Asymptotic Achievability of the Cramér-Rao Lower Bound of Channel Estimation for Reconfigurable Intelligent Surface Assisted Communication System

To achieve the joint active and passive beamforming gains in the reconfigurable intelligent surface assisted millimeter wave system, the reflected cascade channel needs to be accurately estimated. Many strategies have been proposed in the literature to solve this issue. However, whether the Cram\'er-Rao lower bound (CRLB) of such estimation is achievable still remains uncertain. To fill this gap, we first convert the channel estimation problem into a sparse signal recovery problem by utilizing the properties of discrete Fourier transform matrix and Kronecker product. Then, a joint typicality based estimator is utilized to carry out the signal recovery task. We show that, through both mathematical proofs and numerical simulations, the solution proposed in this letter can in fact asymptotically achieve the CRLB.