Structured SCMA Codebook Design by Joint Parameter Optimization Based on Union Bound

In the structured codebook design for sparse code multiple access (SCMA) systems, the constellation structure, constellation mapping matrix (CMM), and bit labeling are critical factors influencing the error performance of optimized codebooks. However, existing multi-stage codebook design methods limit the potential coding gain. Besides, although the minimum Euclidean distance (MED) is commonly used as the performance criterion for additive white Gaussian noise (AWGN) channels, existing works indicate that the MED does not always reflect the actual error performance. This letter proposes a novel structured codebook design for joint parameter optimization based on the union bound, which addresses the mismatch of MED and enhances the error performance. Specifically, we develop strategies for constructing the one-dimensional constellations, CMMs, bit labeling set, and treat these factors as optimizable parameters. The union bound is employed as the design metric to jointly optimize the aforementioned parameters with genetic algorithm (GA). Simulation results demonstrate the superiority of the proposed codebook design method.