Intelligent reflecting surface (IRS) is a promising solution to enhance the wireless communication capacity both cost-effectively and energy-efficiently, by properly altering the signal propagation via tuning a large number of passive reflecting units. In this paper, we aim to characterize the fundamental capacity limit of IRS-aided point-to-point multiple-input multiple-output (MIMO) communication systems with multi-antenna transmitter and receiver in general, by jointly optimizing the IRS reflection coefficients and the MIMO transmit covariance matrix. We consider narrowband transmission under frequency-flat fading channels, and develop an efficient alternating optimization algorithm to find a locally optimal solution by iteratively optimizing the transmit covariance matrix or one of the reflection coefficients with the others being fixed. Numerical results show that our proposed algorithm achieves substantially increased capacity compared to traditional MIMO channels without the IRS, and also outperforms various benchmark schemes.
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