Exact Closed-Form Solution for Detection Probability in Cognitive Radio Networks With Switch-and-Examine Combining Diversity

Abstract

In this study, we analyze spectrum sensing performance by investigating amplify-and-forward based cooperative relaying in underlay cognitive radio networks with switch-and-examine combining diversity technique in which the maximal ratio combining and energy detector schemes are employed at the destination. First, we derive closed-form expressions for both the probability density functions and the probability of detections (P-d) of the end-to-end signal-to-noise ratios at the output of the switch-and-examine combiner over Rayleigh fading channel. Then, the optimal detection threshold and switching threshold values with optimizing error rate (P-e) using the differential evolution algorithm are obtained. Finally, we present some numerical results through the receiver operating characteristics curves utilizing the newly derived closed-form expressions and we verify that the numerical curves precisely match with the simulation results, validating our proposed theoretical analysis.