Globecom 2013 - Cognitive Radio and Networks Symposium

Cluster-based Cooperative Spectrum Sensing In

Two-layer Hierarchical Cognitive Radio Networks

Wenxuan Lin1,2, Ying Wang1,2, Weiheng Nil,2

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications Email: wangying@bupt.edu.cn

Abstract- The paper investigates cluster-based Cooperative Spectrum Sensing (CSS) issues in two-layer hierarchical Cog­nitive Radio Networks (CRNs). Most previous studies focus on hard decision fusion under the assumption of perfect reporting channels. However, wireless channels are not error-free in reality. Therefore, we propose a novel cluster-based CSS scheme with imperfect reporting channels between SUs and cluster heads (CHs) to optimize cluster strategy. A weighted reporting channel method is adopted in our analysis. To further reduce the complexity, 1 st order Taylor series expansion approximation scheme is proposed. Numerical results show that the proposed scheme achieves a satisfying performance.

I. INTRODUCTION

Cognitive radio (CR) has been under active consideration in recent years to deal with the conflict among the steady spectrum demand of primary users (PUs). By sensing and adapting to the surrounding environment, secondary users (SUs) are able to opportunistically utilize spectrum holes without causing intolerable interference to PUs. However, due to the features of wireless sensing channel, i.e., high penetration loss, shadowing, and multi path fading, it is difficult for a SU to obtain fast and accurate results by implementing spectrum sensing alone in cognitive radio networks (CRNs). To enhance the sensing performance, cooperative spectrum sensing (CSS), which allows multiple SUs to conduct spectrum sensing cooperatively, is proposed in [1][2].

There exists two categories of CRN infrastructures, i.e., cen­tralized CRNs (CCRNs)[3] and distributed CRNs (DCRNs)[4]. In the CCRN, a fusion center (FC) is responsible for receiving sensing results submitted by all SUs to decide the status of PUs. However, in the DCRNs, no FC exists and SUs should exchange sensing information with each other to make a final decision. In this paper, we focus on CCRNs.

In cooperative CCRN s, the performance of spectrum sens­ing is improved as the quantity of cooperative SUs increases. However, too many cooperative SUs result in the further difficulties of gathering the global sensing data at a local place in real communication systems [5] as well as leading to higher overhead in sensing results collection and less time for data transmission. To overcome this drawback, cluster­based CSS schemes are studied to ameliorate the etlects on the performance by grouping SUs with close properties in [6].

Some recent works have studied cluster-based CSS CRNs. Both hard and soft fusion rules are analyzed in [6]. In [7], ditlerent clustering strategies are compared in cluster-based CCRNs, the optimal parameters including decision threshold,

fusion rules, and number of clusters are investigated in [8]­[10], respectively. From the perspective of data transmission, [11] investigated sensing-throughput tradeotl in cluster-based cooperative CRNs.

Most of these works aforementioned are focused on the performance improvement with hard decision fusion under the assumption of perfect reporting channels. However, such assumption is not practical in real communication application scenario. Moreover, the imperfection characteristic of report­ing channels affects the clustering strategy and sensing fusion performance of CCRNs. In this paper, we focus on the CCRN under the imperfect channels between SUs and CHs. And the soft fusion rule and a weighted reporting channel method are adopted in the analysis. Numerical results show that the proposed schemes achieve a satisfying performance.

The advantages in this paper include:

1): unlike the traditional clustering strategies based on geographic location, the proposed scheme is based on the channel states between SUs and CHs. Besides, the number of the clusters and the reporting channel quality of CHs are jointly considered to improve the performance of cognitive systems.

2): the reporting channels between SUs and CHs are con­sidered imperfect [12].

3): the soft fusion rule is adopted as shown in [6], which demonstrates a superior performance than hard fusion rules. Moreover, the optimal weighted reporting channels at FC is achieved.

4): 1st order Taylor series expansion approximation scheme is proposed to achieve a satisfying performance as well as reduce the complexity.

The remainder of the paper is organized as follows. In Section II, system model and assumptions are introduced. The cluster-based CSS problem. Numerical results are analyzed and discussed in Section IV. Section V concludes the paper.

