Joint Activity and Channel Estimation for Extra-Large MIMO Systems

Abstract

Extra large MIMO (XL-MIMO) systems are subject to spatial non-stationarity forming visibility regions (VRs), which leads to a sub-array-wise sparse structure of the channel matrix. When XL-MIMO systems operate in grant-free access mode, in which only a fraction of the potential users are active during a given time slot, it follows that the channel matrix possesses a doubly-sparse and user-specific structure such that the activity of each user and each sub-array can be jointly modeled by a nested Bernoulli-Gaussian distribution. This article considers the joint activity and channel estimation (JACE) problem in XL-MIMO systems subject to this so-defined spatial non-stationarity, tackling this challenging inference problem. Our main contributions are 1) to introduce the novel Bernoulli-Gaussian model to simultaneously capture the aforementioned two distinct structured sparsities, and 2) a new bilinear Bayesian inference algorithm capable of jointly estimating the associated channel coefficients, user activity patterns, sub-array activity patterns ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a.k.a$ </tex-math></inline-formula> . spatial non-stationarity), boosted by expectation maximization (EM)-based auto-parameterization. In addition, to shed light on a realistic modeling of VRs, we also introduce a Matérn-cluster point process (MCPP)-based approach to imitate the clustered activity pattern due to spatial non-stationarity. The efficacy of the proposed bilinear JACE algorithm is confirmed by numerical simulations, which show that the proposed method not only significantly outperforms the state-of-the-art (SotA) but also can reach the performance of a genie-aided scheme over wide signal-to-noise-ratio (SNR) ranges, in both uniformly-random and MCPP-based sub-array activity scenarios.