Implementation of Group-Approximate Expectation Propagation Algorithm for Uplink MIMO-SCMA Detection Using 16-Point Codebook

The complexity of conventional massage propagation algorithm (MPA) for detection of sparse code multiple access (SCMA) grows exponentially as the size of the codebook increases, posing a challenge for hardware implementation of large-size codebooks. Expectation propagation algorithm (EPA) has shown its superiority owing to its linear complexity with respect to the codebook size. In this paper, we propose log-domain group-approximate EPA (GA-EPA) for further complexity reduction. The mother constellation points are partitioned into several groups, which can simplify the calculation of posterior probability. Compared to conventional EPA, log-domain GA-EPA can reduce approximately 76.4% of multiplications and 53.8% of divisions for MIMO-SCMA signal detection. A GA-EPA detector is then designed in 40nm CMOS technology, we use customized floating-point to shorten word-lengths and to exploit the property of exponential function for accomplishing 17% total area reduction and more than 99% table reduction. From the synthesis results, our design for MIMO-SCMA detection with 16-point codebook from 4 receiving antennas can achieve a throughput of 364Mbps at an operating frequency of 167MHz. Compared to the prior MPA-related implementations, our work outperforms in normalized hardware efficiency and demonstrates a promising solution for large codebook cardinality.