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Channel estimation in reconfigurable intelligent surfaces (RIS)-aided systemsis crucial for optimal configuration of the RIS and various downstream taskssuch as user localization. In RIS-aided systems, channel estimation involvesestimating two channels for the user-RIS (UE-RIS) and RIS-base station (RIS-BS)links. In the literature, two approaches are proposed: (i) cascaded channelestimation where the two channels are collapsed into a single one and estimatedusing training signals at the BS, and (ii) separate channel estimation thatestimates each channel separately either in a passive or semi-passive RISsetting. In this work, we study the separate channel estimation problem in afully passive RIS-aided millimeter-wave (mmWave) single-user single-inputmultiple-output (SIMO) communication system. First, we adopt avariational-inference (VI) approach to jointly estimate the UE-RIS and RIS-BSinstantaneous channel state information (I-CSI). In particular, auxiliaryposterior distributions of the I-CSI are learned through the maximization ofthe evidence lower bound. However, estimating the I-CSI for both links in everycoherence block results in a high signaling overhead to control the RIS inscenarios with highly mobile users. Thus, we extend our first approach toestimate the slow-varying statistical CSI of the UE-RIS link overcoming thehighly variant I-CSI. Precisely, our second method estimates the I-CSI ofRIS-BS channel and the UE-RIS channel covariance matrix (CCM) directly from theuplink training signals in a fully passive RIS-aided system. The simulationresults demonstrate that using maximum a posteriori channel estimation usingthe auxiliary posteriors can provide a capacity that approaches the capacitywith perfect CSI.

Channel Estimation in RIS-Enabled mmWave Wireless Systems: A Variational Inference Approach