Joint Active and Passive Beamforming Design for the IRS-Assisted MIMOME-OFDM Secure Communications

The effective combination of physical layer security communication and intelligent reflecting surface (IRS) technology has recently attracted extensive attention to improve the system security. Unlike existing works that mostly focus on single-carrier systems, we consider an IRS-assisted multi-carrier MIMO wireless physical layer security communication system, which consists of a legitimate transmitter, a legitimate receiver, an IRS node and an eavesdropper. With the aim of maximizing the sum secrecy rate, the multi-carrier transmit beamforming and IRS reflecting coefficient matrix are jointly optimized under the constraints on the transmit power budget and unit modulus of IRS reflecting coefficients. Since the formulated problem is non-convex, an alternate optimization (AO) algorithm is proposed to deal with it. Specifically, for the given IRS reflecting coefficient matrix, the minorization-maximization (MM) scheme is adopted to approximate the objective function of the subproblem and following that, the closed-form solution of the multi-carrier transmit beamforming is obtained through the Lagrange multiplier method. Then, for the given multi-carrier beamforming, the IRS reflecting coefficient matrix is also optimized through the MM scheme and a suboptimal closed-form solution that satisfies the KKT conditions is derived. Moreover, the discussion is extended to the discrete IRS phase shift case and a heuristic projection method (HPM) is then proposed. Finally, the simulation results validate the effectiveness of the proposed AO based algorithm.