Beamforming Optimization for RIS-Assisted RF Sensing in Multipath NLOS Environments

Reconfigurable intelligent surfaces (RIS) have emerged as a key technology for enhancing radar performance, particularly in nonline-of-sight RF sensing. This letter investigates joint transmit and RIS beamforming for RIS-assisted radar in multipath environments, considering both amplitude-phase RIS (AP-RIS) and phase-only RIS (P-RIS). To efficiently optimize RIS configurations, we develop a projection gradient method for AP-RIS and a manifold gradient descent approach for P-RIS, both significantly reducing computational complexity. We also analyze detection performance metrics, including false alarm and detection probabilities, providing a theoretical foundation for system evaluation. Simulation results demonstrate that AP-RIS improves detection performance by leveraging amplitude-phase control to optimize indirect paths, while P-RIS achieves performance gains through optimized phase shifts, despite its unit-modulus constraint. Both schemes significantly outperform the conventional method that neglects indirect paths in strong multipath environments.