Energy detection of unknown signals in Gamma-shadowed Rician fading environments with diversity reception

This study presents a comprehensive performance analysis of an energy detector over Gamma-shadowed Rician fading channels, namely Rician fading channels with the fluctuating line-of-sight components following the Gamma distribution. This composite multi-path/shadowing model has been shown to provide a remarkably accurate fading characterisation while leading to closed-form expressions for important channel statistics. Rapidly convergent infinite series representations are firstly derived for the average probability of detection and the area under the receiver operating characteristic curve for the no-diversity reception case. These results are then extended to the case of maximal ratio, equal gain and selection diversity. To this end, novel analytical expressions for the statistics of the end-to-end signal-to-noise ratio of equal gain and selection diversity receivers, operating over Gamma-shadowed Rician fading channels are derived. Analytical results are substantiated by Monte Carlo simulation, as well as by extensive numerically evaluated results.