Eyad Shtaiwi, Hongliang Zhang, Sriram Vishwanath, Moustafa Youssef, Ahmed Abdelhadi, Zhu Han

Reconfigurable Intelligent Surfaces (RISs) are planner surfaces that include a large number of passively radiating elements. By changing the phase shifts of these passive elements, RISs can shape the propagation environment. This requires accurate channel state information. However, the Channel Estimation (CE) process is challenging because transmitting and/or signal processing means being unworkable at the RIS. This paper investigates the CE problem for an Uplink (UL) channel for a RIS-aided Multi-user Multiple-Input Multiple-Output (MU-MIMO) system. In particular, we propose an algorithm to estimate the composite channel, the separate RIS-based channels, and the direct channel for the RIS-assisted system by exploiting symmetric positive definite (SPD) properties matrices; e.g., invertibility and existence of global minimum, and the uniqueness of the Chelosky decomposition. We divide the entire RIS surface into small sub-RISs, and by controlling the changes in these phase shifts for every sub-RIS surfaces, we can estimate the overall channel. Moreover, we propose a simple passive pilot sequence scheduling scheme and jointly adjusting the phase shift coefficients of elements on each sub-RIS unit. Simulation results justify the efficiency and effectiveness of the proposed approach algorithm.