Capacity and cutoff rate for M-ray NCFSK signals on Rayleigh fading channels with GSC reception

In this paper, we calculate the channel capacity and cutoff rates for M-ary noncoherent FSK (NCFSK) signals on L-diversity Rayleigh fading channels when the receiver employs generalized selection combining (GSC). With GSC reception, the largest K samples among the available L square-law device outputs, for each decision hypothesis, are combined prior to the detection stage. Optimal code rates are found, based on channel capacity and cutoff rates with both hard and soft decision decoding. which minimize the required bit signal-to-noise ratio E_b/N_o for reliable communication. We show, through numerical results, that, for a given code rate, the GSC receiver complexity K (the order of noncoherent combining) and the modulation alphabet size M can be traded off to obtain minimum required E_b/N_o. Also, for a given multipath diversity order L, and a given code rate, we show that diminishing returns in the minimum required E_b/N_o is observed by combining more multipaths.