II. SY STEM MODEL AND ASSUMPTIONS

Fig.l shows the system model of a two-layer hierarchical cooperative CRN. There is one FC in the SU network. Without loss of generality, we assume there are N SUs which are divided into K clusters and K CHs in the CRN. We denote that the kth cluster has nk (nk :;:, 0 and nk is an integer) SUs,

K which subjects to L nk = N.

k=l

978-1-4799-1353-4/13/$31.00 ©2013 IEEE 1082

Globecom 2013 - Cognitive Radio and Networks Symposium

Fe

Fig. I. System Model in Two-tier Hierarchical Cognitive Radio Network

The following four steps are conducted in the cluster-based CRN.

1) Local sensing and clustering: All SUs perform local spectrum sensing simultaneously to detect the state of PUs. Using the energy detection method, the spectrum sensing for the ith SU is formulated as a hypothetical testing problem as follows:

() { ni ( rn) , 7io (l ) Yi rn = hi * s(rn) + ni(rn), 7i1

where 7io and 7i1 denote the absence and the presence of the PU, respectively.i E N represents the ith SU and N represents the number of SUs. Yi(rn) represents the rnth received signal sample by the ith SU, s( rn) represents the rnth transmitted signal sample from the PU and (J"� represents covariance of s (rn). ni (rn) represents the received noise sam­ple at the ith SU which follows circular symmetric complex Gaussian (CSCG) distribution denoted as N(O, (J"�) for all the SUs. hi represents the transmitted signal sample complex channel gain of the sensing channel between the PU and the ith SUo The instantaneous detection signal-to-noise ratio (SNR) at

the ith SU given as I i = Ihil:a:. In this paper, the additive CTu

white Gaussian noise (AW GN) environment is considered. For the AW GN environment, all the SUs have the same channel coefficient hi due to all the SUs having the identical path loss. That is, all the SUs have the same instantaneous detection SNR

(11 = 12 = . . . = IN = I) in the AWGN environment.

Given the above hypothetical problem, the testing statistic for energy detector denoted as Vi is in the following:

1 M Vi =

M 2..: IYi(rn)12, m=l

(2)

where !vI represents the sampling times within the sensing time.

When Ai[ is very large, given the central limit theorem, every SU follows a Gaussian distribution denoted as N(/Lo, (J"6) with respect to a large number of M. We denote I = (J"; / (J"� . And then we have

For a large number of !vI, Vi can be approximated as the following Gaussian distribution according to the central limit theorem. Therefore, each SU with the same SNR follows a Gaussian distribution denoted as N(/Lo, (J"6) :

(3)

2) CMs Selection: In each cluster, the CH collects the sensing information submitted by its CMs.

3) CHs reporting: All the CHs send the aggregated sensing information to Fe.

4) Final decision: FC collects the sensing information with different weights and makes a final decision.

III. OPTIMIZATION PROBLEM FORMULATION

In this section, we formulate an optimal cluster-based CSS scheme to minimize the probabilities of false alarm with the target probability of detection (P d).

A. Cluster-based CSS Process

In this subsection, we consider a two-phase reporting proto­col in the two-layer hierarchical CRN that all the CHs receive the soft sensing information from their CMs and all the CHs send the aggregated sensing information to Fe.

In the first phase, the CMs in the same cluster report their soft sensing information to their CH, and the cluster result of the kth CH is denoted as Vk. Define a cluster-member assignment as p = {Pk,i E {O,l}lk E {1,2, ... ,K}, i E

{I, 2, ... , N}}. And we assume that each SU can only be assigned to one CH. Then, we have Pk,i = 1 when the ith SU has been assigned to the kth CH, and Pk,i = 0 otherwise.

In this setting, we have L�l Pk,i = nk. In other words, nk in

the following discussion is equivalent to L�l Pk,i' However, if nk = 0, it means the cluster result of the kth is denoted as Vk = 0, moreover, the quantity of the cluster decreased by 1.

