Integrated Beam Assignment Design for RIS-Assisted Sensing Based onFlow Shape Optimization

Introduction: The rapid advancement of wireless technologies has led to the exploration of systems that integrate sensing and communication functionalities, with Reconfigurable Intelligent Surfaces (RIS) playing a key role in enhancing next-generation (6G) communication systems, particularly in Integrated Sensing and Communication (ISAC) systems. This paper investigates RIS-assisted ISAC systems and aims to address the non-convex optimisation problem associated with passive beamforming under manifold constraints. We propose a joint optimisation model to enhance both radar and communication performance, and we explore a novel alternating optimisation algorithm to solve this complex problem efficiently. Methods: This paper develops a joint optimization model for passive beamforming under manifold constraints to address the complexity of this non-convex optimization problem. An innovative alternating algorithm is proposed by leveraging the advantages of beamforming optimization to handle such non-convex constraints. This algorithm decomposes the original problem into manageable subproblems and solves them optimally for both the signal matrix and the phase-shift matrix within an alternating optimization framework. In the optimization of the phase-shift matrix, we apply the Riemannian trust-region method along with the penalty function approach. Furthermore, we investigate the trade-off between radar and communication performance in two distinct operational modes, namely strict and trade-off modes. Results: The integration of RIS into ISAC systems markedly enhances communication quality and service. In particular, the trade-off mode yields higher communication rates, and the resulting beamforming pattern more closely aligns with the desired configuration. Moreover, simulation results show that at an SNR of 10 dB, the AO-RTR trade-off scheme with p=0.2 achieves a sum rate of approximately 14 bit/s/Hz. This represents a significant increase in the communication rate compared to the scenario without RIS assistance. Conclusion: The study underscores the potential advantages of integrating RIS into ISAC systems for next-generation 6G wireless technologies. By proposing a joint optimization model and an alternating optimization algorithm, this work offers an effective solution to the nonconvex optimization challenges associated with passive beamforming under manifold constraints.