Another look at the BER performance of FFH/BFSK with product combining over partial-band jammed Rayleigh-fading channels

Product combining (PC) is a well-known diversity technique that effectively combat the effect of partial-band jamming (PBJ) affecting fast-frequency hopping/frequency-shift-keying (FFH/FSK) systems. In this paper, we present two approaches for the average bit error rate (BER) evaluation of FFH/FSK systems with PC over Rayleigh channels subject to PBJ. We first rely on the fact that the decision statistic at the output of PC receivers can be viewed as a product of F-variates to obtain the average BER in the form of a rapidly converging infinite series, which can be readily evaluated numerically for cases of practical interest. We then rely on the theory of H function random variables to present a second approach for the average BER evaluation of PC over partial-band jammed Rayleigh-fading channels. The final closed-form formula is expressed in terms of the Meijer's G function, which can be easily evaluated using common mathematical softwares for small values of the diversity order. Based on this result, we also develop another infinite series representation for the average BER. Numerical experiments show that the latter series representation offers a speed-up factor in evaluating the average BER for high values of the diversity order. The mathematical formalism is illustrated by numerical examples showing the effect of various parameters on the performance of the system.