  Recently, intelligent reflecting surface (IRS) has emerged as an appealing
technique that enables wireless communications with low hardware cost and low
power consumption. In this letter, we consider an IRS-assisted point-to-point
multi-input multi-output (MIMO) system, where a source communicates with its
destination with the help of an IRS. Our goal is to maximize the spectral
efficiency of this system by jointly optimizing the (active) precoding at the
source and the (passive) phase shifters (PSs) at the IRS. However, this turns
out to be an intractable mixed integer non-convex optimization problem. To
circumvent the intractability, we propose a new sum-path-gain maximization
(SPGM) criterion to obtain a high-quality and efficient suboptimal solution to
this problem. Specifically, the PSs are first designed based on a simplified
optimization problem, which aims to maximize the sum-gains of the spatial paths
between the source and the destination. Then, a low-complexity alternating
direction method of multipliers (ADMM) algorithm is utilized to solve this
simplified problem. Finally, with the above obtained PSs, the source precoding
is derived by performing the singular value decomposition (SVD) on the
effective channel between the source and the destination. Numerical results
demonstrate that the proposed scheme can achieve near-optimal performance.
