Joint optimization scheme and sum constellation distribution for multi-user Gaussian multiple access channels with finite input constellations

Phase adjusting and power adjusting input schemes of non-orthogonal Gaussian multiple access channels (GMAC) for two-user with finite input constellations have been studied. In this paper, the input scheme for multi-user is jointly optimized by both powers and phases. This scheme is deduced from the constellation constrained (CC) capacity of multi-user GMAC. Performance analysis indicates that the proposed input scheme outperforms previous input schemes for most SNR and achieves the largest enlargement of CC capacity region at high SNR values. Motivated by the properties of sum constellation's distance distribution, a procedure to efficiently obtain optimal multi-user input schemes is proposed for MPSK input constellations.