ADMM-based Detector for Large-scale MIMO Dense Code-domain NOMA Systems

Sparse code multiple access (SCMA) is a popular code-domain (CD) non-orthogonal multiple access (NOMA) technique that excels in segregating multiple users' signals. In SCMA, sparse codewords are detected using the powerful message-passing algorithm (MPA). However, SCMA systems suffer from a limited diversity order (DO). Conversely, dense code multiple access (DCMA) systems, which do not possess a sparse nature, benefit from the full DO offered by dense codewords. Despite this advantage, the MPA detector is not feasible for DCMA systems due to the lack of sparsity. To address these challenges, we present an iterative linear detector for CD-NOMA systems based on the alternating direction method of multipliers (ADMM). In this approach, the standard maximum likelihood (ML) detection problem for CD-NOMA systems is converted into a sharing optimization problem, which is then solved in a distributed manner. The reformulation of CD-NOMA system models enables resource-wise processing using the ADMMalgorithm. The proposed detector effectively addresses the detection problem for both dense and sparse coded NOMA systems. By reformulating the system model, we make single input multioutput (SIMO) and spatially modulated (SM) CD-NOMA systems special cases of spatial multiplexing CD-NOMA (SMX-CD-NOMA) for detection. Furthermore, the ADMM algorithm's resource-wise processing approach is proposed to solve the detection problem in various multiple-input multiple-output (MIMO) CD-NOMA systems. Overall, the proposed ADMM-based detector offers a robust and versatile solution for enhancing the performance and practicality of CD-NOMA systems, particularly in the context of emerging 6G wireless networks.