CRB Optimization for Intelligent Reflecting Surface-Assisted NLOS Wireless Sensing

In this paper, we investigate an intelligent reflecting surface (IRS)-assisted non-line-of-sight (NLOS) wireless sensing system, where an IRS aids an access point (AP) in estimating the parameters of a target in its NLOS region. The AP transmits signals and detects the target based on echoes propagating through the AP-IRS-target-IRS-AP channel. A key challenge in IRS-assisted NLOS sensing is the inherent scaling ambiguity, which arises when the degrees of freedom (DoFs) provided by the AP-IRS channel are insufficient to uniquely estimate both the complex path gain and angular parameters of the target. To address this issue, we introduce a two-stage sensing scheme that leverages the diversity of the IRS illumination pattern. Within this framework, we derive a compact Cramér-Rao Bound (CRB) expression for direction-of-arrival (DOA) estimation, enabling the decoupled optimization of the AP’s transmit beamformer and IRS phase shifts via CRB minimization. Specifically, the optimal beamformer is obtained in a closed form, while the IRS reflective coefficients are optimized using a majorization-minimization (MM)-based algorithm. Simulation results demonstrate the superiority of the proposed method, achieving lower CRB and MSE compared to benchmark schemes, particularly in challenging scenarios where the AP-IRS channel DoFs are insufficient to resolve the scaling ambiguity.