Error Analysis of an Optimal Rotated M-PSK Constellation in a SOMA-Based Wireless Communication System

In this work, we consider a two-user receive diversity wireless communication system with a rotated M-ary phase-shift keying (M-PSK) modulation, also known as semi-orthogonal multiple access (SOMA), for data transmission at the transmitter. At the receiver of the considered wireless communication system, each user utilizes a maximum ratio combining (MRC) technique and an optimal maximum-likelihood (ML) rule for transmitted data detection. We provide an analytical framework for the error analysis of the receive diversity wireless communication system and derive the closed-form expressions of the symbol error probability (SEP) for the users. Further, we also obtain the asymptotic expressions of the SEP at a high signal-to-noise ratio (SNR). We provide a numerical solution for the problem of finding the optimal rotation angle for the M-PSK constellation minimizing the SEP. The effects of the system parameters, namely, the number of diversity branches, SNR, and M, on the optimal rotation angle are demonstrated via numerical results. Furthermore, the simulation results corroborate the presented analytical results.