SNR Increase Per-Bit-Increase for MPSK and MQAM Signals and SNR Penalty of Using MPSK over MQAM for a Rayleigh Fading Channel

For an AWGN channel, the required SNR-increase-per-bit-increase (SNR_inc/bit_inc), in bits per symbol, to maintain the same symbol error rate (SER) for one or two dimension modulation schemes, such as MPSK and MQAM, is known. In this paper, we present similar results for a Rayleigh fading channel. It is found that the required SNR_inc/bit_inc in a fading channel consists of two parts-one is the same as that for an AWGN channel, and the other one is the extra SNR increase due to the fading. The latter is large (over 2dB) for a small constellation size (M) and negligible with a large M. It also decreases as the diversity order (DO) increases. In addition, we present simple closed-form expressions for the SNR penalty of using MPSK over QAM signals for Rayleigh fading. It is found that the extra penalty due to fading increases and approaches a constant as M increases. It decreases as the DO increases. Simulation results match the theoretical analysis.