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Intelligent reflecting surfaces (IRSs) are promising enablers for next-generation wireless communications due to their reconfigurability and high energy efficiency in improving poor propagation condition of channels, e.g., limited scattering environment. However, most existing works assumed full-rank channels requiring rich scatters, which may not be available in practice. To analyze the impact of rank-deficient channels and mitigate the ensued performance loss, we consider a large-scale IRS-aided MIMO system with statistical channel state information (CSI), where the double-scattering channel is adopted to model rank deficiency. By leveraging random matrix theory (RMT), we first derive a deterministic approximation (DA) of the ergodic rate with low computational complexity and prove the existence and uniqueness of the DA parameters. Then, we propose an alternating optimization algorithm for maximizing the DA with respect to phase shifts and signal covariance matrices. Numerical results will show that the DA is tight and our proposed method can effectively mitigate the performance loss induced by channel rank deficiency.

IRS-aided MIMO Systems over Double-scattering Channels: Impact of Channel Rank Deficiency