Adaptive M-FSK modulation for power limited systems

We propose a variable-rate and fixed-power noncoherent M-FSK (NC-MFSK) modulation scheme for power limited systems over Nakagami fading channels. We compare the proposed system with two versions of the 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. We first derive the average spectral efficiency of our proposed system as a function of the received carrier-to-noise ratio (CNR). Our results show that the adaptive scheme exhibits up to a 9 dB power gain compared to the adaptive NC-BFSK scheme for very low values of the received CNR. We also derive the average bit error rate (BER) for both the adaptive and NC-BFSK schemes. The resulting average BER for the adaptive scheme has an improvement of about four orders of magnitude compared to that of the fixed nonadaptive scheme. Finally, we derive the probability of outage for both adaptive and fixed schemes. The probability of outage for the adaptive scheme has an improvement of approximately one order of magnitude compared to that of the fixed scheme.