A Suboptimal Algorithm for SCMA Codebook Design over Uplink Rayleigh Fading Channels

Sparse Code Multiple Access (SCMA) is a novel non-orthogonal multiple access technique for 5G systems. In this paper, we propose a suboptimal algorithm for SCMA codebook design over uplink Rayleigh fading channels. In uplink channels, the pairwise error probability (PEP) is derived firstly, based on which the diversity gain and the coding gain of SCMA are analyzed. According to the analysis, the multi-dimensional mother constellation design is formulated as a non-convex optimization problem, aiming to enlarge two factors to achieve a better coding gain. Furthermore, the optimization problem is simplified as a convex second-order cone programming problem to obtain a suboptimal solution. Simulation results show that the bit error ratio (BER) performance is improved significantly on account of the enlarged factors.