Ergodic Capacity Maximization of RIS-assisted Millimeter-Wave MIMO-OFDM Communication Systems

Reconfigurable intelligent surface (RIS) has attracted extensive attentions in recent years. However, most research focuses on the scenario of the narrowband and/or instantaneous channel state information (CSI), while wide bandwidth with the use of millimeter-wave (mmWave) (including sub-THz) spectrum is a major trend in next-generation wireless communications, and statistical CSI is more practical to obtain in realistic systems. Thus, we fill the blank by looking at the ergodic capacity of RIS-assisted mmWave multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) communication systems. The widely used Saleh-Valenzuela channel model is adopted to characterize the mmWave channels and only the statistical CSI is available. We first derive the approximations of the ergodic capacity by means of the majorization theory and Jensen's inequality. Then, an alternating optimization based algorithm is proposed to maximize the ergodic capacity by jointly designing the transmit covariance matrix at the base station and the reflection coefficients at the RIS. Specifically, the design of the transmit covariance matrix is transformed into a power allocation problem and solved by spatial-frequency water-filling. The reflection coefficients are optimized by the Riemannian conjugate gradient algorithm. Simulation results corroborate the closeness of the derived ergodic capacity approximations and the effectiveness of the proposed algorithms.