Hypercube-Based SNR-Adaptive Multidimensional Constellation Design for Uplink SCMA Systems

Designing multidimensional constellations (MdCs) is an integral part of sparse code multiple access (SCMA). Since the optimal maximum a posteriori (MAP) receiver for SCMA is too complex in most applications, one highly popular technique is the near-optimal message passing algorithm (MPA), 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 (e.g., low-latency and/or low-complexity and/or energy-sensitive applications), the performance gap between MAP and MPA becomes significant, especially at low-to-medium SNRs. Inspired by the promising features of hypercubes when used along with bit-interleaved coded modulation, we construct novel MdCs which are based on a unitary rotation of a hypercube by a rotation angle that aims to achieve the minimum frame-error-rate (FER). By exploiting special properties of hypercubes, we fit a second-order rational polynomial to a few measured FER samples, and find a close-to-optimal rotation angle at each SNR and MPA iteration. Our proposed MdCs provide substantial performance gains (as much as 2 dB) in comparison to the best known SCMA MdCs in the literature, especially 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.