XL-MIMO Near-Field Localization with Bayesian Message Passing

Extra-large scale massive multiple-input multipleoutput (XL-MIMO) significantly enhances the spectral efficiency. Meanwhile, XL-MIMO also positions the communication system within a near-field propagation region. In this paper, the XL-MIMO near-field localization problem is broke down into direction-of-arrival (DOA) estimation and distance estimation by employing the virtual far field model. For DoA estimation, the off-grid sparse Bayesian learning (SBL) is used together with a covariance error matching technique to improve the grid refinement. Specifically, the off-grid error is modeled as a matrix uncertainty perturbation problem, and solved by the proposed matrix uncertainty generalized approximate message passing (MUGAMP) algorithm. In order to reduce the computational complexity arising from the large-scale antenna array, an alternating direction GAMP (ADGAMP) algorithm is further proposed to iteratively optimize the grid mismatch and DOA estimation. For distance estimation, a spectrum power function minimization problem is formulated after the DOA estimation. It is then solved by the eigenvalue decomposition (EVD). Simulation results demonstrate that the proposed ADGAMP+EVD localization method has better positioning accuracy and exhibits lower computational complexity compared with the state-of-theart methods.