Intelligent Reflecting Surface: Joint Optimal Training Sequence and Refection Pattern

We investigate channel estimation for an intelligent reflecting surface (IRS) aided wireless communication system with a multi-antenna access point (AP), an multi-element IRS, and a set of multiple users, each with a single antenna. Our goal is to minimize mean square error (MSE) of estimating the channels of direct and cascaded links from the AP to each user via the IRS elements by jointly optimizing the training sequence of the AP and reflection pattern of the IRS. To solve this challenging problem, we first find the joint optimal structure and reflection pattern for the training sequence, and then, we convert the problem into a convex form to design the optimal training sequence efficiently. To reduce the computational complexity, we also propose a suboptimal training sequence in closed form. Numerical results show that the proposed scheme outperforms baseline schemes.