Joint design of transmit waveform and passive beamforming for RIS-assisted ISAC system

The joint design of the transmit waveform and passive beamforming is the key issue in the reconfigurable intelligent surface (RIS) assisted integrated sensing and communication (ISAC) systems. The existing methods are the joint waveform design without RIS or the sensing-first joint waveform design with RIS. Different from these methods, the fair sensing-communication joint waveform design with RIS is studied in this paper. For this purpose, we simultaneously optimize the waveform and RIS phase shifts to maximize the sensing Signal-to-Interference-and-Noise-Ratio (SINR) and minimize the communication Multiple User Interference (MUI). Due to the constant modulus (CM) constraint and the fractional programming form of the SINR expression, the resulted optimization problem is hard to solve. To address these issues, an Alternating Gradient-descent on Riemannian Manifold (AGRM) method is proposed. First, a dinkelbatch-GRM algorithm is derived to maximize SINR, by fixing the RIS phase shifts. Then, a GRM algorithm is given to mitigate MUI, while fixing the waveform. Finally, the overall AGRM algorithm is presented to solve the original problem. Simulation results show that the communication achievable rate and the sensing SINR of the proposed method are 2.33 bits/s/Hz and 5.6 dB higher than [17] and [30,31].