A Low-Complexity Codebook Design Scheme for SCMA Systems Over an AWGN Channel

As a promising wireless access technique, sparse code multiple access (SCMA) directly maps the input bits to the transmitted multidimensional codewords according to the SCMA codebook. In general, SCMA codebook optimization and detector simplification are independent of each other. In this article, we propose a simplified SCMA codebook with a separable structure for implementing a low-complexity detector. For codebook design, a separable codebook structure is proposed to simplify the maximization of the minimum Euclidean distance (MED). With this structure, multiple one-dimensional complex codebooks corresponding to one resource element (RE) are determined by maximizing the MED of the superimposed codewords. Then, the entire codebook set is obtained based on a structure indicator matrix and the separable codebook structure. The proposed codebook has a larger MED than obtained by existing codebooks. Benefiting from the separable codebook structure, the signals transmitted over each RE can be independently used to recover the corresponding input bit information. Therefore, we propose a parallel maximum a posteriori (P-MAP) detector consisting of several low-complexity MAP detectors to reduce the complexity of the conventional multiuser message passing (MP) detector in SCMA. At the receiver, each RE is assigned a low-complexity MAP detector. Simulation results show that the proposed codebook outperforms the known optimal codebook over an AWGN channel. Moreover, the run time of the P-MAP detection algorithm is reduced by 99.8% compared to the Log-MPA algorithm. With the proposed codebook design scheme and the P-MAP detector, an SCMA unit can be separated into two independent non-SCMA units, which significantly increases system flexibility.