Design of Spatial-Slow-Time Constant-Modulus Waveform Transmission and Receive Adaptive Filter for Dual-Function Radar Communications with Reconfigurable Intelligent Surface

We study the problem of jointly designing spatial-slow-time unimodular waveforms and receive adaptive filter for dual-function radar communications with reconfigurable intelligent surface (RIS), which aims to mitigate interference for radar and meanwhile to transfer accurate symbols for communications. Hence, we maximize the signal-to-interference-plus-noise ratio at the radar receiver via devising a joint optimization of the waveform transmission, receive filter, and phase control of the RIS, wherein we enforce mean square error based constraints for communications. A non-convex optimization problem is therefore formulated. To solve it, we choose a cyclic manner that transforms the formulated design into sub optimization problems. In particular, we exploit majorization-minimization techniques followed by the consensus alternating direction method of multipliers for finding solutions to these sub problems. Therein lies a set of properly elaborated surrogate and Lagrangian functions, which finally lead to closed-form expressions for iterations. Simulation results verify the superiority of our proposed algorithm in terms of different aspects.