Enhancing MIMO Covert Communications via Intelligent Reflecting Surface

Abstract

This letter investigates the multi-input multi-output (MIMO) covert communication aided by intelligent reflecting surface (IRS) against a multi-antenna warden. We establish a design framework for IRS-assisted MIMO covert communication system, which aims to maximize covert rate by jointly optimizing the transmit covariance matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {R}$ </tex-math></inline-formula> at transmitter and phase shift matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {Q}$ </tex-math></inline-formula> at IRS. Due to the unit modulus constraint of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {Q}$ </tex-math></inline-formula> and the highly coupling of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {R}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {Q}$ </tex-math></inline-formula> , we propose an alternating optimization algorithm to solve it. Specifically, the sub-problem of optimizing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {R}$ </tex-math></inline-formula> for given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {Q}$ </tex-math></inline-formula> is convex, and we can derive a closed-form solution. Then, we propose a minorization-maximization algorithm to tackle the sub-problem of optimizing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {Q}$ </tex-math></inline-formula> for fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {R}$ </tex-math></inline-formula> , where we translate the problem to the maximization of a proper lower bound of the objective function which is then solved by the sequential rank-one constraint relaxation algorithm. Simulation results demonstrate the effectiveness and superiority of the proposed algorithm in terms of boosting covert rate under the surveillance of a multi-antenna warden.