Single Sparse Graph Enhanced Expectation Propagation Design for Uplink MIMO-SCMA

Sparse code multiple access (SCMA) and multiple input multiple output (MIMO) are considered as two efficient techniques to provide both massive connectivity and high spectrum efficiency for future machine-type wireless networks. This paper proposes a single sparse graph (SSG) enhanced expectation propagation algorithm (EPA) receiver, referred to as SSG-EPA, for uplink MIMO-SCMA systems. Firstly, we reformulate the sparse codebook mapping process using a linear encoding model, which transforms the variable nodes (VNs) of SCMA from symbol-level to bit-level VNs. Such transformation facilitates the integration of the VNs of SCMA and low-density parity-check (LDPC), thereby emerging the SCMA and LDPC graphs into a SSG. Subsequently, to further reduce the detection complexity, the message propagation between SCMA VNs and function nodes (FNs) are designed based on EPA principles. Different from the existing iterative detection and decoding (IDD) structure, the proposed EPA-SSG allows a simultaneously detection and decoding at each iteration, and eliminates the use of interleavers, de-interleavers, symbol-to-bit, and bit-to-symbol LLR transformations. Simulation results show that the proposed SSG-EPA achieves better error rate performance compared to the state-of-the-art schemes.