A Fast Iterative Shrinkage Thresholding Algorithm for Min-Max Secrecy Outage Probability Optimization in IRS-Assisted Uplink Systems

This paper investigates a fairness optimization problem of physical layer security (PLS) in an intelligent reflecting surface (IRS) assisted multi-user uplink communication system. Due to the lack of eavesdroppers' instantaneous channel state information (CSI), we adopt secrecy outage probability (SOP) as a security performance metric, for which a min-max SOP minimization problem is formulated. To solve this problem efficiently, an alternating optimization (AO) scheme is proposed, which combines smoothing techniques with a fast iterative shrinkage thresholding algorithm (FISTA) to alternately optimize receive beamforming vectors and IRS phase shift matrix. Compared to conventional semidefinite relaxation (SDR) method, the proposed scheme reduces computational overhead significantly. Simulation results confirm that it not only achieves a significantly lower SOP but also improves computational efficiency substantially.