Average BER Analysis for $M$-ary FSK Signals in Nakagami-$q$ (Hoyt) Fading With Noncoherent Diversity Combining

This paper analyzes the average bit error rate (BER) of noncoherent M-ary frequency-shift keying (FSK) signals over multichannel nonidentically distributed Nakagami-q (Hoyt) fading employing diversity combining. The first part of the paper considers the conventional postdetection noncoherent equal-gain combiner (NC-EGC), in which a Fourier series inversion formula is employed to derive a simple and rapidly converging series-based expression for the system average BER. This expression is valid for arbitrary values of received average signal-to-noise ratios (SNRs) and fading parameters. The derived expression is then compared with some existing ones in the literature, and the results show a large reduction in computational complexity, particularly when M and/or the diversity order increases. In the second part, a new noncoherent combiner is proposed to achieve improvements over the conventional NC-EGC. It is also shown that this new combiner results in a simple closed-form expression for the system average BER that is given in terms of elementary functions; hence, it can be easily numerically evaluated with noticeable computation efficiency.