Performance of Cooperative Spectrum Sensing with

2011 IEEE 22nd International Symposium on Personal, Indoor and Mobile Radio Communications

Performance of Cooperative Spectrum Sensing with Correlated Cognitive Users' Decisions Lamiaa Khalid and Alagan Anpalagan

Department of Electrical and Computer Engineering Ryerson University, Toronto, Canada

Abstract- Cooperative spectrum sensing is employed in cog­

nitive

radio

network

to

reliably detect

the

primary

users'

transmissions by fusing the sensing data of individual secondary users. In this paper, we study the performance of cooperative spectrum sensing, in terms of the system probability of detection, when the secondary users' local decisions are correlated. We use a correlation model that is indexed by a single parameter and fix the fusion rule to one of three decision rules which are the OR, AND and Majority Voting rules. Our results show that the performance of cooperative spectrum sensing degrades with the increase in correlation between the secondary observations for all the fusion rules considered. We also show that, whether the OR or Majority Voting rule is superior depends mainly on the correlation index. When the secondary users' local decisions are independent, the Majority Voting rule outperforms the OR and AND fusion rules. However, as the correlation between the local decisions increases, the OR fusion rule outperforms the other two rules. Also, as the correlation index increases, for the same system probability of false alarm, higher signal-to-noise ratio is required to be received at the secondary users to achieve the same system probability of detection for all the fusion rules considered.

I.

INTRODUCTION

As the demand for high speed wireless applications in­ creases, exploiting spectrum opportunities, which are restricted by the current static frequency allocation scheme, becomes essential in solving the spectrum scarcity problem. Cogni­ tive radio technology offers a possible solution to improve spectrum efficiency by opportunistically accessing the unused licensed spectrum in dynamically changing environments [1]. Cognitive radios (CR) employ spectrum sensing to determine vacant licensed frequency bands and restrict their secondary transmissions to those empty bands while limiting harmful interference to licensed systems [2]. Spectrum sensing is often considered as a detection problem in which the main challenge is the detection of the weak signal from a primary transmitter through the local observations of CR users. Several detection techniques can be used in spectrum sensing such as energy detection, matched filter detection, and cyclostationary feature detection [3]. In this paper, we focus on the energy detection approach since it has low computational and implementation complexities and prior knowledge of the primary users' signal is not needed [4]. Cooperative detection refers to spectrum sensing methods where information from multiple CR users are incorporated for primary user detection. Several recent works have demon­ strated that cooperative spectrum sensing, which leverages spatial diversity, provides a solution to problems that arise in sensing due to noise uncertainty, fading, and shadowing 978-1-4577-1348-4/11/$26.00 ©2011 IEEE

and it also greatly increases the probability of detection in fading channels [4]. In [5], it was shown that cooperating with all users in the network does not necessarily achieve the optimum performance; and constant detection rate and constant false alarm rate were used for optimally selecting the CR users with highest primary user's signal-to-noise ratio (SNR) for cooperation. The fusion rules considered there are the AND and OR rules and the results are limited to the case where the observations of the CR users are independent. In [6], it has been shown that the optimal fusion rule when the sensor observations are conditionally independent is a Majority Voting rule in the case of binary local detectors. Although the independence assumption on the sensor observations simplifies the problem, this assumption is not practical in the case where the proximity of the sensors results in correlated observations. The local observations will be dependent if one detects a random signal in noise or if the detector noise samples are correlated when detecting a deterministic signal in noise [7]. The performance of a distributed detection system with given local decision rules and correlated local decisions was studied in [8] and the optimum decision fusion rule in the Neyman-Pearson sense was derived and analyzed. In [9], the performance degradation of cooperative sensing under exponentially-correlated log-normal shadowing was investi­ gated in terms of missing opportunities. The problem of fusing the decisions made at the cooperating sensors when the CR users observe conditionally dependent data due to correlated shadowing was studied in [10] and a suboptimal temporal detector was proposed based on a linear quadratic detector, which uses partial statistical knowledge to improve detection performance. Their results show that the suboptimal LQ de­ tector outperforms the counting rule only when the correlation between the secondary users is strong. Also, their results were based on the assumption that the noise observations are independent. This assumption might not hold if the physical proximity of the local detectors results in the noise on each detector being dependent. In [11], a joint spatial-temporal spectrum sensing scheme for CR network was proposed. In the proposed scheme, a fusion center use estimates of the primary transmitter's location and transmit power obtained during spatial sensing to select a subset of the secondary nodes that decide on the absence or presence of the primary user. The main contributions of this paper are: (i) We analyze the impact of correlated CR users' observations on the perfor­ mance of cooperative spectrum sensing schemes while fixing the fusion rule to one of the three binary decision rules: OR

635

rule, AND rule, and Majority Voting rule. (ii) We derive the system probabilities of detection and false alarm, when the CR observations are correlated under both hypothesis, for the three aforementioned fusion rules. (iii) We use the Neyman­ Pearson (NP) criterion to optimize the network probability of detection with constraint on the network probability of false alarm when the local decisions are correlated. The rest of this paper is organized as follows: In section II, we introduce the system model. In section III, we present the correlation model used in our analysis. Based on those models, we derive the system probability of detection and false alarm for the different fusion rules in section IV . Results are presented in section V . Section VI concludes this paper.

