FollowSpot: Enhancing Wireless Communications via Movable Ceiling-Mounted Metasurfaces

Abstract

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 $μ$; the discrete primal variables are now easy to optimize when $μ$ is held fixed, but the optimization problem of $μ$ is nonconvex. Second, we show that the optimization of continuous $μ$ can be recast into a discrete optimization problem with only $LM$ possible solutions, so the optimal $μ$ 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.

Figures (13)

• Figure 1: Resembling the theatre spotlight, the FollowSpot scheme aims to project the signal beam onto the target receiver (which is the actuator in our case) by placing multiple MTSs properly.
• Figure 2: In this example, the ceiling is divided into multiple square zones. Each MTS can move around within its zone; each small square area of the zone represents a possible position of the MTS, and the current position of each MTS is highlighted in red. For instance, for a particular MTS $m$, its four possible positions are indexed by $\{1,2,3,4\}$, and it is currently placed at position $3$. This model is considered later in simulations in Section \ref{['sec:simulation']}.
• Figure 3: Illustration of the proposed algorithm. Consider two MTSs each with 2 possible positions. (a): The optimal position of MTS 1 depends on the unit vector $\mu$; if $\mu$ lies in the yellow sector, $h_{1,2}$ leads to a larger $f(\bm{X})$ so we should place MTS 1 at position 2; if $\mu$ lies in the purple sector, $h_{1,1}$ is better so we should place MTS 1 at position 1. (b): Similarly, if $\mu$ lies in the blue sector, we should place MTS 2 at position 1; if $\mu$ lies in the green sector, we should place MTS 2 at position 2. (c): Now we combine the sectorizations of MTSs 1 and 2 to obtain a total of 4 sectors; we just try out each sector for $\mu$ to see which yields the largest $f(\bm{X})$, thereby obtaining the global optimum. Most importantly, for the general case, the total number of sectors after combination is $O(ML)$, so the proposed algorithm is scalable.
• Figure 4: Illustration of the "fake" transition point. Recall that the optimal positions depend on which sector $\mu$ lies in. The sectors are formed by a set of straight-line cuts. Each cut passes through the origin and intersects with the unit circle at two positions; an intersection is referred to as a transition point if the optimal position of MTS changes when $\mu$ passes through it. (a): When $L=2$, there is one straight-line cut, and the two intersections are both transition points. (b): When $L=3$, there are three straight-line cuts and hence six intersections; however, three intersections (marked in gray) are between two sectors that lead to the same optimal position of MTS 1, so the optimal position does not change when $\mu$ passes through any of them; these gray intersections are referred to as "fake" transition points. (c): When $L=4$, there are six straight-line cuts and thus twelve intersections; observe that nine of them are fake transition points. For the general case, there are $ML(L-1)/2$ straight-line cuts and $ML(L-1)$ intersections, but the number of fake transition points depends on the specific case.
• Figure 5: SNR boost vs. the number of MTSs $M$.

Theorems & Definitions (3)

• Remark 1
• Theorem 1
• Remark 2