Large-scale multi-input multi-output (MIMO) code domain non-orthogonal multiple access (CD-NOMA) techniques are one of the potential candidates to address the next-generation wireless needs such as massive connectivity, and high reliability. This work focuses on two primary CD-NOMA techniques: sparse-code multiple access (SCMA) and dense-code multiple access (DCMA). One of the primary challenges in implementing MIMO-CD-NOMA systems is designing the optimal detector with affordable computation cost and complexity. This paper proposes an iterative linear detector based on the alternating direction method of multipliers (ADMM). First, the maximum likelihood (ML) detection problem is converted into a sharing optimization problem. The set constraint in the ML detection problem is relaxed into the box constraint sharing problem. An alternative variable is introduced via the penalty term, which compensates for the loss incurred by the constraint relaxation. The system models, i.e., the relation between the input signal and the received signal, are reformulated so that the proposed sharing optimization problem can be readily applied. The ADMM is a robust algorithm to solve the sharing problem in a distributed manner. The proposed detector leverages the distributive nature to reduce per-iteration cost and time. An ADMM-based linear detector is designed for three MIMO-CD-NOMA systems: single input multi output CD-NOMA (SIMO-CD-NOMA), spatial multiplexing CD-NOMA (SMX-CD-NOMA), and spatial modulated CD-NOMA (SM-CD-NOMA). The impact of various system parameters and ADMM parameters on computational complexity and symbol error rate (SER) has been thoroughly examined through extensive Monte Carlo simulations.

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