The reporting error i':lk,i is subjected to fading between the ith SU and the kth CH. And it follows a Gaussian distribution denoted as N(O, (J"�J . Since Vi and i':lk,i are statistically independent of each other, when nk > 0, we have

with

/Lk (5)

(6)

and Vk = 0 otherwise. Since the CHs are selected with the besting reporting

channels, each of which in one cluster is fixed in the CRN, for simplicity, the reporting channels between CHs and FC are assumed to be perfect. In the second transmission phase

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Globecom 2013 - Cognitive Radio and Networks Symposium

in which all CHs transmit the aggregated soft information through the perfect reporting channels to the FC with different weights. Defining a weight coefficient set as w = {Wk IkE {I, 2, ... , K}} where L;�=1 Wk = 1, the energy signals re­ceived at the FC is given by

K

V = LWkVk, k=l

(7)

where Wk denotes the weight factor of the kth CH subject to their contributions to the performance. Moreover, when nk = 0, Wk = 0, and Vk is irrelevant to V. Therefore V follows the Gaussian distribution with

/Lo, K

L

(8)

(9)

Given a pre-fixed threshold A, the probability of false alarm Pf and the probability of detection Pd are given by

A-(l+,)(J� ) ",K w� .• ((1+2,)n,o-;, � 2 ) L..k=l � !VI + L.. Pk,iO" k.i {n,#O} 1=1

(10)

(11)

where Q(.) is the complementary distribution function of the standard Gaussian.

B. Problem Formulation

In the subsection, our objective is to minimize the proba­bility of false alarm (Pf) with a targeted detection probability (p d). Therefore the optimization problem can be formulated into:

max Pf {"\,p,w}

(12a)

s.t. Pd:;:, Pd, (12b) K

LWk = 1, (12c) k=l K

LPk.i = 1, (12d) k=l

where P d denotes as the target probability of detection to sufficiently protect PU.

In the context of CRN, the PU's signal power received by the SUs is very low, which means I « 1. Thus, for a targeted detection probability, P d, the probability of the false alarm is approximately given by,

Pf(p,w)

� Q ( Q-'(P,,:

� Q (Q-'(P") I

with

(14)

when nk > O. Therefore, the optimal problem in (12) can be transformed

into

max Pf {p,w}

(I Sa)

K

s.t. LWk = 1, (ISb) k=l K

LPk.i = 1, (1Sc) k=l

IV. SOLUTION OF THE OPTIMIZATION PROBLEM

The above optimization problem in (15) is a combinatorial optimization problem involving both discrete and continuous variables. In order to reduce the computational complexity for practical scenario, we first optimize w with specific p to minimize Pf. Therefore, the combinatorial optimization problem is transformed into a discrete optimization problem. An exhausting search could be used to find the optimization solution to such a problem. However, the search complexity is too high to make such strategy to be used in realistic application. In order to more efficiently solve this problem, a 1st order Taylor series expansion approximation scheme is proposed.

A. Weight Fusion Rule

To simplify the solution, a reasonable w should be deter­mined.

Proposition 1: The optimal values of w with specific p, K to minimize the Pf are given by

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(13)

Globecom 2013 - Cognitive Radio and Networks Symposium

Wk {n,=O}

4 N 1/( (Tn + 1 '" 2 ) n,M 11:2 D Pk,iO"k,i , i=l

N ' ",K /( (T4 1 '" 'J ) Dk=l 1 n,)v! + ;'[ D Pk,iO"k,i {n,?"O} ,=1

= O. (16)

Proof: The optimization problem to minimize the Pj w.r.1. w under specific p, K can be transformed into

maxPj {w}

(17a)

K

s.t. LWk= 1, (l7b) k=l

Since mllllmlzlllg Q( �) equals to minimizing x. Thus, the relationship between Pj and w above in (17) can be transformed into:

min w

K

L k=l

{n;?"O} K

s.t. LWk = 1. k=l

(ISa)

(1Sb)

Let c be nonnegative Lagrangian multiplier, and then the Lagrangian for the optimization problem is given by

K K

f(w) = L w�ak + c(l - L Wk). (19) k=l k=l

{n;?"O} {n,?"O} Different f ( w) w.r.1. w, the above problem can be repre­

sented as:

Therefore, we have

l/ak Wk = -..."..,..:---��=1 l/ak {n,C#O}

(20)

(21)

(22)

B. 1st Order Taylor Series Expansion Approximation Scheme

Given the solution of weight fusion rule, the probability of the false alarm is given by substituting (16) into (13),

Therefore, the optimal problem can be reformulated as follows:

s.t.

