Joint Design for STAR-RIS Aided ISAC: Decoupling or Learning

Integrated sensing and communication (ISAC) technology effectively enables spectrum and hardware sharing between radar and communication. Moreover, ISAC outperforms traditional separate radar and communication systems in terms of both power consumption and spectral efficiency. This paper investigates the dual-functional (DF) constant modulus waveform design for simultaneously transmitting and reconfigurable intelligent surface (STAR-RIS)-aided ISAC. To investigate the performance trade-off, the weighted sum of multi-user interference (MUI) energy and waveform discrepancies is minimized via jointly optimizing the transmit waveform and the reflection and transmission coefficient matrices at STAR-RIS. Furthermore, both cases of independent and coupled phase shifts at STAR-RIS are investigated. For independent phase shifts, we develop an alternating direction method of multipliers (ADMM)-based algorithm to decouple the original problem into several tractable subproblems that facilitates the derivation of a closed-form solution to each subproblem. In the scenario with the coupled phase shifts, we first formulate the optimization problem as a Markov decision process, employing a twin delayed deep deterministic policy gradient (TD3)-based deep reinforcement learning approach to address it. Simulation results verify the effectiveness of the proposed schemes, demonstrating STAR-RIS's superiority over conventional RIS. Moreover, the adopted protocol of STAR-RIS can maintain an excellent balance between performance and complexity.