On the Design of Near-Optimal Sparse Code Multiple Access Codebooks

Sparse code multiple access (SCMA) is one of the competitive non-orthogonal multiple access (NOMA) techniques for the next generation of communication systems. In this paper, a systematic construction procedure for the design of SCMA codebooks under various channel environments is proposed in order to achieve near-optimal designs, especially for cases which consider small-scale SCMA parameters. The procedure includes the rotation angle design, the construction of multi-dimensional codebooks, and the design of labelling rules. The detailed design criteria and the related properties are derived and investigated. A low-complexity construction algorithm is further proposed for the cases of fading channels. Numerical results show that the designed SCMA codebooks provide improvements in error performance for all of the considered channel conditions, when compared to the codebooks presented in the prior literature.