Variational Bayesian Near-Field Channel Estimation for Distributed MIMO Systems

Distributed multiple-input multiple-output (MIMO) is a promising architecture for future wireless systems because cooperation among geographically separated base stations (BSs) improves coverage, spectral efficiency, and link reliability. However, the large effective aperture formed by distributed BSs makes near-field effects non-negligible and complicates accurate channel state information acquisition. Existing near-field estimators often suffer from modeling errors caused by approximate angle–range decoupling or from the high storage and computational costs of dense two-dimensional sparse representations. This article proposes an off-grid variational Bayesian channel-estimation framework for the considered distributed near-field MIMO geometry, which comprises equally spaced, collinear BS reference points and aligned uniform linear arrays (ULAs) with common inter-element spacing. We establish a geometry-coupled model based on the exact geometric spherical-wave phase response and map the local direction–range parameters observed by different BSs into a common reference coordinate system, yielding a two-dimensional jointly sparse representation. An independent-vector variational Bayesian inference algorithm then decomposes the high-dimensional multiuser recovery problem into user-specific posterior subproblems. It operates directly on the received pilot matrices, avoiding pilot–matrix inversion and the resulting distortion of noise statistics. A two-dimensional skewed off-grid update is further embedded in an expectation-maximization procedure to jointly refine angle and range offsets, mitigating basis mismatch while permitting a coarser initial dictionary. Simulation results support the effectiveness of the proposed method in the evaluated scenarios.