Efficient Channel Estimation With Shorter Pilots in RIS-Aided Communications: Using Array Geometries and Interference Statistics

Accurate estimation of the cascaded channel from a user equipment (UE) to a base station (BS) via each reconfigurable intelligent surface (RIS) element is critical to realizing the full potential of the RIS's ability to control the overall channel. The number of parameters to be estimated is equal to the number of RIS elements, requiring an equal number of pilots unless an underlying structure can be identified. In this paper, we show how the spatial correlation inherent in the different RIS channels provides this desired structure. We first optimize the RIS phase-shift pattern using a much-reduced pilot length (determined by the rank of the spatial correlation matrices) to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference. In addition to considering the linear minimum MSE (LMMSE) channel estimator, we propose a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information. We call this the reduced-subspace least squares (RS-LS) estimator and optimize the RIS phase-shift pattern for it. This novel estimator significantly outperforms the conventional LS estimator. For both the LMMSE and RS-LS estimators, the proposed optimized RIS configurations result in significant channel estimation improvements over the benchmarks.