Joint Beamforming Design for the STAR-RIS-Enabled ISAC Systems With Multiple Targets and Multiple Users

In this paper, the sensing beam pattern gain under simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS)-enabled integrated sensing and communications (ISAC) systems is investigated, in which the dual-functional base station (DFBS) provides multiple targets sensing in the presence of environment clutters and communicates with multiple users simultaneously. However, multiple targets detection introduces new challenges, since the STAR-RIS cannot directly send sensing beams and detect targets, the DFBS is required to analyze the echoes of the targets. While the echoes reflected by different targets through STAR-RIS come from the same direction for the DFBS, making it difficult to distinguish them. To circumvent this issue, we first introduce the signature sequence (SS) modulation scheme to the STAR-RIS-enabled ISAC system, thus ensuring that DFBS can detect different targets through the SS modulated sensing beams. Next, via the joint beamforming design of DFBS and STAR-RIS, we develop a max-min sensing beam pattern gain problem, and meanwhile, considering the communication quality requirements, the interference limitations of multi-targets and clutters, the passive nature constraint of STAR-RIS, and the total transmit power limitation. Then, to tackle the complex non-convex problem, we propose an alternating optimization method to divide it into two sub-problems and iteratively solve them until convergence. For the former, by relaxing the rank-one constraint, the problem is transformed into the standard convex quadratic semi-definite program and can be solved through the semi-definite relaxation and semi-definite programming algorithms. For the latter, the penalty-based algorithm is used to convert the rank-one constraints as penalty terms to the objective function, and the successive convex approximation method is leveraged to solve it. Finally, simulation results are conducted to validate the benefits and efficiency of our proposed scheme.