Joint Low-Rank and Sparse Bayesian Channel Estimation for Ultra-Massive MIMO Communications

TL;DR

The paper tackles channel estimation for ultra-massive MIMO under spatial non-stationarity by proposing a joint low-rank and sparse Bayesian estimator (LRSBE) that operates in the beam domain. It decomposes each beam-domain channel into independent low-rank and sparse components and solves a jointly regularized recovery problem via an EM framework, using block sparse Bayesian learning for the sparse part and gradient/SVT-based updates for the low-rank part. The approach yields substantial NMSE gains over state-of-the-art methods (OMP, ISTA, SBE, BSBE) across varying SNRs and antenna counts, while reducing computational complexity. These results illustrate the practical utility of exploiting both low-rankness and sparsity in ultra-massive MIMO channel estimation, with implications for 6G-scale deployments.

Abstract

This letter investigates channel estimation for ultra-massive multiple-input multiple-output (MIMO) communications. We propose a joint low-rank and sparse Bayesian estimation (LRSBE) algorithm for spatial non-stationary ultra-massive channels by exploiting the low-rankness and sparsity in the beam domain. Specifically, the channel estimation integrates sparse Bayesian learning and soft-threshold gradient descent within the expectation-maximization framework. Simulation results show that the proposed algorithm significantly outperforms the state-of-the-art alternatives under different signal-to-noise ratio conditions in terms of estimation accuracy and overall complexity.

Figures (4)

• Figure 1: Illustration of (a) low-rankness and (b) sparsity of the space domain and beam domain channels ($M$ = 1024).
• Figure 2: Comparison of average NMSEs versus SNR for different algorithms ($M=256, N=5$).
• Figure 3: CDFs of NMSEs with (a) $M= 256, N = 5$, (b) $M= 1024, N = 5$ and (c) $M = 256, N = 10$ (SNR = -10 dB).
• Figure 4: Average NMSEs with different combinations of $M$ and $N$ (SNR = -10 dB).