K

maxPj {p}

LPk,i = 1, k=l

(24a)

(24b)

In order to further decrease computation complexity, a

1 st order Taylor series expansion approximation scheme is presented in the following

K

L

K

L k=l

{ndO} K N

2 �k=l � Pk,iO"k,i N!vl {ndO} i=l

- -- + -'-----'----�--CT4 ( T4 )2 n .....l1.. M K N

OC L L Pk,iO"L k=l i=l

(25)

Moreover, the pt order Taylor series expansion approxima­tion scheme can be obtained in Algorithm I via the following recursion procedures:

Algorithm l Ist Order Taylor Series Expansion Ap­proximation Scheme Step 1: Initialization

• Initialize N = {I, 2, ... , N}, JC zeros[K, N];

Step 2: Iteration

• for i = 1 : N

{I, 2, ... , K} and p

(k*, i) = arg min{(T� J, i EN; Pk*.i = 1; k ' end

N • Calculate nk = 2: Pk,i;

i=l • for k = 1 : K While ng = 0 do

CT4 1 N end } Initialize JC' = JC - {kG} ;

1/ C1n + 2 LPbCT�J tep 3: Finalization 1� nk nk ' "=1 Calculate K = card(JC ) ,

p, nk. K is achieved. (23)

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Globecom 2013 - Cognitive Radio and Networks Symposium

20 � � � 100 1� 1� 1� 1� 200 Number of Secondary Users (N)

Fig. 2. Probability of False Alarm versus the Number of SUs

V. NUMERICAL RESULTS

A. Simulation Setup

In this section, simulation results and discussions are pre­sented to evaluate the effectiveness of our proposed schemes in the two-layer CRN. The system is set up as follow: The targeted probability of detection threshold P d is 0.9, the sampling times m = 2000, the SNR I is -20dB for all SUs. Furthermore, we assume that the channel between SUs and CHs are subject to Rayleigh fading with zero mean and variance (J"�rn,ch = 4 * 10-8.

B. Simulations on Effectiveness of Different Setup for N, K

In this subsection, the simulations are conducted to illustrate the effectiveness of different setup on different parameters.

Fig.2 depicts the impact of the number of SUs on the probability of false alarm Pj under random cluster-based CSS scheme and 1 st order Taylor series expansion scheme. The simulation setup is given under K = 5. Obviously, the prob­ability of false alarm of the two schemes both first decreases and then increases as the number of cooperative SUs increases. Furthermore, 1st order Taylor series expansion scheme has a better performance than random cluster-based CSS scheme, because the probability of false alarm mainly depends on the cluster strategy when the number of cooperative SUs are large.

Fig.3 shows the impact of the quantity of CHs on the probability of false alarm Pj under random cluster-based CSS scheme and 1 st order Taylor series expansion scheme. The simulation setup is given under N = 300. Obviously, the performance of random cluster-based CSS scheme remains constant but that of pt order Taylor series expansion scheme has a better performance as the number of cooperative SUs. It is because random cluster-based CSS scheme mainly depends on the number of SUs, however, the proposed scheme mainly depends on cluster strategy.

'0 g 10.6 :0 co .D e � 108 .c f-

10 20 30 40 50 60 70 Number of CHs (K)

80 90 100

Fig. 3. Probability of False Alarm versus the Number of CHs

VI. CONCLUSIONS

In this paper, we investigate cluster-based CSS issues in two-layer hierarchical CRNs. To apply to the practical CRNs, imperfect report channels and soft data fusion rule are taken into account. We first formulate an optimization problem to improve the accuracy of spectrum sensing. In order to efficiently and effectively solve such problem. 1st order Taylor expansion approximation scheme is proposed. Finally, both derivation and numerical results show that the proposed scheme achieve a satisfying performance.

ACKNOWLEDGMENT

This work is supported by Beijing Natural Science Founda­tion (4132050), National Nature Science Foundation of China (61121001), Program for Changjiang Scholars and Innovative Research Team in University (No.IRTI049).

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