Spatially correlated channel estimation for RIS‐assisted MIMO systems with correlated gaussian perturbation

Abstract

This paper studies the problem of spatially correlated channel estimation for reconfigurable intelligent surface (RIS)‐assisted multiple‐input multiple‐output (MIMO) systems with arbitrarily correlated Gaussian perturbation. In particular, composite RIS channel estimation is first explored based on minimum mean square error (MMSE) method, and optimal training sequence design of pilots with MSE minimization. Applying the Kronecker‐structured model, correlated composite RIS‐related channels and correlated Gaussian perturbation are then characterized. The optimal training sequence structure and spatial training power allocation conditions are derived, and the choice of the optimal training sequence length is also analyzed. Finally, numerical results are provided to assess the performance of the proposed estimate method under different training sequence structures, the optimal length of the training sequence, and information statistics. Extensive numerical results show that the proposed estimate method has supreme performance compared to state of‐the‐art baseline methods (e.g. maximum likelihood and two‐sided linear channel estimation methods).