Variable-rate noncoherent M-FSK modulation for power limited systems over Nakagami-fading channels

We propose a variable-rate and fixed-power non-coherent M-ary frequency shift keying (NC-MFSK) modulation scheme for power limited systems over Nakagami-fading channels. We first address the system performance from the average link spectral efficiency, the average bit-error rate (BER), and the probability of outage perspectives assuming that perfect channel estimates are available at the transmitter within a permissible delay. We compare the proposed system with two versions of the noncoherent binary FSK (NC-BFSK) scheme. The former is the fixed or the blind one, which has no feedback information, and the latter is a kind of an adaptive one wherein a feedback channel is provided to inform the transmitter whether to transmit or not. Our results show that the proposed adaptive MFSK scheme exhibits the following gains: up to a 9- and 37-dB power gain from the average spectral efficiency perspective compared to those for the adaptive and fixed NC-BFSK schemes, respectively, at very low values of the received carrier-to-noise ratio and improvements of about four orders and one order of magnitude from the average BER and probability of outage perspectives, respectively, compared to those of the fixed NC-BFSK scheme. We then study the system performance in the case of outdated estimates. It is shown that only the average BER gets affected by outdated estimates. Our analysis shows that the system is insensitive to normalized delays f_dτ up to 10^-2 where f_d is the doppler frequency and τ is the time delay. We also propose an adaptive switching thresholds scheme to better mitigate the effect of the feedback delay.