Sparse Channel Estimation Under Basis Mismatch for RIS-Assisted Systems

Reconfigurable Intelligent Surface (RIS) system channel estimation involves many channel parameters and is costly. However, RIS is often used in millimeter-wave (mmWave) frequencies where sparse channel estimation can be used. Compressive sensing is a popular, computationally efficient sparse recovery method whose observation basis is constructed via discretizing the wave arrival/departure angles at the antennas. The naturally-occurring misalignment between actual and quantized angles manifests itself as a basis mismatch, producing novel issues in the context of RIS that are addressed in the present paper. In particular, the discretization of the angular domain may either be performed at all nodes, e.g., transmitter, receiver, and RIS, or it may be done only at the two ends, namely at the transmitter and the receiver. The performance and relative merits of these two approaches have been unknown to date, and are a topic of this paper. Examining the effect of angle quantization and its misalignment issue requires a carefully constructed equivalent formulation of the RIS channel model, which is part of the contributions of this paper. We study the relative performance of end-point vs. full discretization and explore the effect of RIS training states on the severity of basis mismatch, something that is unique to the RIS scenario. We also demonstrate the impact of dictionary size and training resources on the estimation performance using each of the approaches.