Closed-Form Analysis of Relay-Based Cognitive Radio Networks Over Nakagami- $m$ Fading Channels

We propose a general framework for a comprehensive performance analysis of cooperative spectrum sensing (CSS) in cognitive radio (CR) networks. Specifically, we investigate the detection accuracy of a relay-based CR network over independent nonidentical Nakagami- m fading channels. Based on the probability density function (pdf) approach, we derive new exact and approximated closed-form expressions for the average detection probability and the average false alarm probability employing two diversity combining techniques, namely, the maximal ratio combining (MRC) scheme and the selection combining (SC) scheme. We also investigate the convergence rate of infinite series that appears in the derived exact closed-form expressions and propose to use a powerful acceleration algorithm that allows for the series termination with a finite number of terms. The results obtained reveal the importance of including the relaying link statistics and the combination techniques in the performance analysis of CR networks. The derived closed-form expression can be used to determine the energy threshold and the relaying power constraint that meet a given detection accuracy value over nonidentically distributed Nakagami- m fading.