in underlay mode, T I

j can not exceedPR j’s predefined threshold �j .

2.3. Uplink SINR Definition

According to the definition of SINR in Reference [13],we can calculate the uplink SINR of PT k as follows:

ξpk = h

pbk P

pk

N0 + Is + Ip − hpbk P

pk

, ∀k ∈ N tp (4)

where hpbk denotes the power attenuation from PT k to

the BS. Ppk denotes the transmission power of PT k.

N0 denotes the background noise received by the BS.Is and Ip denotes the interference received by the BSfrom all the active SUs and PTs, respectively. Is and Ipcan be expressed as follows:

Is =ns∑

i=1

hsbi P s

i xi (5)

Ip =nt

p∑k=1

hpbk P

pk (6)

where hsbi and h

pbk denote the power attenuation from

SU i and PT k to the BS, respectively. Similar asEquation (2), we have

hsbi = Gs

iGb

(dsbi )n

, ∀i ∈ Ns (7)


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and

hspk = G

ptk Gb

(dspk )n

, ∀k ∈ N tp (8)

where dsbi and d

spk denote the distance from SU i and

PT k to the BS, respectively. Gptk and Gb denote the

antenna gains of PT k and the BS, respectively.Similar to the uplink SINR of PTs calculated in

Equation (4), we have the uplink SINR of the activeSU i as follows:

ξsi = hsb

i P si

N0 + Is + Ip − hsbi P s

i

, if xi = 1, ∀i ∈ Ns

(9)

2.4. QoS Definition and Requirement

In this paper, DTR is used as the major QoS metric.Given uplink SINR ξ, according to Shannon’s channelcapacity formulation, the uplink maximum DTR λ is

λ = Blog2(1 + ξ) (10)

Let λsqi and λ

pqk denote the minimum uplink DTR

required by SU i and PT k, respectively. ξsqi and ξ

pqk

denote the required uplink SINR for SU i and PT k,respectively. Therefore, according to Equation (10), wecan obtain

ξsqi = 2

λsqiB − 1, if xi = 1, ∀i ∈ Ns (11)

and

ξpqk = 2λ

pqk

/B − 1, ∀k ∈ N tp (12)

In order to guarantee that the uplink DTR is no lessthan λ

sqi and λ

pqk for SU i and PT k, respectively, the

uplink SINR should be equal or higher than ξsqi and

ξpqk , respectively.

2.5. The Operator Problem Formulation

We take the perspective of the operator at the BS. Theproblem of our interest is to control the transmissionpower of SUs and PTs, and find out an optimal subsetof SUs such that the total secondary revenue outputis maximized. At the same time, we should considerthe interference limitation on PRs, and the uplink QoSrequirements of both PTs and SUs. The problem is

formulated as follows:

argxi,Psi,P

pk

maxns∑

i=1

rixi (13)

subject to

ns∑i=1

τijxi ≤ �j, ∀j ∈ N rp (14)

xi ∈ {0, 1}, ∀i ∈ Ns (15)

ξpk ≥ ξ

pqk , ∀k ∈ N t

p (16)

ξsi ≥ ξ

sqi , if xi = 1, ∀i ∈ Ns (17)

ξsi = 0, if xi = 0, ∀i ∈ Ns (18)

P si = 0, if xi = 0, ∀i ∈ Ns (19)

P si ∈ [0, P s

max], ∀i ∈ Ns (20)

Ppk ∈ [0, Pp

max], ∀k ∈ N tp (21)

where constraint (14) represents that the interferencefrom all SUs to PRs can not exceed the predefinedinterference thresholds. Constraints (16) and (17)represent that the QoS (in terms of SINR) requirementof PTs and active SUs should be guaranteed,respectively. Constraints (18) and (19) indicate that ifthe SU i is not allowed to access the channel, the SINRand the transmission power of the SU i should be 0.Constraints (20) and (21) represent the power limitationof SUs and PTs, respectively. P s

max and Ppmax denote the

maximum transmission power of all the SUs and PTs,respectively.

The defined optimization problem should solve thetransmission power of PTs and SUs, and find out theoptimal subset of SUs simultaneously. In the followingsections, we will propose a power control scheme tomeet all the constraints above. Based on the powercontrol scheme, we will transform the optimizationproblem into a d-KP problem.

3. Power Control for PTs and SUs

In this section, we will propose a power control schemefor PTs and SUs to satisfy the constraints in Equations(16–21).


