Capacity of AWGN and Rayleigh Fading Channels with $M$-ary Inputs

Since the performance of Turbo and Low Density Parity Check Code (LDPC) codes are very close to Shannon limit, a great deal of attention has been placed on the capacity of additive white Gaussian noise (AWGN) and fading channels with arbitrary channel inputs. However, no closed-form solution has been developed due to the complicated Gaussian integrations. In this paper, we investigate the capacities of AWGN and Rayleigh fading channels with M-ary inputs, e.g. phase shift keying (PSK) and quadrature amplitude modulation (QAM). By firstly adopting successive interference cancellation (SIC) and the entropy power Gaussian approximation, the capacity of an AWGN channel with M-QAM and M-PSK modulations can be approximated as the superposition of the capacity of an AWGN channel with BPSK modulation. Furthermore, the ergodic capacity of a Rayleigh fading channel can be derived directly by averaging the instantaneous capacity of an AWGN channel with respect to the probability density function (PDF) of the fading channel gain. Simulation results verify the effectiveness of the proposed method for estimating the capacity of AWGN and Rayleigh fading channels of all SNR ranges.