Energy Detection based Optimal Linear Cooperative Spectrum Sensing in Cognitive Radio Networks

*Dong-Chan Oh, Yong-Hwan Lee

Seoul National University

e-mail : mac81@ttl.snu.ac.kr, ylee@snu.ac.kr

Abstract

We consider cooperative spectrum sensing in cognitive radio systems to minimize the false alarm probability while maintaining the protection level of primary user. It may not be able to reliably detect weak primary user’s signal in the presence of channel fading or shadowing. We combine the test statistics of all users for final decision by considering the relationship between the false alarm and detection probability.

This work was supported by the Seoul R&BD Program (10544)

I. Introduction

Cognitive radio (CR) networks need to reliably detect weak primary user’s signal transmitted in an unknown format [1]. It is of great importance for spectrum sensing to minimize the false alarm probability while maintaining the protection level of primary user [2]. Individual local spectrum sensing may not provide reliable detection performance due to shadowing and fading effect. This problem can be alleviated by means of cooperative sensing. Simple cooperative schemes consider the use of hard decision based on AND and OR logic rules, but they may not provide desired performance mainly due to information loss caused by local decisions [2]. The performance can be improved by softly combining local test statistics of individual users with equal weight. However, when users experience shadowing or fading, it may not minimize the false alarm probability.

In this paper, we consider cooperative spectrum sensing where each user experiences different interference-to-noise power ratio (INR). To improve performance, the test statistics of users are summed with different weight for final decision. The optimum weight for each test statistic is determined to minimize the false alarm probability while maintaining the protection level of primary user.

The rest of this paper is organized as follows. Section II describes the cognitive radio system model and Section III describes the proposed sensing

scheme. Section IV verifies the performance of the proposed scheme by computer simulation. Finally, conclusions are given in Section V.

II. System model

Consider sensing environment where [eqn: M] CR users are located within an edge of primary user’s transmission range and may potentially interfere with primary user’s communication. We assume that all users report their average INR and test statistics to the fusion center. The test statistic of user [eqn: k] for energy detection can be represented as

[eqn: T _{k} (N)= {cases{{1} over {N} sum _{n=1} ^{N} LEFT | u(n) RIGHT | ^{2}&``````````H _{0}#{1} over {N} sum _{n=1} ^{N} LEFT | sqrt {d _{k} ^{- alpha }} h _{k} (n)s(n)+u(n) RIGHT | ^{2}&``````````H _{1}}}]	(1)

where [eqn: N] denotes the number of samples, [eqn: n] denotes the sample index, [eqn: d _{k}] and [eqn: alpha] denote distance from primary user to CR user [eqn: k] and path loss exponent, respectively, [eqn: h_{ k}(n)] denotes the channel impulse response for CR user [eqn: k], [eqn: s(n)] denotes the signal from primary user with zero mean and variance [eqn: sigma _{s} ^{2}], [eqn: u(n)] denotes zero-mean circular-symmetric complex Gaussian noise with variance [eqn: sigma _{u} ^{2}], and [eqn: H _{0}] and [eqn: H _{1}] represent hypothesis corresponding to the absence and presence of primary user’s signal, respectively.

Using data fusion, the final test statistic used for final decision can be represented as

[eqn: T(M)= sum _{k=1} ^{M} w _{k} T _{k} (N)`]           (2)

where [eqn: w _{k}] is non-negative combining weight associated with user [eqn: k]. Without loss of generality, we assume that [eqn: sum _{k=1} ^{M} w _{k} ^{2} =1].

Ⅲ. Proposed Cooperative Sensing

Assume that [eqn: s(n)] is circular-symmetric complex Gaussian distributed and [eqn: N] is large, By the central limit theorem [3], it can be seen that [eqn: T(M)] is Gaussian distributed as

[eqn: T(M) SIM {cases{N LEFT ( sigma _{u} ^{2} sum _{k=1} ^{M} w _{k} ,` {sigma _{u} ^{2}} over {N} sum _{k=1} ^{M} w _{k} ^{2} RIGHT )&`````,H _{0}#N LEFT ( sigma _{u} ^{2} sum _{k=1} ^{M} w _{k} LEFT ( gamma _{k} +1 RIGHT ) ,` {sigma _{u} ^{4}} over {N} sum _{k=1} ^{M} w _{k} ^{2} LEFT { 2 gamma _{k} ^{2} + LEFT ( gamma _{k} +1 RIGHT ) ^{2} RIGHT } RIGHT )&`````,H _{1}}}]                                                  (3)

where [eqn: gamma _{k} =d _{k} ^{- alpha } sigma _{s} ^{2} / sigma _{u} ^{2}] is an average received INR of the CR user [eqn: k] under hypothesis [eqn: H _{1}].

