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Hypercube-Based Multidimensional Constellation Design for Uplink SCMA Systems

The design of multidimensional constellations (MdCs) is an integral part of the construction of a sparse code multiple access (SCMA) system. Since the optimal maximum likelihood (ML) receiver for SCMA is too complex in most applications, one highly popular detection technique is the message passing algorithm (MPA), which exploits the sparsity structure of SCMA. MPA is a near-optimal technique, where its performance improves with increasing the signal-to-noise ratio (SNR) and the number of iterations. When the number of MPA iterations has to be limited, the performance gap between ML and MPA becomes significant, specially at low-to-medium SNRs. In this paper, we design novel SCMA MdCs based on optimized unitary rotations on hypercubes. The proposed MdCs provide substantial performance gains in comparison to the best known SCMA MdCs in the literature, specially in low-to-medium SNR regions when the number of MPA iterations has to be low, and in the presence of 5G-compliant LDPC codes.