FollowSpot: Enhancing Wireless Communications via Movable Ceiling-Mounted Metasurfaces

This paper studies the optimal placement of ceiling-mounted metasurfaces (MTSs) to help focus the wireless signal beam onto the target receiver, as inspired by the theatre spotlight. We assume that a total of $M$ MTSs are deployed, and that there are $L$ possible positions for each MTS. The resulting signal-to-noise (SNR) maximization problem is difficult to tackle directly because of the coupling between the placement decisions of the different MTSs. Mathematically, we are faced with a nonlinear discrete optimization problem with $L^M$ possible solutions. A remarkable result shown in this paper is that the above challenging problem can be efficiently solved within $O(ML^2\log(ML))$ time. There are two key steps in developing the proposed algorithm. First, we successfully decouple the placement variables of different MTSs by introducing a continuous auxiliary variable $\mu$; the discrete primal variables are now easy to optimize when $\mu$ is held fixed, but the optimization problem of $\mu$ is nonconvex. Second, we show that the optimization of continuous $\mu$ can be recast into a discrete optimization problem with only $LM$ possible solutions, so the optimal $\mu$ can now be readily obtained. Numerical results show that the proposed algorithm can not only guarantee a global optimum but also reach the optimal solution efficiently.