Energy Detection of Unknown Signals over Composite multipath/shadowing Fading Channels

In this paper, the performance analysis of an energy detector is exploited over composite multipath/shadowing fading channels, which is modeled by Rayleigh-lognormal (RL) distribution. Based on an approximate channel model which was recently proposed by the author, the RL envelope probability density function (pdf) is approximated by a finite sum of weighted Rayleigh pdfs. Relying on this interesting feature, the performance of energy detector over RL fading channel is investigated and approximate closed-form expression is derived for the detection probability ( ). Further, results are extended to diversity reception case, where selection diversity (SC) technique is adopted to improve the detection performance. Selection Diversity is one of the most simplest diversity techniques, in which, the receiver simply picks the signal with the largest SNR among the received signals. In this regard, an approximate closed-form expression is derived for the pdf of the resulting signal-to-noise ratio (SNR) of SC receiver. Using this approximated pdf, an analytical closed-form expression is derived for the  of energy detector with SC diversity. The presented analysis is validated by numerical and simulation results.