Uplink Channel Estimations for Hybrid RIS-Aided Multi-User Communication Systems

Abstract

A reconfigurable intelligent surface (RIS), also known as an intelligent reflecting surface, has gained significant attention as a promising technology for future wireless communication systems. In this thesis, we address the uplink channel estimation problem for multi-user communication systems that utilize a hybrid reconfigurable intelligent surface (HRIS), which is capable of simultaneously reflecting and sensing the impinging signals. First, we jointly design the pilot sequences transmitted by user equipments (UEs) and the amount of phase shifts applied by the HRIS for accurate channel estimation. We formulate a multi-objective optimization problem in terms of the mean squared errors of UEs-to-RIS and RIS-to-base station (BS) channels, and approximate it by assuming that the BS has a perfect estimate of the UEs- to-RIS channel. As a result, a sufficient condition is derived for a feasible solu- tion to be Pareto-optimal to the approximated problem, which simultaneously achieves the Cramér-Rao bounds. We propose two joint designs that satisfy the sufficient condition when the pilot length is at least as long as the product of the numbers of HRIS elements and UEs. The proposed design solutions are easy to implement and lead to computationally efficient channel estimations. Numerical results demonstrate that the proposed joint designs outperform non-joint designs that use randomized phase shifts and conventional channel estimation methods for passive RISs. Second, we propose alternating channel estimation methods, namely the alternating least squares (ALS) and alternating minimum mean square error (AMMSE) algorithms. The key idea involves leveraging information from the received signal at the HRIS (soft information) rather than relying directly on the estimate of the UEs-to-RIS channel (hard information). Moreover, by incor- porating second-order information on the channels, we derive cross-covariance and covariance matrices to perform the MMSE channel estimation on each channel. One major finding is that the covariance matrices for UEs-to-RIS channels are dependent on the RIS-to-BS channel estimate, and vice versa. Consequently, the proposed AMMSE method iteratively updates the covari- ance matrices until convergence. Simulation results validate the effectiveness of our proposed AMMSE and ALS methods in reducing the pilot overhead of the conventional channel estimation method. Furthermore, the AMMSE and ALS channel estimation methods exhibit superior MSE performance compared to the passive RIS channel estimation methods.