Joint Visibility Region Detection and Channel Estimation for XL-MIMO Systems via Alternating MAP

We investigate a joint visibility region (VR) detection and channel estimation problem in extremely large-scale multiple-input-multiple-output (XL-MIMO) systems, where near-field propagation and spatial non-stationary effects exist. In this case, each scatterer can only see a subset of antennas, i.e., it has a certain VR over the antennas. Because of the spatial correlation among adjacent sub-arrays, VR of scatterers exhibits a two-dimensional (2D) clustered sparsity. We design a 2D Markov prior model to capture such a structured sparsity. Based on this, a novel alternating maximum a posteriori (MAP) framework is developed for high-accuracy VR detection and channel estimation. The alternating MAP framework consists of three basic modules: a channel estimation module, a VR detection module, and a grid update module. Specifically, the first module is a low-complexity inverse-free variational Bayesian inference (IF-VBI) algorithm that avoids the matrix inverse via minimizing a relaxed Kullback-Leibler (KL) divergence. The second module is a structured expectation propagation (EP) algorithm which has the ability to deal with complicated prior information. And the third module refines polar-domain grid parameters via gradient ascent. Simulations demonstrate the superiority of the proposed algorithm in both VR detection and channel estimation.