Performance Analysis for Multi-User Holographic MIMO Downlink with Matched Filter Precoding

Holographic MIMO (HMIMO) has emerged as a promising solution for future wireless systems by enabling ultra-dense, spatially continuous antenna deployments. While prior studies have primarily focused on electromagnetic (EM) modeling or simulation-based performance analysis, a rigorous communication-theoretic framework remains largely unexplored. This paper presents the first analytical performance study of a multi-user HMIMO downlink system with matched filter (MF) precoding - a low-complexity baseline scheme. By incorporating multipath propagation, mutual coupling, and element excitation, we derive a novel closed-form expression for the MF signal-to-interference-plus-noise ratio (SINR) using an equivalent random variable model. Leveraging bivariate gamma distributions, we then develop tractable throughput approximations under full, partial, and no channel state information (CSI) scenarios. Additionally, we formulate a max-min beamforming problem to benchmark optimal user fairness performance. Numerical results validate the accuracy of the proposed framework and reveal that MF precoding achieves competitive performance with strong robustness to low SINR and CSI uncertainty.