Analysis and Optimization of Multi-RIS-Assisted Dual-Functional Radar-Communication Systems via Free Probability Theory

Dual-functional radar-communication (DFRC) has been widely concerned in future communication systems. By aggregating communication and detection resources, DFRC enables improved communication data rate as well as continual real-time sensing capability. However, the spectral efficiency of the communication channel will be inevitably compromised since the transceiver design has to take into account both of the communication and radar oriented beampatterns. In this paper, the reconfigurable intelligent surface (RIS) panels are deployed to assist the design of multi-antenna DFRC transceivers, where the RIS panels introduce additional degree-of-freedom to accommodate the dual-functional beampattern. First, applying the operator-valued free probability theory, we derive the closedform expression of the asymptotic achievable rate of the multi-RIS-assisted MIMO DFRC systems in presence of general Rician fading. Then, we propose an alternating optimization (AO) algorithm to jointly optimize the transmit signals of the DFRC transmitter and the phase shifts of the reflecting elements of the RIS panels, which achieves an optimal tradeoff between the achievable rate and the desired radar beampattern. Simulation results verify the accuracy of the asymptotic expression of the achievable rate. In addition, the deployment of RISs and the proposed AO algorithm are proven to improve both the detection and communication performance.