Joint Optimization of Constellation With Mapping Matrix for SCMA Codebook Design

Sparse code multiple access (SCMA) is being considered as a promising multiple access solution for 5G systems. A distinguishing feature of SCMA is that it combines the procedures of bit to constellation symbol mapping and subsequent spreading using multidimensional codebooks differentiated by users. Such codebooks dominate the system implementation as a main source of not only performance gain but also design complexity. This letter presents a joint constellation with mapping matrix design for SCMA codebooks, which formulates the constellations optimization as a nonconvex quadratically constrained quadratic programming problem based on a set of well-constructed mapping matrices. We elaborately solve the problem to achieve outperformance over existing SCMA design in terms of bit error rate (BER). For improving practicality, an approximate approach is further proposed to reduce the complexity significantly with a limited BER loss.