Intelligent Reflecting Surface Enabled Sensing: Cramér-Rao Bound Optimization

• Published in: IEEE transactions on signal processing Vol. 71; pp. 2011 - 2026
• Main Authors: Song, Xianxin, Xu, Jie, Liu, Fan, Han, Tony Xiao, Eldar, Yonina C.
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Array signal processing; Beamforming; Closed form solutions; Cramer-Rao bounds; Cramér-Rao bound; Design optimization; Direction of arrival; Direction-of-arrival estimation; Estimation; Exact solutions; Intelligent reflecting surface; joint transmit and reflective beamforming; Linear arrays; Mathematical analysis; Matrices (mathematics); non-line-of-sight wireless sensing; Optimization; Reconfigurable intelligent surfaces; Sensors; Signal to noise ratio; Wireless communication; Wireless sensor networks
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2023.3280715

This article investigates intelligent reflecting surface (IRS) enabled non-line-of-sight (NLoS) wireless sensing, in which an IRS is deployed to assist an access point (AP) to sense a target at its NLoS region. It is assumed that the AP is equipped with multiple antennas and the IRS is equipped with a uniform linear array. We consider two types of target models, namely the point and extended targets, for which the AP aims to estimate the targets direction-of-arrival (DoA) and the target response matrix with respect to the IRS, respectively, based on the echo signals from the AP-IRS-target-IRS-AP link. Under this setup, we jointly design the transmit beamforming at the AP and the reflective beamforming at the IRS to minimize the Cramér-Rao bound (CRB) on the estimation error. Towards this end, we first obtain the CRB expressions in closed form. It is shown that for the point target, the CRB for estimating the DoA depends on both the transmit and reflective beamformers; while for the extended target, the CRB for estimating the target response matrix only depends on the transmit beamformers. Next, we optimize the joint beamforming design to minimize the CRB for the point target via alternating optimization, semi-definite relaxation, and successive convex approximation. We also obtain the optimal transmit beamforming solution in closed form to minimize the CRB for the extended target. Numerical results show that for both cases, the proposed designs based on CRB minimization achieve improved sensing performances than other traditional schemes.