Optimal decision threshold for eigenvalue-based spectrum sensing techniques

Abstract

This paper investigates optimization of the sensing threshold that minimizes the total error rate (i.e., the sum of the probabilities of false alarm and missed detection) of eigenvalue-based spectrum sensing techniques for multiple-antenna cognitive radio networks. Four techniques are investigated, which are maximum eigenvalue detection (MED), maximum minimum eigenvalue (MME) detection, energy with minimum eigenvalue (EME) detection, and the generalized likelihood ratio test (GLRT) detection. The contribution of this paper is of four parts. Firstly, we present the derivative of the matrix-variate confluent hypergeometric function, which is required for the MED case. Secondly, we derive the probabilities of false alarm for both cases MME and EME detection. Thirdly, we derive the probability of missed detection for the GLRT detector. Finally, we provide the exact expressions required to obtain the optimal sensing thresholds for all cases. The simulation results reveal that for all the investigated cases the chosen optimal sensing thresholds achieve the minimum total error rate.