A capacity-based codebook design method for sparse code multiple access systems

Sparse code multiple access (SCMA) is a novel non-orthogonal multiple access scheme, which exploits a multidimensional constellation based on the non-orthogonal spreading technique. The SCMA multi-user codebook design is the bottleneck of system performance and there is no design guideline from the perspective of capacity. In this paper, a novel SCMA codebook design scheme is proposed to maximize the sum rate, where we transfer the design of multi-dimensional constellation sets to the optimizing of series of 1-dimensional complex codewords. Specifically, a basic M-order pulse-amplitude modulation (PAM) is optimized and then the angles of rotation between the input 1-dimensional constellation and the basic M-PAM constellation can be obtained within a feasible calculation complexity to improve the sum-rate. Finally, the series of 1-dimensional complex codewords are combined to construct multi-dimensional codebooks based on Latin square criterion. Numerical results illustrate that the proposed codebook outperforms the existing codebook by 1.3 dB over AWGN channel and 1.1 dB over Rayleigh channel in terms of bit error rate (BER) performance.