  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 multiple targets and multiple users exist. However,
multiple targets detection introduces new challenges, since the STAR-RIS cannot
directly send sensing beams and detect targets, the dual-functional base
station (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 impossible to distinguish them. To address
the issue, we first introduce the signature sequence (SS) modulation scheme to
the ISAC system, and thus, the DFBS can detect different targets by the
SS-modulated sensing beams. Next, via the joint beamforming design of DFBS and
STAR-RIS, we develop a maxmin sensing beam pattern gain problem, and meanwhile,
considering the communication quality requirements, the interference
limitations of other targets and users, 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 quadratic semidefinite program subproblems and decouple the coupled
variables. Drawing on mathematical transformation, semidefinite programming, as
well as semidefinite relaxation techniques, these two subproblems are
iteratively sloved until convergence, and the ultimate solutions are obtained.
Finally, simulation results are conducted to validate the benefits and
efficiency of our proposed scheme.
