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.

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