Joint Channel Estimation and Active User Detection for Massive Grant-Free Access in XL-MIMO System

Abstract

The extra-large multiple-input–multiple-output (XL-MIMO) technique has demonstrated significant potential for future wireless communications. In this article, we investigate the joint channel estimation (CE) and active user detection (AUD) for massive grant-free access in XL-MIMO systems. The conventional efficient joint CE and AUD algorithms rely on the channel sparsity in the angular domain, which is unattainable in the XL-MIMO system due to the near-field effect. To tackle this challenge, we construct a spherical wave domain transform (SWT) matrix to transform the near-field channels into the sparse spherical wave (SW)-domain channels, taking into account both angular and distance information. Furthermore, we establish an off-grid model to characterize the discretization-induced mismatch between the continuous angle-distance parameters and their predefined SW-domain sampling grids. This mismatch stems from the finite resolution of the SWT matrix and leads to energy leakage in the SW-domain channel representation. On this basis, we formulate the joint CE and AUD as a Bayesian inference problem and propose the expectation maximization SW-domain-based message passing (EM-SWB-MP) algorithm to solve it. Specifically, the expectation maximization (EM) algorithm is developed to estimate the off-grid deviations, thereby mitigating the energy leakage caused by discretization-induced basis mismatch. Given the refined off-grid model, the SW-domain-based message passing (SWB-MP) algorithm leverages the sparsity of the SW-domain channel to achieve the estimation of the equivalent channel through an efficient message passing process, thereby accomplishing joint CE and AUD. The simulation results demonstrate that the proposed EM-SWB-MP algorithm substantially outperforms the benchmark approximate message passing MMV (AMP-MMV) algorithm, reducing the AUD error rate and the CE error by 89% and 83%, respectively.