An Efficient Codebook Design for Uplink SCMA

Sparse code multiple access (SCMA) is one of the most intensively investigated non-orthogonal multiple access (NOMA) techniques for the fifth generation communication (5G) system. In this paper, a new multi-stage optimization approach for codebook design is proposed for the uplink SCMA system. The proposed schemes includes two parts: i) multi-dimensional mother constellation design ii) mapping matrix design. Firstly, the multi-dimensional complex mother constellation design is implemented by a series of two-dimensional real constellations which can be obtained by the lattice theory and the symbol switch algorithm (SSA). The Secondly, we construct user-specific mapping matrix by optimizing the phase rotation of the user constellation to effectively reduce the interference between the multi-user codewords superimposed on every single time-domain resource elements (REs). Finally, the multi-user codebooks are generated by combining the multi-dimensional mother constellation and the user-specific mapping matrix. The simulation results demonstrate that the proposed codebooks can greatly decrease bit error rate (BER) value compared to the existing codebooks under different channels, different codebook sizes and different overloading ratios, and the performance is also improved for the large-scale SCMA codebook. More importantly, in order to verify the proposed codebook applicability, two different message passing algorithm (MPA) are used to simulate the SCMA system with different codebook sizes, both of which obtain faster convergence speed and better BER performance than other existing codebooks.