  In this paper, we consider a 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. The main
content is as follows: first, we propose a novel strategy for generating
artificial noise signals in the considered covert scenario. Then, we leverage
the statistical information of channel coefficients to optimize the basis
matrix of the artificial noise signals space in the absence of accurate channel
fading information between the friendly interference nodes and the legitimate
receiver. The optimization problem aims to design artificial noise signals
within the space to facilitate covert communication while minimizing the impact
on the performance of legitimate communication. Second, a customized Rimannian
Stochastic Variance Reduced Gradient (R-SVRG) algorithm is proposed to solve
the non-convex problem. In the algorithm, 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. Third, we
theoretically prove the convergence of the proposed algorithm to a stationary
point. In the end, we evaluate the performance of the proposed strategy for
generating artificial noise signals through numerical simulations. The results
demonstrate that our approach significantly outperforms the Gaussian artificial
noise strategy without optimization.
