Joint Beamforming Design for STAR-RIS Enabled ISAC System With Statistical CSI

In this paper, we investigate a simultaneously transmitting and reflecting reconfigurable intelligent surface (STARRIS) enabled integrated sensing and communications (ISAC) system in which the dual-functional base station (BS) communicates with a multi-antenna user and detects a non-cooperative target simultaneously by transmitting joint signals containing communication information and dedicated sensing waveform. Our objective is to maximize the achievable ergodic rate within the constraints of transmit power and sensing signal-to-clutter-plusnoise ratio (SCNR) by jointly designing the transmit covariance matrices at the BS and the transmission and reflection phase shift matrices for the STAR-RIS based on only statistical channel state information (CSI). Firstly, we prove that the dedicated sensing waveforms do not provide any additional gains from the SCNR perspective and derive the asymptotic sensing SCNR and the asymptotic achievable ergodic rate in large-system regime, based on which the optimization problem is reconstructed. Subsequently, the closed-form optimal covariance matrix for the communication signal is derived by using the modified waterfilling algorithm, and the transmission and reflection phase shift matrices for the STAR-RIS are obtained through the projected gradient ascent algorithm. Finally, an alternating optimization framework is proposed to obtain the covariance matrix for the communication signal and the transmission and reflection phase shift matrices for the STAR-RIS. Numerical results are conducted to verify the effectiveness of the proposed method and demonstrate the performance trade-off between the achievable ergodic rate and the sensing SCNR.