Asynchronous Multi-User Detection for Code-Domain NOMA: Expectation Propagation Over 3D Factor-Graph

Code-domain non-orthogonal multiple access (NOMA) is a promising technology to achieve ubiquitous massive connections for 5G and beyond. In application scenarios with high channel dynamics or simplified scheduling procedures, multi-user signals face the difficulty of accurate synchronization. The resulted asynchronous inter-user interference (IUI) is too complex to be modeled or alleviated by conventional multi-user detection algorithms. To effectively characterize the asynchronous IUI for code-domain NOMA, this paper constructs a three-dimensional (3D) factor-graph by introducing time delay as an additional dimension and develops the corresponding message passing mechanisms. Then, a novel 3D-expectation propagation algorithm (3D-EPA) is proposed for low-complexity asynchronous multi-user detection. The proposed 3D-EPA iterates between per-user estimation, which projects the asynchronous interference via Gaussian approximation, and inter-user message passing, which propagates the previous estimates among the users to refine the approximation. We also extend the 3D-EPA to multi-antenna scenarios and analyze its state evolution. Simulation results show that the proposed asynchronous NOMA system with 3D-EPA even outperforms its synchronous counterpart, especially under high overloadings.