  This work considers a dual-functional radar and communication (DFRC) system
with an active reconfigurable intelligent surface (RIS) and a potential
eavesdropper. Our purpose is to maximize the secrecy rate (SR) of the system by
jointly designing the beamforming matrix at the DFRC base station (BS) and the
reflecting coefficients at the active RIS, subject to the
signal-to-interference-plus-noise-ratio (SINR) constraint of the radar echo and
the power consumption constraints at the DFRC-BS and active RIS. An alternating
optimization (AO) algorithm based on semi-definite relaxation (SDR) and
majorizationminimization (MM) is applied to solve the SR-maximization problem
by alternately optimizing the beamforming matrix and the reflecting
coefficients. Specifically, we first apply the SDR and successive convex
approximation (SCA) methods to transform the two subproblems into more
tractable forms, then the MM method is applied to derive a concave surrogate
function and iteratively solve the subproblems. Finally, simulation results
indicate that the active RIS can better confront the impact of "multiplicative
fading" and outperforms traditional passive RIS in terms of both secure data
rate and radar sensing performance.
