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To achieve the joint active and passive beamforming gains in thereconfigurable intelligent surface assisted millimeter wave system, thereflected cascade channel needs to be accurately estimated. Many strategieshave been proposed in the literature to solve this issue. However, whether theCram\'er-Rao lower bound (CRLB) of such estimation is achievable still remainsuncertain. To fill this gap, we first convert the channel estimation probleminto a sparse signal recovery problem by utilizing the properties of discreteFourier transform matrix and Kronecker product. Then, a joint typicality basedestimator is utilized to carry out the signal recovery task. We show that,through both mathematical proofs and numerical simulations, the solutionproposed in this letter can in fact asymptotically achieve the CRLB.

Asymptotic Achievability of the Cram\'er-Rao Lower Bound of Channel Estimation for Reconfigurable Intelligent Surface Aided Communication Systems