Energy Detection of Unknown Signals over Cascaded Fading Channels

Energy detection is a favorable mechanism in several applications relating to the identification of deterministic unknown signals such as in radar systems and cognitive radio communications. The present work quantifies the detrimental effects of cascaded multipath fading on energy detection and investigates the corresponding performance capability. A novel analytic solution is firstly derived for a generic integral that involves a product of the Meijer $G-$function, the Marcum $Q-$function and arbitrary power terms. This solution is subsequently employed in the derivation of an exact closed-form expression for the average probability of detection of unknown signals over $N$*Rayleigh channels. The offered results are also extended to the case of square-law selection, which is a relatively simple and effective diversity method. It is shown that the detection performance is considerably degraded by the number of cascaded channels and that these effects can be effectively mitigated by a non-substantial increase of diversity branches.