Block Compressive Sensing Based Multi-User Detection for Uplink Grant-Free Codebook-Based NOMA

A codebook (CB)-based non-orthogonal multiple access (NOMA) is an efficient variant of code-domain (CD) NOMA (CD-NOMA) that leverages multi-dimensional constellations (MDC) to achieve significant performance gains over spread-sequence CD-NOMA. This paper focuses on developing block-sparsity models (Model-1 and Model-2) for grant-free CB-based NOMA systems. The frame-wise static block sparsity model exhibits both block and structured sparsity, enhancing detection performance. Furthermore, this work includes the design of a multi-user detection algorithm for joint activity and data detection (JADD) tailored to the aforementioned models. The inherent block-sparsity structure in grant-free CB-based NOMA systems is leveraged to develop a block-compressive sensing (BCS) framework for multi-user detection. This framework achieves robust reconstruction performance with minimal computational complexity. The paper introduces a first significant jump (FSJ)-aided block subspace pursuit algorithm (FSJ-BSP), which performs JADD without requiring prior knowledge of the sparsity level. This adaptability makes the proposed algorithm well-suited for practical 6G networks.