Advanced Nonlinear SCMA Codebook Design Based on Lattice Constellations

The design of efficient sparse codebooks in sparse code multiple access (SCMA) system have attracted tremendous research attention in the past few years. This paper proposes a novel nonlinear SCMA (NL-SCMA) that can subsume the conventional SCMA system which is referred to as linear SCMA, as special cases for downlink channels. This innovative approach allows a direct mapping of users' messages to a superimposed codeword for transmission, eliminating the need of a codebook for each user. This mapping is referred to as nonlinear mapping (codebook) in this paper. Hence, the primary objective is to design the nonlinear mapping, rather than the linear codebook for each user. We leverage the Lattice constellation to design the superimposed constellation due to its advantages such as the minimum Euclidean distance (MED), constellation volume, design flexibility and shape gain. Then, by analyzing the error patterns of the Lattice-designed superimposed codewords with the aid of the pair-wise error probability, it is found that the MED of the proposed nonlinear codebook is lower bounded by the ``single error pattern''. To this end, an error pattern-inspired codebook design is proposed, which can achieve large MEDs of the nonlinear codebooks. Numerical results show that the proposed codebooks can achieve lower error rate performance over both Gaussian and Rayleigh fading channels than the-state-of-the-art linear codebooks.