In this paper, we introduce an intelligent reflecting surface (IRS) to provide a programmable wireless environment for physical layer security. By adjusting the reflecting coefficients, the IRS can change the attenuation and scattering of the incident electromagnetic wave so that it can propagate in a desired way toward the intended receiver. Specifically, we consider a downlink multiple-input single-output (MISO) broadcast system where the base station (BS) transmits independent data streams to multiple legitimate receivers and keeps them secret from multiple eavesdroppers. By jointly optimizing the beamformers at the BS and reflecting coefficients at the IRS, we formulate a minimum-secrecy-rate maximization problem under various practical constraints on the reflecting coefficients. The constraints capture the scenarios of both continuous and discrete reflecting coefficients of the reflecting elements. Due to the non-convexity of the formulated problem, we propose an efficient algorithm based on the alternating optimization and the path-following algorithm to solve it in an iterative manner. Besides, we show that the proposed algorithm can converge to a local (global) optimum. Furthermore, we develop two suboptimal algorithms with some forms of closed-form solutions to reduce the computational complexity. Finally, the simulation results validate the advantages of the introduced IRS and the effectiveness of the proposed algorithms
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