Two-Stage Channel Parameters and Covariance Estimation for RIS-Aided MIMO With Angular Dispersion

Abstract

In this study, we propose a cascaded channel covariance matrix (C-CCM) estimation framework for millimeter-wave (mmWave) reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) systems that explicitly accounts for the angular spread (angular dispersion) effect. We derive analytical expressions for the C-CCM under angular spread, demonstrate how angular spread shapes its eigenvalue distribution, and calculate the effective rank of the C-CCM in the presence of angular spread. For C-CCM estimation, we introduce a two-stage transmission protocol. The first stage performs user activity detection and coarse cascaded angular localization, whereas the second stage focuses on fine parameter and C-CCM estimation over the identified cascaded angular region (CAR) through low-overhead scans. In the first stage, the optimal generalized likelihood ratio test (GLRT) detector requires a seven-dimensional (7D) parameter search, which is computationally impractical. To address this limitation, we propose a practical 2D periodogram-based fast Fourier transform (FFT) peak detector (2D-FFT-PD). In the second stage, we first reduce the dimension of the received signal and then develop a reduced-dimensional subspace-aware maximum likelihood (SA-ML) estimator for estimating the base parameters of the C-CCM. In addition, we derive the Cramér–Rao bound (CRB) for parameter estimation and establish a normalized mean-square error (NMSE) bound for C-CCM estimation. The performance of the proposed framework is evaluated in terms of probability of detection, root-mean-square error (RMSE), NMSE, relative efficiency metric (REM), and signal-to-interference-and-noise ratio (SINR). Simulation results demonstrate that the proposed framework outperforms existing state-of-the-art methods and achieves performance fairly close to the theoretical bounds.