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. First, 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. Next, we consider capacity maximization for
broadband transmission in a general MIMO orthogonal frequency division
multiplexing (OFDM) system under frequency-selective fading channels, where
transmit covariance matrices can be optimized for different subcarriers while
only one common set of IRS reflection coefficients can be designed to cater to
all subcarriers. To tackle this more challenging problem, we propose a new
alternating optimization algorithm based on convex relaxation to find a
high-quality suboptimal solution. Numerical results show that our proposed
algorithms achieve substantially increased capacity compared to traditional
MIMO channels without the IRS, and also outperform various benchmark schemes.
In particular, it is shown that with the proposed algorithms, various key
parameters of the IRS-aided MIMO channel such as channel total power, rank, and
condition number can be significantly improved for capacity enhancement.

本文旨在研究和优化多输入多输出（MIMO）通信系统中，智能反射面（IRS）能够有效提高无线通信容量的最基本限制，提出了一种交替优化算法和基于凸松弛的交替优化算法以达到局部最优解和高质量的次优解。结果表明，相较于传统 MIMO 信道， IRS 通道的关键参数可以被显著地提高以获得更高的容量增长。