A Bayesian Framework For Cascaded Channel Estimation in RIS-Aided mmWave Systems

TL;DR

This work tackles the challenge of estimating cascaded RIS‑aided mmWave channels, where the product of RIS‑related path gains induces non‑Gaussian statistics that degrade LMMSE performance. It introduces a Bayesian framework using a complex adaptive Laplace prior for the cascaded gains and derives a variational inference algorithm under a hierarchical model to perform approximate posterior inference. The VI updates yield a Gaussian posterior for the main coefficient vector, with Gamma and generalized inverse Gaussian posteriors for auxiliary variables, and the final cascaded channel is reconstructed as c_k_hat = W_k m_alpha_k. Numerical results show the proposed estimator outperforms LS, LMMSE, and VI with a Student’s‑t prior in terms of NMSE, including scenarios with angle uncertainty, highlighting its practical potential for RIS‑assisted mmWave communications.

Abstract

In this paper, we investigate cascaded channel estimation for reconfigurable intelligent surface (RIS)-aided millimeter-wave multi-user communication systems. Since the complex channel gains of the cascaded RIS channel are generally non-Gaussian, the use of the linear minimum mean squared error (LMMSE) estimator leads to inevitable performance degradation. To tackle this issue, we propose a variational inference-based framework that approximates the complex channel gains using a complex adaptive Laplace prior, which effectively captures their probability distributions in a tractable way. Numerical results demonstrate that the proposed estimator outperforms conventional estimators including least squares and LMMSE in terms of cascaded channel estimation error.

Figures (2)

• Figure 1: NMSE comparison versus number of blocks.
• Figure 2: NMSE comparison under angle uncertainty.