Abstract-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. Index Terms-Complex Wishart matrix, cooperative spectrum sensing, eigenvalue-based detection.
The exact distribution of the condition number of a complex Wishart matrix has been used to calculate the threshold expression in REF without the need of a lookup table.
On the Performance of Eigenvalue-Based Cooperative Spectrum Sensing for Cognitive Radio
IEEE Journal of Selected Topics in Signal Processing
IEEE Journal of Selected Topics in Signal Processing
Mathematics Computer Science