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3.1. Power Control for PTs

In order to achieve maximum secondary revenue inthe CogCell, the transmission power on PTs should becontrolled by the BS. Let N denote the sum of N0, Is,and Ip. According to Equation (4), we obtain

N = N0 + Is + Ip

=(

1 + 1

ξpk

)h

pbk P

pk , ∀k ∈ N t

p (22)

Imagine the scenario that there is no SU admitted tothe BS, then Is is equal to 0. After an SU is admittedto the BS, Is will increase. In order to keep the sameuplink SINR of PTs, the transmission power of PTswill increase. However, it can not exceed the powerlimitation P

pmax. Otherwise, this SU cannot be admitted.

When the power of PTs does not change, reducing ξpk

can increase the value of N according to Equation (22).In this case, Ip is fixed because the power of PTs isfixed. Thereafter, the value of Is should increase, whichmeans either more SUs are admitted to the BS or theadmitted SUs can transmit with more power. However,ξ

pk cannot be less than the required threshold ξ

pqk .

Therefore, we can choose the lower bound of ξpk for PUs

to allow as many SUs as possible to access the channelto the BS. In another word, ξ

pk = ξ

pqk (∀k ∈ N t

p).For any PT k (k ∈ N t

p), the above Equation (22)

should always be true. Let fpk denote (1 + 1/ξ

pk )hpb

j .

The minimum value of all fpk can be denoted by f

pmin

as follows:

fpmin = min

∀k∈N tp

fpk

= min∀k∈N t

p

(1 + 1

ξpk

)h

pbk

= min∀k∈N t

p

(1 + 1

ξpqk

)h

pbk (23)

To guarantee the transmission power of PTs less thanP

pmax, the BS should control the power of PT k as

Ppk = f

pmin

fpk

ωpPpmax, ∀k ∈ N t

p (24)

where ωp is a positive constant, ωp ∈ (0, 1].Meanwhile, we can obtain N as follows:

N = fpk P

pk

= ωpfpminP

pmax, ∀k ∈ N t

p (25)

Thereafter, the detailed power control scheme forPTs can be expressed in Algorithm 1.

Algorithm 1 Power Control for PUs

Input: hpbk , ξ

pqk , nt

p

Output: N, Ppk

1: for k = 1 to ntp do

2: fpk = (1 + 1

ξpqk

)hpbk

3: end for4: obtain f

pmin according to Equation (23)

5: choose ωp

6: calculate N according to Equation (25)7: for k = 1 to nt

p do

8: Ppk = N

fpk

9: end for

3.2. Power Control for SUs

If SU i is allowed to access the channel to the BS, thenxi is equal to 1. According to Equations (9) and (22),we can obtain

P si = N(

1 + 1/ξsi

)hsb

i

(26)

After the procedure of power control for PTs, wecan obtain the value of N expressed in Equation (25).Meanwhile, in order to reduce the power of SU i toadmit as many SUs as possible, the SINR ξs

i shouldreduce as much as possible until it reaches the lowerbound ξ

sqi . Therefore, the power used by SU i can be

calculated as

P si = N(

1 + 1/ξsqi

)hsb

i

(27)

Let f si denote (1 + 1

ξsqi

)hsbi . Recall the power

constraint expressed in Equation (20), if the powercalculated by Equation (27) is more than P s

max, thisSU can not be admitted. Hence, we can have a primalrule for admitting SUs.

Rule 1: If N/f si > P s

max (i ∈ Ns), then xi = 0, P si

= 0.

After applying Rule 1, the set of possible SUs ischanged from Ns to N ′

s.Recall the expression of interference from SU i to

PU j in Equation (1), with the help of Equations (23),


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(25), and (27), we can obtain

τij = hspij P s

i

= hspij

hsbi

ξsqi

1 + ξsqi

N

= Gprj

Gb

(dsbi

dspij

)nξ

sqi

1 + ξsqi

N (28)

Thus, we can calculate the interference τij (i ∈ N ′s

and j ∈ N rp) from every SU to every PR according to

Equation (28). However, the operator can not allowSU i to transmit if there exists a PR j (j ∈ N r

p)where the interference from SU i exceeds its predefinedthreshold �j .

Rule 2: If ∃j ∈ N rp , τij > �j (i ∈ N ′

s ), then xi = 0,P s

i = 0.

After applying Rule 2, the set of possible SUs ischanged from N ′

s to N ′′s . Therefore, the primal power

and admission control scheme for SUs can be expressedas follows in Algorithm 2.

Algorithm 2 Primal power and admission control forSUs

Input: N, hsbi , ξ

sqi , Ns

Output: P si , N ′′

s

1: Obtain N from Algorithm 12: for i = 1 to ns do3: Calculate P s

i according to Equation (27).4: if P s

i > P smax then

5: P si = 0

6: xi = 07: Remove i from Ns8: else9: for j = 1 to nr

p do10: Calculate τij according to Equation (28).11: if τij > �j then12: P s

i = 013: xi = 014: Remove i from Ns15: Break;16: end if17: end for18: end if19: end for20: Store the remaining Ns to N ′′

s

4. Admission Control

Based on the power control scheme in the previoussection, the uplink SINR requirements are satisfied.However, the interference constraints are still notguaranteed. In this section, we will take the interferenceconstraints into account, and formulate the admissioncontrol problem as a classical multidimensionalknapsack problem. Then, we introduce three methodsto solve this problem, i.e., an exact solution withdynamic programming, an approximate solution withgreedy heuristic, and an MSRA which is proposed byReference [8].

4.1. A Multidimensional Knapsack ProblemModeling

We model the admission control problem as amultidimensional knapsack (d-KP) problem as follows.We are given an instance of the knapsack problem withSU set N ′′

s , consisting of n′′s SUs, and nr

p PRs. SU i canprovide revenue ri to the BS, while causing interferenceτij to PR j. The interference threshold for PR j is �j .Then, the objective is to select a optimal subset of N ′′

sso that the total secondary revenue for the BS from theselected SUs is maximized, and the total interferencefor each PR j does not exceed �j .

argximax

∑i∈N ′′

s

rixi (29)

subject to:

∑i∈N ′′

sτijxi ≤ �j, ∀j ∈ N r

p (30)

xi ∈ {0, 1}, ∀i ∈ N ′′s (31)

where N ′′s is the SUs left after applying Rules 1 and 2

in the previous section.

4.2. Problem Solution

The d-KP problem is classified as a NP-hardoptimization problem, which cannot be solved inpolynomial time [14]. Many algorithms, which canbe categorized into two types: exact algorithms andheuristic algorithms, have been proposed to solvethe d-KP problem. The branch-and-bound method[15], and dynamic programming [16,17] can be usedto find an exact optimal solution of the problem.However, these methods have high computation load


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[14]. Heuristic algorithms, which aims to computefeasible solutions of ‘reasonable quality’ within‘reasonable running time’ [14], is more feasible thanthe optimal algorithms. Typical heuristic algorithmsinclude greedy-type heuristic algorithm, relaxation-based heuristic algorithm, etc.

In this section, we describe an optimal solutionwith dynamic programming and a basic heuristicalgorithms called greedy heuristic algorithm. In orderto compare the performance of different algorithm,we also introduce a minimal SINR removal algorithm(MSRA) used in Reference [8].

4.2.1. An optimal solution with dynamicprogramming

Dynamic programming algorithm employs a recursiveequation to search for optimal solutions for every subsetof SUs. The recursive equation is defined as follows:

r(i, �1, . . . , �nrp) =

r(i + 1, �1, . . . , �nrp) if τij > �j, ∃j ∈ N r

p

max{r(i + 1, �1, . . . , �nrp), ri

+ r(i + 1, �1 − τi1, . . . , �nrp− τinr

p)} otherwise

(32)

where �1, . . . , �nrp

is the remaining interference powercan be tolerated by PR 1, . . . , nr

p after some SUs areadmitted by the BS. The termination condition is wheni reaches n′′

s from the beginning value 1.

r(n′′s , �1, . . . , �nr

p) =

{0 τn′′

s j > �j, ∃ j ∈ N rp

r(n′′s ) otherwise

(33)

After these recursive operations, we can obtain theoptimal result of the secondary revenue. Then we cantrace back to determine those SUs that can be admitted.

The time complexity of this algorithm is dependenton the recursive times. The maximal recursive timesis 2n′′

s . In each recursive operation, it requires nrp

comparison operations to find out if the interferencepower exceeds the threshold. Therefore, in the worstcase, the total time complexity is O(2n′′

s × nrp).

