  In this paper, we investigate the design of secure transmission frameworks
with an intelligent reflecting surface (IRS). Our design aims to minimize the
system energy consumption in cases of rank-one and full-rank access point
(AP)-IRS links. To facilitate the design, the problem is divided into two
parts: design of beamforming vector at AP and phase shift at IRS. In the
rank-one channel model, the beamforming vector design and phase shift design
are independent. A closed-form expression of beamforming vector is derived.
Meanwhile, some algorithms, including the semidefinite relaxation algorithm and
projected gradient algorithm, are taken to solve the phase shift problem in the
case of instantaneous channel, and in the statistical channel model, the impact
of phase shift on the overall system is analyzed. However, since beamforming
and phase shift depend on each other in the full-rank model, we refer to
conventional wiretap model and utilize an eigenvalue-based algorithm to obtain
beamforming vector, while the aforementioned two phase optimization schemes are
also applied. Simulation results show that the IRS-enhanced system is
envisioned to improve physical layer security.