The decision on the occupancy of a certain subchannel to a threshold The performance of the detection algorithm is characterized by two probabilities: the probability of detection, and the probability of false alarm, The terms and are defined as the probabilities of detecting a primary user signal on the considered subchannel when the subchannel is occupied and vacant, respectively. Therefore, the probabilities of detection and false alarm for each subchannel k are given by, k can be obtained by comparing the test statistic

"(k.

Pd, Pf

Pf.

k _ _ P(Yik > "/kIH1,k) pd ("/k) -

Yk Pd

- N(a2 IhkI2) ) Q( .../"/k2N(a 2 21hk12)a2 ' +

+

(6)

and (7)

II. S Y STEM MODEL We consider a cognitive radio network with M secondary cognitive radio users which can opportunistically access a wideband licensed spectrum allocated to L primary users. We assume that the total spectrum is divided into K orthogonal subchannels and that the primary users do not occupy the entire bandwidth simultaneously. Therefore, some of the sub­ channels will be available for use by the secondary users. The problem of detecting the presence of primary users is equiva­ lent to distinguishing between the two following hypotheses,

xk(n)-

{ vhkk(n), sk(n)

+

vk(n),

HO,k H1,k

(1)

Xk( n) hk Sk( t) vk( n), 0"2. sk( n) vk( n) HO,k H1,k,

where is the received signal on the kth subchannel at the CR user at the nth time instant, is the kth subchannel gain which is assumed to be constant during the detection interval and is the primary user's transmitted signal on the kth subchannel. The noise, is assumed to be a Gaussian process with zero mean and variance Without loss of generality, and are assumed to be independent. The goal of spectrum sensing is to decide for each subchannel k between two hypotheses, the hypothesis that and the primary user is absent and present, respectively. The test statistics for the energy detector for the kth subchannel is computed as the sum of the received signal energy over an interval of N samples, and is given by [5]: N-l

Yk n=LO !xk( n)!2.

(2)

=

skvk( n()n),,

In this paper, we assume that the noise, is real Gaussian noise and the primary user signal, is BPSK modulated signal. For a large number of samples N, using the central limit theorem [12], the distribution of the test statistics, can be approximated by a Gaussian distribution with mean and variance given by [13],

Yk,

{ (N Na2, rk)a2, _ { 2Na4, [Yikj2(N 2r

j_ E[Yk V:

ar

+

+

k)a4,

HO,k H1,k HO,k H1,k

(3)

It is clear that we desire the probability of detection to be large to provide sufficient protection for the primary users, while the probability of false alarm should be kept as small as possible to prevent underutilization of the licensed spectrum. III.

SPECTRUM SENSING UNDER CORRELATED

Cooperative sensing is the process of making a final decision for the network based on the sensing data that is collected from various secondary users. We consider the case in which each individual CR user i, i M, makes a one-bit hard decision, on the absence or presence of the primary user based on the sensing information, such that,

dk,i,

=

dk,". where

{

1,

0,

1 ...

if if

Yk,i � "/k Yk,i < "/k

(8)

Yk,i is the test statistic on the subchannel for the (2) for each user kth

ith user and is given by

i.

Each CR user then sends this one bit decision to the fusion center which makes the final decision regarding the occupancy of the kth subchannel. We further assume that the local decisions are correlated and the correlation coefficients are given by:

dk i

,'tgk IH"k] =E[dk" E IIdk"IH"k J, ,'1.1 dk" ,'1.2 ···dk" J, iElk =p( dk,il = 1, dk,i2 = 1, ... , dk,igk = 1 !H j,k),

[

,'I.

]

(9)

E[x!Hj,kl P[x!Hj,kl Hj,k, h ...h,v !1,h...! ,gk.gk lk (10) E [II dk,i!Hj,k] 1 if lk For Ilk! 1, we have, E[dk,i!H1,kl P(dk,i 1!H1,k) PJ,i, (11) and, E[dk,i!Ho,k] P(dk,i l!Ho,k) PJ,i, (12) where PJ,i and pj i are the probability of detection and false alarm of the secondary user on the subchannel,

where and are the conditional expectation and conditional probability given where j 0,1, respectively, � {I, 2, 3, , M}, is the cardinality and iv E number of set And, =

=

=

=

=

tEh