4.2.2. A greedy heuristic algorithm

Greedy heuristic algorithms always use an efficiencyei to denote the preference of choosing an item i.A general framework to define ei was proposed by

Reference [18] as follows:

ei = ri∑nrp

j=1 ϕjτij

(34)

where ϕj is the relevance value for the ‘importance’to the interference constraint j (

∑i∈N ′′

sτijxi ≤ �j). In

this paper, we choose ϕj as follows:

ϕj =∑

i∈Ns′′τij − �j (35)

If ϕj ≤ 0, the interference constraints on PR j

is already satisfied. Therefore, the correspondingconstraint j will be removed from the d-KP problem.Then, we employN r

p′ as the subset ofN r

p , whereϕj > 0(∀j ∈ N r

p′). Thereafter, we can obtain the efficiency as

follows:

ei = ri∑j∈N r

p′

( ∑i∈N ′′

s

τij − �j

)τij

(36)

Then, we sort SU i (i ∈ N ′′s ) according to the

decreasing order of ei. After that, we select the SUwith the highest efficiency ei at every time in the restset of SUs, and accumulate the interference power toevery PU j (j ∈ N r

p′) until one of the value reaches

its corresponding threshold �j . The details of thisalgorithm is shown in Algorithm 3.

The time complexity of this algorithm mainlyconsists of two parts: time spent on calculating ei i.e.,(n′′

s )2 × n′p, and time spent on sorting ei. If we employ

a quick sort algorithm, the time complexity on sortingin the worst case will be O((n′′

s )2). Therefore, the totaltime complexity of this algorithm in the worst case isO((n′′

s )2 × n′p).

4.2.3. Minimal SINR removal algorithm

MSRA has been used in Reference [8] to achievemaximum secondary revenue. It is a greedy-typemethod but does not consider the revenue efficiency.


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Algorithm 3 Greedy heuristic algorithm

Input: N ′′s , N r

p, τij

Output: N ′′′s

1: for i in N ′′s do

2: for j in N rp do

3: Calculate ϕj according to Equation (35)4: if ϕj ≤ 0 then5: Update N r

p by removing PR j

6: if N rp is empty then

7: Return8: end if9: end if

10: Calculate ei according to Equation (36)11: end for12: end for13: Sort SUs in the decreasing order of ei

14: Select the first SU according to the order15: while All the constraints are valid by adding the

selected SU do16: Add this SU to N ′′′

s17: Select the next SU according to the order18: end while

Instead, it removes the SUs with minimal SINRuntil all the interference constraints on PRs aresatisfied. The details of this algorithm is shown inAlgorithm 4.

Algorithm 4 Minimal SINR removal algorithm

Input: N ′′s , ξi

Output: N ′′′s

1: Sort SUs according to the increasing order of SINRξi

2: while N ′′s is not empty, and there exists one

constraint invalid do3: Remove one SU with the minimal SINR4: Update N ′′

s5: end while6: Store the updated N ′′

s to N ′′′s

The time complexity of this algorithm mainlyconsists of one part: the time spent on sorting ξi. Wehere employ quick sort, the same sorting algorithmas in the previous method. Therefore, the total timecomplexity of this algorithm in the worst case isO((n′′

s )2).

5. QoS Aware Admission and PowerControl Schemes

In Section 3, we have proposed a power controlscheme for PTs and SUs. In Section 4, we haveintroduced several methods to solve the admissioncontrol problem. In this section, we will express how dothe QoS aware admission and power control schemeswork.

Figure 2 shows the flow chart of our proposedQoS aware admission and power control schemes.Firstly, the QoS requirements in terms of minimalDTR demand of all PTs and SUs are transformed intoSINR requirement. The mapping method is shown inEquations (11) and (12). Secondly, the transmissionpower of all PTs is controlled by the BS in orderto allow as many SUs as possible to be admitted tothe BS, while the QoS requirements of all PTs areguaranteed. Thirdly, the transmission power of all SUsis controlled by the BS in order to satisfy the QoSrequirements of all the active SUs, and the transmissionpower of all SUs is less than the maximum transmissionpower. Finally, we employ three methods, dynamicprogramming, greedy heuristic, and MSRA to ensurethe interference from all the active SUs to the PRs isless than the predefined threshold. For convenience, wecall our three QoS aware admission and power controlschemes using different algorithms: QAPC-dynamic,QAPC-greedy, and QAPC-MSRA, respectively. In thefollowing section, we will show the performance ofeach scheme.

