On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio

In this paper, the distribution of the ratio of extreme eigenvalues of a complex Wishart matrix is studied in order to calculate the exact decision threshold as a function of the desired probability of false alarm for the maximum-minimum eigenvalue (MME) detector. In contrast to the asymptotic analysis reported in the literature, we consider a finite number of cooperative receivers and a finite number of samples and derive the exact decision threshold for the probability of false alarm. The proposed exact formulation is further reduced to the case of two receiver-based cooperative spectrum sensing. In addition, an approximate closed-form formula of the exact threshold is derived in terms of a desired probability of false alarm for a special case having equal number of receive antennas and signal samples. Finally, the derived analytical exact decision thresholds are verified with Monte-Carlo simulations. We show that the probability of detection performance using the proposed exact decision thresholds achieves significant performance gains compared to the performance of the asymptotic decision threshold.

[1]  Vijay K. Bhargava,et al.  Cognitive Wireless Communication Networks , 2007 .

[2]  Z. Bai.  METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES , A REVIEW , 1999 .

[3]  Yong-Hwan Lee,et al.  Energy Detection Based Spectrum Sensing for Sensing Error Minimization in Cognitive Radio Networks , 2009, Int. J. Commun. Networks Inf. Secur..

[4]  Yonghong Zeng,et al.  Eigenvalue-based spectrum sensing algorithms for cognitive radio , 2008, IEEE Transactions on Communications.

[5]  C. Tracy,et al.  The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: β = 1, 2, 4 , 1997, solv-int/9707001.

[6]  A. Edelman.  Eigenvalues and condition numbers of random matrices , 1988 .

[7]  Anant Sahai,et al.  Some Fundamental Limits on Cognitive Radio , 2004 .

[8]  Ying-Chang Liang,et al.  Covariance Based Signal Detections for Cognitive Radio , 2007, 2007 2nd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks.

[9]  Roberto Garello,et al.  Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in wishart matrices , 2009, IEEE Communications Letters.

[10]  Moe Z. Win,et al.  On the capacity of spatially correlated MIMO Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[11]  Yonghong Zeng,et al.  Spectrum-Sensing Algorithms for Cognitive Radio Based on Statistical Covariances , 2008, IEEE Transactions on Vehicular Technology.

[12]  Hüseyin Arslan,et al.  A survey of spectrum sensing algorithms for cognitive radio applications , 2009, IEEE Communications Surveys & Tutorials.

[13]  Pascal Bianchi,et al.  Performance analysis of some eigen-based hypothesis tests for collaborative sensing , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[14]  Yonghong Zeng,et al.  Maximum Eigenvalue Detection: Theory and Application , 2008, 2008 IEEE International Conference on Communications.

[15]  Simon Haykin,et al.  Cognitive radio: brain-empowered wireless communications , 2005, IEEE Journal on Selected Areas in Communications.

[16]  Tharmalingam Ratnarajah,et al.  Eigenvalues and Condition Numbers of Complex Random Matrices , 2005, SIAM J. Matrix Anal. Appl..

[17]  Roberto Garello,et al.  Exact non-asymptotic threshold for eigenvalue-based spectrum sensing , 2009, 2009 4th International Conference on Cognitive Radio Oriented Wireless Networks and Communications.

[18]  Yonghong Zeng,et al.  Sensing-Throughput Tradeoff for Cognitive Radio Networks , 2008, IEEE Transactions on Wireless Communications.

[19]  R.W. Brodersen,et al.  Cyclostationary Feature Detector Experiments Using Reconfigurable BEE2 , 2007, 2007 2nd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks.

[20]  V. Tarokh,et al.  Cognitive radio networks , 2008, IEEE Signal Processing Magazine.

[21]  A. Ghasemi,et al.  Collaborative spectrum sensing for opportunistic access in fading environments , 2005, First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005..

[22]  Yonghong Zeng,et al.  Maximum-Minimum Eigenvalue Detection for Cognitive Radio , 2007, 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications.