Submodular Optimization for Placement of Intelligent Reflecting Surfaces in Sensing Systems

Intelligent reflecting surfaces (IRS) and their optimal deployment are the new technological frontier in sensing applications. Recently, IRS have demonstrated potential in advancing target estimation and detection. While the optimal phase-shift of IRS for different tasks has been studied extensively in the literature, the optimal placement of multiple IRS platforms for sensing applications is less explored. In this paper, we design the placement of IRS platforms for sensing by maximizing the mutual information. In particular, we use this criterion to determine an approximately optimal placement of IRS platforms to illuminate an area where the target has a hypothetical presence. After demonstrating the submodularity of the mutual information criteria, we tackle the design problem by means of a constant-factor approximation algorithm for submodular optimization. Numerical results are presented to validate the proposed submodular optimization framework for optimal IRS placement with worst case performance bounded to $1-1/e\approx 63 \%$.