Robust Resource Allocation for RIS-Aided Multi-User SLAC System

This paper considers a reconfigurable intelligent surface (RIS)-aided multi-user simultaneous localization and communication (SLAC) system with statistical position uncertainty, where an RIS is deployed to simultaneously enhance the quality of service. To this end, we first derive the closed-form Cramér-Rao lower bound concerning position parameters as the localization metric and also provide the achievable rate metric for communication services. Then, the joint robust design of subcarrier groups, beamforming vectors, and the phase-shift matrix of the RIS is formulated as a stochastic bi-objective optimization problem to maximize expected localization and communication metrics. Due to the nonlinearity of the multi-objective function and the coupling between optimizing variables, the resulting problem is highly non-convex. Accordingly, we transform the expected achievable rate into an analytical form and further develop a novel unified successive convex approximation (U-SCA)-based iterative algorithm to obtain a robust resource allocation strategy. In particular, we derive closed-form solutions of beamforming vectors and the phase-shift matrix of RIS to decrease the computational complexity. In addition, we also analyse the convergence of the proposed U-SCA-based algorithm. Simulation results demonstrate the effectiveness of the presented method.