Channel Estimation For RIS-Assisted MIMO Systems with Hardening Effects

Estimating accurate channel state information (CSI) is a prerequisite to benefit from the deployment of reconfigurable intelligent surfaces (RISs). However, pilot overhead is required for estimating the high-dimensionality cascaded channel in RIS-assisted wireless communication systems in addition to considering the scaling ambiguity for separate channel decomposition. In this paper, we exploit a large number of elements at a RIS and the resulting slow variations of the channels between the RIS and the user terminals (UTs). Specifically, we exploit the channel hardening effect between the RIS and UTs and propose an algorithm to estimate the individual channel components for the RIS-assisted system based on the conjugate-gradient method. Moreover, we resolve the channel ambiguity in estimating the separate channels and introduce a three-interval sounding procedure where in the first two intervals we eliminate the product of the RIS-UTs channel matrix with its Hermitian and replace it with a diagonal matrix. Thereby, we transform the channel estimation problem into a tractable form and avoid the bi-linearity in RIS-assisted systems. Then, we deploy the conjugate gradient method to estimate the BS-RIS channel, which is assumed to be constant. In the last sounding phase, the RIS-UTs channel is estimated using conventional techniques such as the least-squares (LS) or minimum mean square error (MMSE) estimators. The results confirm that hardening phenomena between the RIS and UTs channel make the channel estimation problem in the RIS-assisted system feasible and avoid the high degree of non-convexity.