Intelligent Reflecting Surface Enabled Sensing: Cram\'er-Rao Lower Bound Optimization

This paper 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 in its NLoS region. It is assumed that the AP is equipped with multiple antennas and the IRS is equipped with a uniform linear array. The AP aims to estimate the target's direction-of-arrival (DoA) with respect to the IRS, 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 Cram\'er-Rao lower bound (CRLB) on estimation error. Towards this end, we first obtain the CRLB expression for estimating the DoA in closed form. Next, we optimize the joint beamforming design to minimize the CRLB, via alternating optimization, semi-definite relaxation, and successive convex approximation. Numerical results show that the proposed design based on CRLB minimization achieves improved sensing performance in terms of mean squared error, as compared to the traditional schemes with signal-to-noise ratio maximization and separate beamforming.