Joint Sparse Channel Estimation and Multiuser Detection Using Spike and Slab Prior-Based Gibbs Sampling for Uplink Grant-Free NOMA

Large-scale multiuser detection (MUD) is a critical aspect for the emerging sixth generation (6G) networks. Accurate and efficient recovery of users from vast amounts of data is the key aspect for massive machine-type communications (mMTC). Grant-free non-orthogonal multiple access (GF-NOMA) has been recognized as a suitable multiple access technique for mMTC scenarios. Leveraging the inherent sparsity poverty of mMTC combining with GF-NOMA, MUD can be recast as a compressive sensing (CS) problem. However, the existing schemes are facing the challenge of limited accuracy and high computational complexity. In this paper, we first focus on the study of joint channel estimation (CE) and MUD under the single measurement vectors (SMV) model, where a novel approach using spike-and-slab priors with Gibbs sampling (SS-GS) is proposed to solve the MUD problem. To exploit the structural sparsity and improve the recovery performance, we also devise a truncated spike-and-slab priors with Gibbs sampling approach (TSS-GS) under the multiple measurement vectors (MMV) model to retrieving transmitted signals through the channel. The MMV model is transformed into a new model to better exploit signal sparsity. We compare the performance of the proposed methods with traditional detectors. Extensive simulation experiments and analysis are presented to demonstrate the advantages of the proposed algorithm in terms of performance and efficiency.