For givne sensing threshold [eqn: lambda], the probabilities of false alarm and detection can be represented as            [eqn: P _{f} LEFT ( lambda RIGHT ) =Q LEFT { sqrt {{N} over {sum _{k=1} ^{M} w _{k} ^{2}}} LEFT ( {lambda } over {sigma _{u} ^{2}} - sum _{k=1} ^{M} w _{k} ^{} RIGHT ) RIGHT }]           (4)

and

[eqn: P _{d} LEFT ( lambda RIGHT ) =Q LEFT { sqrt {{N} over {sum _{k=1} ^{M} w _{k} ^{2} LEFT { 2 gamma _{k} ^{2} + LEFT ( gamma _{k} ^{} +1 RIGHT ) ^{2} RIGHT }}} LEFT ( {lambda } over {sigma _{u} ^{2}} - sum _{k=1} ^{M} w _{k} ^{} LEFT ( gamma _{k} ^{} +1 RIGHT ) RIGHT ) RIGHT }]                                                  (5)

where [eqn: Q(.)] is Q-function [3], It can be seen that the lower the false alarm probability, the higher the achievable throughput of users. For a desired detection probability [eqn: bar{P _{d}}], it is desirable to optimize the combining weight [eqn: w _{k}] to minimize the false alarm probability. For a given [eqn: bar{P _{d}}], the threshold [eqn: lambda] can be determined from (5). Then, the false alarm probability can be represented as

[eqn: P _{f} =Q LEFT ( sqrt {sum _{k=1} ^{M} w _{k} ^{2} LEFT { 2 gamma _{k} ^{2} + LEFT ( gamma _{k} ^{} +1 RIGHT ) ^{2} RIGHT }} Q ^{-1} LEFT ( bar{P _{d}} RIGHT ) + sqrt {N} sum _{k=1} ^{M} w _{k} ^{} gamma _{k} ^{} RIGHT )]                                                  (6)

The use of cooperative spectrum sensing is effective when the signal strength of ongoing user is weak, i.e., low INR region. As [eqn: gamma _{k} -> 0], it can be shown that the false alarm probability is approximated as

[eqn: P _{f} SIMEQ Q LEFT ( Q ^{-1} LEFT ( bar{P _{d}} RIGHT ) + sqrt {N} sum _{k=1} ^{M} w _{k} ^{} gamma _{k} ^{} RIGHT )]        (7)

Since [eqn: Q(x)] is a decreasing function of [eqn: x] and [eqn: Q ^{-1} LEFT ( bar{P _{d}} RIGHT )] is independent of linear weight [eqn: w _{k}], the optimal linear combining weight [eqn: w _{k}] satisfying following condition should be designed.

[eqn: pile{max#w _{1} ^{} ,w _{2} ^{} ,...,w _{M} ^{} : sum _{k=1} ^{M} w _{k} ^{2} =1} LEFT { sum _{k=1} ^{M} w _{k} ^{} gamma _{k} ^{} RIGHT }]         (8)

Using Cauchy-Schwarz inequality [3], the optimal linear combining weights can be represented as

[eqn: w _{k} ^{} = {gamma _{k} ^{}} over {sqrt {sum _{k=1} ^{M} gamma _{k} ^{2}}}]                 (9)

IV. Performance evaluation

In this section, the proposed cooperative sensing scheme is evaluated and compared with conventional scheme. We assume that an INR range of CR users is form -10 to -5 dB and the number of sample used to channel sensing is 100. Fig. 1 depicts sensing performance of the proposed scheme according to the number of CR users when the target probability of detection [eqn: bar{P _{d}} =0.9]. It can be seen that linear combining with proposed optimal weight outperforms other schemes. This is due to the fact that the propose scheme suppress diverse spectrum sensing effect from CR users with low average INR value by imposing different weights proportional to average INR of CR users.

V. Conclusion

We have proposed an optimal linear cooperative spectrum sensing scheme in cognitive radio system. By finding optimum linear weights and operating over a linear combination of local test statistics at fusion center, the proposed scheme can improve spectrum sensing performance.

References

[1] S. Haykin, "Cognitive radio: Brain-empowered wireless communications," IEEE J. Select. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005.

[2] Y.-C. Liang, Y. Zeng, E. Peh, and A.-T. Hoang, "Sensing-Throughput Tradeoff for Cognitive Radio Networks," IEEE Trans. Wireless Commun., vol. 7, no. 4, pp. 1326–1337, Apr. 2008.

[3] J. G. Proakis and M. Salehi, Communication Systems Engineering, Prentice Hall,  1994.

Fig.1 The false alarm probability according to the number of users