  Reconfigurable intelligent surfaces (RISs) have emerged as a prospective
technology for next-generation wireless networks due to their potential in
coverage and capacity enhancement. Previous works on achievable rate analysis
of RIS-assisted communication systems have mainly focused on the
rich-scattering environment where Rayleigh and Rician channel models can be
applied. This work studies the ergodic achievable rate of RIS-assisted
multiple-input multiple-output communication systems in millimeter-wave band
with limited scattering under the Saleh-Valenzuela channel model. Firstly, we
derive an upper bound of the ergodic achievable rate by means of majorization
theory and Jensen's inequality. The upper bound shows that the ergodic
achievable rate increases logarithmically with the number of antennas at the
base station (BS) and user, the number of the reflection units at the RIS, and
the eigenvalues of the steering matrices associated with the BS, user and RIS.
Then, we aim to maximize the ergodic achievable rate by jointly optimizing the
transmit covariance matrix at the BS and the reflection coefficients at the
RIS. Specifically, the transmit covariance matrix is optimized by the
water-filling algorithm and the reflection coefficients are optimized using the
Riemannian conjugate gradient algorithm. Simulation results validate the
effectiveness of the proposed optimization algorithms.
