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.

翻译：大规模多输入多输出（MIMO）码域非正交多址（CD-NOMA）技术是满足下一代无线通信需求（如海量连接与高可靠性）的潜在候选方案之一。本文重点关注两种主要CD-NOMA技术：稀疏码多址接入（SCMA）和密集码多址接入（DCMA）。实现MIMO-CD-NOMA系统的主要挑战之一是设计出计算成本与复杂度均可接受的最优检测器。本文提出一种基于交替方向乘子法（ADMM）的迭代线性检测器。首先，将最大似然（ML）检测问题转化为共享优化问题；将ML检测问题中的集合约束松弛为盒约束共享问题，并通过惩罚项引入替代变量以补偿约束松弛造成的损失。对系统模型（即输入信号与接收信号间的关系）进行重构，使所提出的共享优化问题易于应用。ADMM是一种鲁棒算法，可分布式求解共享问题。所提检测器利用分布式特性降低每次迭代的计算成本与时间。针对三种MIMO-CD-NOMA系统（单输入多输出CD-NOMA（SIMO-CD-NOMA）、空间复用CD-NOMA（SMX-CD-NOMA）和空间调制CD-NOMA（SM-CD-NOMA））设计了基于ADMM的线性检测器。通过大量蒙特卡洛仿真，深入分析了各类系统参数及ADMM参数对计算复杂度与符号错误率（SER）的影响。