An MGF-derivative based unified analysis of incoherent diversity reception of M-ary orthogonal signals over fading channels

Exact error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. Additionally, a new concise, derivative formula is obtained for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (BDPSK) signals. All these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signalling over generalized fading channels (with arbitrary fading parameters). Several numerical examples are presented to illustrate the application of the theory, including the investigation into optimal diversity order in energy-sharing communications, characterization of block orthogonal codes with soft-decision decoding (i.e., MFSK may also be viewed as a form of repetition coding) and analysis of MFSK with space (antenna) diversity.