  In this paper, we propose intelligent reflecting surfaces (IRS) assisted
secure wireless communications with multi-input and multi-output antennas
(IRS-MIMOME). The considered scenario is an access point (AP) equipped with
multiple antennas communicates with a multi-antenna enabled legitimate user in
the downlink at the present of an eavesdropper configured with multiple
antennas. Particularly, the joint optimization of the transmit covariance
matrix at the AP and the reflecting coefficients at the IRS to maximize the
secrecy rate for the IRS-MIMOME system is investigated, with two different
assumptions on the phase shifting capabilities at the IRS, i.e., the IRS has
the continuous reflecting coefficients and the IRS has the discrete reflecting
coefficients. For the former case, due to the non-convexity of the formulated
problem, an alternating optimization (AO)-based algorithm is proposed, i.e.,
for given the reflecting coefficients at the IRS, the successive convex
approximation (SCA)-based algorithm is used to solve the transmit covariance
matrix optimization, while given the transmit covariance matrix at the AP,
alternative optimization is used again in individually optimizing of each
reflecting coefficient at the IRS with other fixed reflecting coefficients. For
the individual reflecting coefficient optimization, the close-form or an
interval of the optimal solution is provided. Then, the proposed algorithm is
extended to the discrete reflecting coefficient model at the IRS. Finally, some
numerical simulations have been done to demonstrate that the proposed algorithm
outperforms other benchmark schemes.
