Parametric channel estimation for RIS-assisted mmWave MIMO-OFDM systems with low pilot overhead

Abstract

We consider the channel estimation problem in a millimeter-wave (mmWave) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system aided by a passive reconfigurable intelligent surface (RIS). Initially, leveraging the inherent sparsity of mmWave channels, we decouple the channel estimation into the recovery of multipath parameters, including spatial frequencies of angles, delays, and complex gains. Subsequently, we employ two training schemes: the first involves a full row rank constrained RIS phase shift pattern, and the second incorporates a Kronecker structure constrained RIS phase shift pattern. These schemes reform channel estimation into estimating parameters from two fifth-order tensor signals, which admit constrained Canonical Polyadic decomposition. Moreover, both tensor signals share Vandermonde-constrained factor matrices, enabling algebraic algorithms for tensor decomposition problems and recovering channel multipath parameters. Theoretical analyses show that the first training scheme has a lower signal processing complexity for channel estimation, while the second attains a higher estimation accuracy. Also, we prove that our proposed two schemes have the same minimum pilot overhead, which is as low as proportional to the product of the number of paths in the two MIMO channels (transmitter-RIS and RIS-receiver). Numerical results validate the effectiveness of our proposed methods.