Unified Analysis of Cooperative Spectrum Sensing Over Composite and Generalized Fading Channels

In this paper, we investigate the performance of cooperative spectrum sensing (CSS) with multiple-antenna nodes over generalized and composite fading channels. To this end, we approximate the probability density function (pdf) of the signal-to-noise ratio (SNR) of various fading channels using the mixture Gamma (MG) distribution. Based on this, we derive an exact closed-form expression and a generic infinite series representation for the corresponding probability of energy detection, along with a finite upper bound for the involved truncation error. Both expressions have a relatively simple algebraic form that gives them convenience in handling both analytically and numerically. Furthermore, the composite effect of multipath fading and shadowing scenarios in CSS is mitigated by applying an optimal fusion rule that minimizes the total error rate (TER), where the optimal number of nodes is derived under the Bayesian criterion, assuming erroneous feedback channels. We also extend the derived average detection probability to include diversity reception techniques, namely, maximal-ratio combining, square-law combining, and square-law selection (SLS). For the SLS, we demonstrate the existence of an error rate floor as the number of antennas of the cognitive radio nodes increases in erroneous decision feedback channels. Accordingly, we derive the optimal rule for the number of antennas that minimizes the TER in the SLS framework. Monte Carlo simulations are presented to corroborate the analytical results and to provide illustrative performance comparisons and insights between different composite fading channels.