Near-Field Channel Estimation for XL-MIMO Systems Using Variational Bayesian Learning

We estimate the uplink channel of an extra largescale multiple-input-multiple-output (XL-MIMO) system, with the base station (BS) consisting of multiple antenna sub-arrays. The BS has a decentralized processing architecture, wherein each sub-array is connected to a local processing unit (LPU), which performs its signal processing tasks. The non-stationarity in XL-MIMO channel causes it to become sparse. We design a decentralized channel estimation algorithm to exploit this sparsity. In this algorithm, each LPU decentrally estimates the channel of a sub-array by exchanging information with other LPUs. This exchange is required to exploit the XL-MIMO sparsity. This decentralized algorithm is designed in two steps. The first step designs a centralized sub-array-based variational Bayesian learning (cS-VBL) algorithm. The second step extends this centralized design to a decentralized S-VBL (dS-VBL) implementation, which converts the centralized hyperparameter updates in cS-VBL algorithm to equivalent decentralized optimization problems. Each LPU decentrally solves this problem using asynchronous alternating direction method of multipliers. We show that the proposed i) cS-VBL and dS-VBL algorithms exploit the XL-MIMO channel sparsity, and outperform their existing centralized and decentralized counterparts; and ii) dS-VBL algorithm is robust to LPU failures, and has a lower complexity than cS-VBL algorithm.