Submodular Optimization for Placement of Intelligent Reflecting Surfaces in Sensing Systems

Zahra Esmaeilbeig, Kumar Vijay Mishra, Arian Eamaz, Mojtaba Soltanalian

Abstract: Intelligent reflecting surfaces (IRS) are increasingly being investigated for novel sensing applications for improving target estimation and detection. While the optimization of IRS phase-shifts has been studied extensively, the optimal placement of multiple IRS platforms for sensing applications is relatively unexamined. In this paper, we focus on selecting optimized locations of IRS platforms by considering a mutual information (MI)-based criterion within the radar coverage area. We demonstrate the submodularity of the MI criterion and then tackle the design problem by means of a constant-factor approximation algorithm for submodular optimization. Numerical results validate the proposed submodular optimization framework for optimal IRS placement with the worst-case performance bounded to 1 - 1/ $e \approx$ 63%.