  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.
