Channel Estimation with Reconfigurable Intelligent Surfaces -- A General Framework

Optimally extracting the advantages available from reconfigurable intelligent surfaces (RISs) in wireless communications systems requires estimation of the channels to and from the RIS. The process of determining these channels is complicated by the fact that the RIS is typically composed of passive elements without any data processing capabilities, and thus the channels must be estimated indirectly by a non-colocated device, typically a controlling base station. In this article, we examine channel estimation for RIS-based systems from a fundamental viewpoint. We study various possible channel models and the identifiability of the models as a function of the available pilot data and behavior of the RIS during training. In particular, we consider situations with and without line-of-sight propagation, single- and multiple-antenna configurations for the users and base station, correlated and sparse channel models, single-carrier and wideband OFDM scenarios, availability of direct links between the users and base station, exploitation of prior information, as well as a number of other special cases. We further conduct numerical comparisons of achievable performance for various channel models using the relevant Cramer-Rao bounds.