Fig. 2. The flow chart for QoS aware admission and powercontrol.


DOI: 10.1002/wcm


6. Numerical Results and Analysis

In this section, we will provide the numerical resultsto demonstrate the performance of our proposedQoS admission and power control schemes: QAPC-dynamic, QAPC-greedy, and QAPC-MSRA.

6.1. Simulation Scenario and Parameters

We implement our proposed schemes on MATLAB.We set the scenario as a cellular area with the BS inthe center. The radius of this cellular is denoted byRmax, and set to 1000 m. The minimum distance fromthe BS to any SUs, PTs and PRs is denoted by Rmin,and is set to 100 m. The topology of SUs is randomlygenerated in a polar coordinate system as follows. Thedistance between SUs and the BS are randomly chosenfrom [Rmin, Rmax], The angles from SUs to the BS arerandomly chosen from [0, 2π]. The topology of PTsand PRs are randomly generated in the same way asSUs. Without loss of generality, the antenna gains ofall SUs, PTs, PRs, and the BS are set to 1. The detailedsimulation parameters are shown in Table II.

The revenue and DTR is allocated according toTable III, where SUs with higher DTR pay morerevenue.

Figure 3 shows the secondary revenue in termsof the number of SUs. In this example, the numberof PTs nt

p is 5. The number of PRs nrp is 5.

The interference threshold of every PR j is setto the same value 10−10W . In every change ofthe number of SUs, we randomly generate thetopology of SUs, PTs, and PRs for 20 times. In themeantime, the DTR demands of every PT and SU

Table II. Simulation parameters.

Symbol Value Symbol Value

Rmax 1000 m Rmin 100 mP

pmax 0.30 W P s

max 0.28 WB 5 MHz N0 1.0 × 10−14

ωp 1 n 4Gb 1 G

ptk

1Gs

i 1 Gprj 1

Table III. DTR and revenue.

DTR (kbps) 16 32 64 128 256 512Revenue 1 2 4 8 16 32

Fig. 3. Secondary revenue in terms of the number of SUs.

are also randomly generated for 20 times. We applyQAPC-dynamic, QAPC-greedy, and QAPC-MSRAfor these 20 times, and calculate the average secondaryrevenue. The result shows that the secondary revenuebecomes higher with increasing number of SUs,which is intuitively understandable. The comparisonindicates that both the dynamic programming andthe greedy schemes achieve higher revenue thanthe MSRA scheme. In the aspect of computationcomplexity, we observe that the dynamic programmingscheme requires prohibitively high computation loadsuch that only the range 10–25 number of SUscan be illustrated. In addition, it is observed thatthe greedy scheme closely approaches the dynamicprogramming scheme, which is the exact solution forthe formulated optimization problem. This verifiesthe good approximation of the proposed heuristicalgorithm.

Figure 4 shows the secondary revenue in terms of thenumber of PRs. In this example, the number of SUs nsis 20. The number of PTs nt

p is 5. The interferencethreshold of every PR j is set as the same value10−10 W. The number of PRs nr

p is changed from 5 to50. In every change of the number of PRs, we randomlygenerate the topology of SUs, PTs, and PRs for 50times. In the meantime, the DTR demands of everyPT and SU are also randomly generated for 50 times.We apply QAPC-dynamic, QAPC-greedy, and QAPC-MSRA for these 50 times, and calculate the averagesecondary revenue. The result shows that the secondaryrevenue drops with increasing number of PRs due to thestricter interference constraint. Again, the comparisonindicates that both the dynamic programming andthe greedy schemes achieve higher revenue than theMSRA scheme. The observation demonstrates that the


DOI: 10.1002/wcm


Fig. 4. Secondary revenue in terms of the number of PRs.

greedy scheme is always approaching the dynamicprogramming scheme.

The interference threshold of PR is a key parameter inthe scheme and it is necessary to investigate its effect onthe performance. Figure 5 shows the secondary revenuein terms of the interference threshold of PRs. In thisexample, the number of SUs ns is 20. The number ofPTs nt

p is 5. The number of PRs nrp is 5. The interference

threshold of PRs is changed from −130 to −90 dBW.In every change of the interference threshold, werandomly generate the topology of SUs, PTs, and PRsfor 100 times. In the meantime, the required QoS levelsof every PT and SU are also randomly generated for 100times. We apply QAPC-dynamic, QAPC-greedy, andQAPC-MSRA for these 100 times, and calculate the

Fig. 5. Secondary revenue in terms of the interferencethreshold of PRs.

average secondary revenue. The result shows that boththe dynamic programming and the greedy schemesachieve no less revenue than the MSRA scheme witheither large or small interference threshold. The curvesalso validate that the greedy scheme approximates thedynamic programming scheme very well.

