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

Integrated sensing and communication (ISAC) technology has been considered as one of the key candidate technologies in the next-generation wireless communication systems. However, when radar and communication equipment coexist in the same system, i.e. radar-communication coexistence (RCC), the interference from communication systems to radar can be large and cannot be ignored. Recently, reconfigurable intelligent surface (RIS) has been introduced into RCC systems to reduce the interference. However, the "multiplicative fading" effect introduced by passive RIS limits its performance. To tackle this issue, 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 the penalty dual decomposition (PDD) framework. Specifically, we initially introduce auxiliary variables to reformulate the coupled variables into equation constraints and incorporate these constraints into the objective function through the PDD framework. Then, we decouple the equivalent problem into several subproblems by invoking the block coordinate descent (BCD) method. Furthermore, we employ the Lagrange dual method to alternately optimize these subproblems. Simulation results verify the effectiveness of the proposed algorithm. Furthermore, the results also show that under the same power budget, deploying double active RISs in RCC systems can achieve higher data rate than those with single active RIS and double passive RISs.