Active-Passive Beamforming Optimization for RIS-Aided mmWave Joint Localization and Communication System

With the remarkable development of the location-aware communications, joint localization and communication (L&C) has become one of the strongest competitors for the 6G key enabling technologies. Meanwhile, the reconfigurable intelligent surface (RIS) has emerged as an important enhancing technology for both communication and localization. In this paper, we investigate a RIS-aided joint L&C system, where the localization and data transmission functions are integrated in a time-division pattern. Specifically, we aim to jointly optimize the covariance matrices of the localization signal and the communication signal, the RIS beamforming matrix and the time division ratio to simultaneously improve the localization and communication performance. An alternating optimization (AO) algorithm is proposed via jointly leveraging the successive convex approximation technique, the semidefinite relaxation method and the projected gradient descent with momentum algorithm, based on which we strike a compelling trade-off between the localization and communication performance. Considering the high computational cost in the large-scale array scenario, we also develop a low-complexity algorithm free of iterations. To analyze the optimality of our proposed AO algorithm, we further consider the special single-user line-of-sight (LoS) scenario and validate that our AO algorithm could achieve the beam alignment, implying its effectiveness. Finally, numerical simulations are carried out to demonstrate the superior performance of our proposed algorithm.