7. Conclusion

In this paper, we have investigated the operator problemin CogCell to maximize the secondary revenue whilesatisfying the constraints of QoS (in terms of DTR)requirements on both PTs and SUs, and the constraintsof interference power on PRs. To address this problem,we proposed a power control scheme for PTs andSUs, and modeled the admission control problem as aninstance of the classical d-KP problem. We introducedan exact algorithm using dynamic programming. Dueto the high computation load by using dynamicprogramming, we also proposed a heuristic algorithmusing greedy method to solve this problem. In order toevaluate the performance of our proposed algorithm,we also introduced the MSRA algorithm used in theliterature. Based on these algorithms, we proposedthree QoS aware admission and power control schemes,called QAPC-dynamic, QAPC-greedy, and QAPC-MSRA, respectively. Results showed that QAPC-dynamic always achieves the highest secondaryrevenue while QAPC-MSRA achieves the leastsecondary revenue. Additionally, the greedy heuristicalgorithm can always approach the similar secondaryrevenue as dynamic programming with much lowercomputation load. Consider the trade-off betweenthe computation complexity and performance gain,QAPC-greedy is recommended.

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Authors’ Biographies

Jie Xiang received his B. Eng. degreein communication engineering fromWuhan University, China, in 2003, andM.Eng. degree in communication andinformation systems from HuazhongUniversity of Science and Technology,China, in 2006, respectively. He iscurrently working toward his Ph.D.degree in Simula Research Laboratory,

and the University of Oslo, Norway. His current researchfocuses on radio resource management, dynamic spectrumaccess schemes, and networking in cognitive radio wirelessnetworks.

Yan Zhang received his Ph.D. degreefrom Nanyang Technological Univer-sity, Singapore. From August 2006,he is working with Simula ResearchLaboratory, Norway. He is currentlyserving the Book Series Editor for thebook series on ‘Wireless Networks andMobile Communications’ (AuerbachPublications, Taylor and Francis Group).

He serves as Program Co-Chair for BROADNETS 2009and IWCMC 2009, Symposium Co-Chair for ChinaCom2009 and ChinaCom 2008, Industrial Co-Chair for MobiHoc2008, Program Co-Chair for UIC-08, Program Vice Co-Chair for IEEE ISM 2007, Publication Chair for IEEEISWCS 2007. His research interests include resource,mobility, spectrum, and energy management in wirelessnetworks.

Tor Skeie is a professor at SimulaResearch Laboratory and the Universityof Oslo. He received an M.S. degreein computer science in 1993 anda Ph.D. degree in computer sciencein 1998, both from the Universityof Oslo. He has several years ofexperience as a researcher in theinterconnection networks domain. His

work mainly focuses on scalability, effective routing,fault tolerance, and quality of service in switchednetwork topologies. Skeie has also for several years beencontributing to wireless networking, hereunder achievingquality of service in wireless LAN, and wireless sensornetworks.

Jianhua He is currently a lecturerin the Institute of Advanced Telecom-munications, Swansea University, UK.He received his B.Eng. and M.Eng.degrees from Huazhong Universityof Science and Technology (HUST),China, and a Ph.D. degree from NanyangTechnological University, Singapore, in1995, 1998, and 2002, respectively. He

joined HUST in 2001 as an Associate Professor. Heworked at University of Bristol on multihop ad hocnetworking from 2004 to 2006 and worked at Universityof Essex on heterogeneous IP network in 2007. His mainresearch interests include protocol design and evaluation ofdynamic spectrum access, multihop networking, resourcemanagement, and QoS provisioning for wireless networks.He has authored or co-authored over 60 technical papers inmajor international journals and conferences. He is servingas an Editor for Wiley’s Wireless Communications andMobile Computing and International Journal of Smart Home,and served as TPC co-chair for International Conferenceon Advanced Infocomm Technology (ICAIT 2009) andfor Workshop on Sensor Networks and Applications(SNA08).


DOI: 10.1002/wcm

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QoS aware admission and power control for cognitive radio cellular networks