Design of Artificial Interference Signals for Covert Communication Aided by Multiple Friendly Nodes

In this paper, we consider the scenario of covert communication aided by multiple friendly interference nodes. The objective is to conceal the legitimate communication link under the surveillance of a warden. We propose a novel strategy for generating artificial noise signals. In the absence of accurate channel fading information between the friendly interference nodes and the legitimate receiver, we leverage the statistical information of channel coefficients to optimize the basis matrix of the artificial noise signals space. The optimization aims to design artificial noise signals within the space to facilitate covert communication while minimizing the impact on the performance of legitimate communication. Due to the non-convex nature of the basis matrix constraints, the optimization problem is challenging to solve. Therefore, we employ the Riemannian optimization framework to analyze the geometric structure of the basis matrix constraints and transform the original non-convex optimization problem into an unconstrained problem on the complex Stiefel manifold for solution. Specifically, we utilize the Riemannian Stochastic Variance Reduced Gradient (R-SVRG) algorithm on the complex Stiefel manifold to solve the problem, significantly reducing the computational burden per iteration compared to full gradient algorithms. Additionally, we theoretically prove the convergence of the proposed algorithm to a stationary point. Finally, the performance of the proposed artificial noise strategy can be evaluated through numerical simulations, and compared to the Gaussian artificial noise strategy without optimization, the proposed strategy significantly improves covert performance.