Joint codebook assignment and power allocation for SCMA based on capacity with Gaussian input

Sparse Code Multiple Access (SCMA) is a non-orthogonal multi-dimensional spreading technique based on layered codebooks. In SCMA, incoming bits are directly mapped to multi-dimensional codewords of pre-defined codebooks. In comparison to simple repetition of QAM symbols in Low Density Signature (LDS), shaping gain of the multi-dimensional constellation is the main advantage of SCMA for performance improvement. Similar to LDS, SCMA can take the advantage of a near optimal Message Passing Algorithm (MPA) receiver with reasonable complexity. In this paper, the uplink SCMA sum capacity is derived and a specific codebook design method is proposed, which can cancel the effect of the dependency between the non-zero entries of codewords. Under this condition, we study the uplink sum-rate optimization problem. A joint codebook assignment and power allocation method is proposed to achieve a near optimal solution. Simulation results show the significant performance gain of the proposed algorithm.