Message passing algorithm based on QR decomposition for an SCMA system with multiple antennas

Sparse code multiple access (SCMA) is a nonorthogonal multiple access scheme based on a multi-dimensional codebook with sparse codewords. The sparsity property of SCMA allows the receiver to take advantage of low-complexity message passing algorithm (MPA) detector with maximum likelihood (ML)-like performance. The use of multiple antennas at the SCMA receiver will improve the detection performance of the MPA at the expense of an increase in complexity. To reduce the complexity of the MPA, we propose an MPA detection scheme based on QR decomposition, referred to as QR-MPA detection, for an SCMA system with multiple antennas. The proposed QR-MPA detection scheme achieves performance close to the optimal MPA performance by converting the factor graph into two subgraphs through QR decomposition and exchanging a posterior probabilities between subgraphs in a circular manner. Simulation results are presented to compare the performance of the proposed QR-MPA detection scheme with that of the conventional MPA detection scheme.