MIMO-SCMA Codebook Design: Joint Optimization of Sum-Rate and Error Performance

Codebook design for overloaded multiple-input multiple-output (MIMO) sparse code multiple access (SCMA) systems is critical, as reliability and spectral efficiency are inherently coupled. Existing approaches often optimize either error performance or spectral efficiency in isolation. In this paper, we propose a joint framework that balances both objectives using a weighted-sum hybrid objective function. To ensure computational efficiency, we adopt a reduced-dimensional parameterization to optimize the generator points of the joint MIMO-SCMA constellations. We show that codebooks designed for single-antenna systems are suboptimal in MIMO settings, highlighting the need for MIMO-aware design. Simulation results demonstrate that the proposed codebooks improve error performance while maintaining competitive sum rate.