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  1. 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 when the RIS is composed of passive elements without any sensing or data processing capabilities, and thus, the channels must be estimated indirectly by a noncolocated device, typically a controlling base station (BS). In this article, we examine channel estimation for passive 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 will consider situations with and without line-of-sight propagation, single-antenna and multi-antenna configurations for the users and BS, correlated and sparse channel models, single-carrier and wideband orthogonal frequency-division multiplexing (OFDM) scenarios, availability of direct links between the users and BS, exploitation of prior information, as well as a number of other special cases. We further conduct simulations of representative algorithms and comparisons of their performance for various channel models using the relevant Cramér-Rao bounds. 
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