To support complex communication scenarios in next-generation wireless communications, this paper focuses on a generalized MIMO (GMIMO) with practical assumptions, such as massive antennas, practical channel coding, arbitrary input distributions, and general right-unitarily-invariant channel matrices (covering Rayleigh fading, certain ill-conditioned and correlated channel matrices). The orthogonal/vector approximate message passing (OAMP/VAMP) receiver has been proved to be information-theoretically optimal in GMIMO, but it is limited to high-complexity LMMSE. To solve this problem, a low-complexity memory approximate message passing (MAMP) receiver has recently been shown to be Bayes optimal but limited to uncoded systems. Therefore, how to design a low-complexity and information-theoretically optimal receiver for GMIMO is still an open issue. To address this issue, this paper proposes an information-theoretically optimal MAMP receiver and investigates its achievable rate analysis and optimal coding principle. Specifically, due to the long-memory linear detection, state evolution (SE) for MAMP is intricately multidimensional and cannot be used directly to analyze its achievable rate. To avoid this difficulty, a simplified single-input single-output variational SE (VSE) for MAMP is developed by leveraging the SE fixed-point consistent property of MAMP and OAMP/VAMP. The achievable rate of MAMP is calculated using the VSE, and the optimal coding principle is established to maximize the achievable rate. On this basis, the information-theoretic optimality of MAMP is proved rigorously. Numerical results show that the finite-length performances of MAMP with practical optimized LDPC codes are 0.5-2.7 dB away from the associated constrained capacities. It is worth noting that MAMP can achieve the same performances as OAMP/VAMP with 0.4% of the time consumption for large-scale systems.

翻译：为支撑下一代无线通信中的复杂通信场景，本文聚焦于具有实际假设的广义MIMO（GMIMO）系统，例如大规模天线、实际信道编码、任意输入分布以及一般右酉不变信道矩阵（涵盖瑞利衰落、特定病态及相关信道矩阵）。正交/向量近似消息传递（OAMP/VAMP）接收机已被证明在GMIMO中具有信息论最优性，但其局限于高复杂度的LMMSE。针对此问题，近期提出的一种低复杂度存储近似消息传递（MAMP）接收机在无编码系统中具有贝叶斯最优性。因此，如何设计一种低复杂度且信息论最优的GMIMO接收机仍是悬而未决的问题。为解决该问题，本文提出一种信息论最优的MAMP接收机，并研究其可达速率分析与最优编码原理。具体而言，由于长记忆线性检测，MAMP的状态演化（SE）呈现复杂的多维特性，无法直接用于分析其可达速率。为规避该难点，本文利用MAMP与OAMP/VAMP的SE不动点一致性特性，提出一种简化的单输入单输出变分状态演化（VSE）方法。通过VSE计算MAMP的可达速率，并建立最大化可达速率的最优编码原理。在此基础上，严格证明了MAMP的信息论最优性。数值结果表明，采用实际优化的LDPC码时，MAMP的有限长性能与相应约束容量的差距为0.5-2.7 dB。值得关注的是，在大规模系统中，MAMP以OAMP/VAMP的0.4%时间消耗即可达到相同的性能。