SCMA Codebooks Optimization Based on Genetic Algorithm

Sparse code multiple access (SCMA) is a nonorthogonal multiple access scheme based on joint modulation and spread spectrum procedure. This scheme allows to increase the number of active users inside a given time-frequency resource. Design of SCMA codebooks is a challenging problem. The paper considers the design of SCMA codebooks based on Genetic Algorithm (GA). In general case, mother constellation is not required for GA, and optimization is performed directly on the codebooks. We present the obtained structured codebooks containing two antipodal codeword pairs. Optimization was carried out to improve SCMA signal performance in additive white Gaussian noise (AWGN) channel by constraining the average energy of codewords. The obtained codebooks have minimum Euclidean distance equal to 0.87 (at unit average power of SCMA signal) and outperform known codebooks in AWGN channel with both Maximum Likelihood (ML) receiver or Message Passing Algorithm (MPA) detection. The comparison of existing and proposed codebooks is performed using computer simulation and union bounds. The asymptotic gain over the best known codebooks is 0.8 dB. As a result of the simulation, proposed codebooks demonstrate similar performance for ML and MPA detection algorithms. The proposed method is suitable for codebook design for other non-orthogonal schemes, e. g., Pattern Division Multiple Access (PDMA).