We focus on the signal detection for large quasi-symmetric (LQS) multiple-input multiple-output (MIMO) systems, where the numbers of both service (M) and user (N) antennas are large and N/M tends to 1. It is challenging to achieve maximum-likelihood detection (MLD) performance with square-order complexity due to the ill-conditioned channel matrix. In the emerging MIMO paradigm termed with an extremely large aperture array, the channel matrix can be more ill-conditioned due to spatial non-stationarity. In this paper, projected-Jacobi (PJ) is proposed for signal detection in (non-) stationary LQS-MIMO systems. It is theoretically and empirically demonstrated that PJ can achieve MLD performance, even when N/M = 1. Moreover, PJ has square-order complexity of N and supports parallel computation. The main idea of PJ is to add a projection step and to set a (quasi-) orthogonal initialization for the classical Jacobi iteration. Moreover, the symbol error rate (SER) of PJ is mathematically derived and it is tight to the simulation results.

翻译：本文聚焦于大尺寸准对称（LQS）多输入多输出（MIMO）系统的信号检测问题，其中服务天线数（M）与用户天线数（N）均较大，且N/M趋近于1。由于信道矩阵病态特性，在平方阶复杂度下实现最大似然检测（MLD）性能极具挑战性。在采用超大孔径阵列的新兴MIMO范式中，空间非平稳性会进一步加剧信道矩阵的病态程度。本文提出投影-雅可比（PJ）方法用于（非）平稳LQS-MIMO系统的信号检测。理论分析与实验验证表明：即便在N/M=1时，PJ方法仍能实现MLD性能。此外，PJ方法具有N的平方阶复杂度并支持并行计算。其核心思想是在经典雅可比迭代中引入投影步骤，并设置（准）正交初始化。本文还推导了PJ方法的符号错误率（SER）数学表达式，且该表达式与仿真结果紧密吻合。