Beamforming optimization of meta-learning algorithm based on gradient descent in RIS-assisted ISAC system

Abstract

In this paper, we study an integrated sensing and communication (ISAC) system assisted by reconfigurable intelligent surface (RIS). Our goal is to minimize the transmit power of the BS by jointly optimizing the active beamforming and the passive beamforming under the constraints of the signal-to-interference-plus-noise ratio (SINR) of users, the Cramer–Rao bound (CRB) of sensing and the unit-modulus of RIS reflection elements. The optimization problem is difficult to solve because the objective function is non-convex and the variables are coupled. In addition, a large number of base station (BS) antennas lead to high-dimensional transmit beamforming vectors. We first prove that the optimization variables in the optimization problem are low-dimensional coefficient matrices and passive beamforming, rather than active and passive beamforming, which reduces the complexity compared with the original problem. In addition, when the sensing channel space belongs to the communication channel space, the dedicated sensing signal is not needed. Inspired by the meta-learning technology that can solve non-convex problems, we propose a meta-learning algorithm based on gradient descent (MLAGD) to design beamforming, which tends to learn dynamic optimization strategies and iteratively update optimization variables. Specifically, we first introduce Lagrangian multipliers to transform the constrained optimization problem into the Lagrangian dual domain, and the manifold-based optimization is employed to handle the unit-modulus constraint. The meta-learning neural networks are constructed to update optimization variables through local loss function, and then network parameters are updated through global loss function. The numerical results show the effectiveness of the algorithm.