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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 at transmitter and phase shift matrix at IRS. Due to the unit modulus constraint of and the highly coupling of and , we propose an alternating optimization algorithm to solve it. Specifically, the sub-problem of optimizing for given is convex, and we can derive a closed-form solution. Then, we propose a minorization-maximization algorithm to tackle the sub-problem of optimizing for fixed , 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.

A closed-form full-rank solution for an optimal transmit covariance matrix over a strictly degraded MIMO wiretap channel and its secrecy capacity are obtained under an interference constraint, in addition to the transmit power constraint. A number of its properties are pointed out. The regimes when one of the constraints is inactive are studied. The interference constraint affects significantly the optimal covariance and induces its new properties, which cannot be found under the total transmit power constraint only.