Joint Beamforming Design for Double Active RIS-assisted Radar-Communication Coexistence

In this paper, we consider a double active RIS-assisted RCC system, which focuses on the design of the radar’s beamforming vector and the active RISs’ reflecting coefficient matrices, to maximize the achievable data rate of the communication system. The considered system needs to meet the radar detection constraint and the power budgets at the radar and the RISs. Since the problem is non-convex, we propose an algorithm based on penalty dual decomposition (PDD) framework. Specifically, we initially introduce auxiliary variables to reformulate the coupled variables into equation constraints and incorporating these constraints into the objective function through the PDD framework. Then, we decouple the equivalent problem into several subproblems by invoking block coordinate descent (BCD) method. Furthermore, we employ the Lagrange dual method to alternately optimize these subproblems. Simulation results verify that under the same power budget, deploying double active RISs in RCC system can achieve higher system performance compared with single active RIS and double passive RISs.