Countering Collaborative Eavesdroppers Under Imperfect CSI: Outage Probability Constraint Transformation and Zeroth-Order Optimization

This paper addresses the challenge of secure transmission in wireless networks in the presence of intelligent collaborative eavesdroppers and when the knowledge of eavesdroppers' channel state information (CSI) is imperfect. The secure outage probability (SOP) constraint, which involves a complex summation of signal-to-interference-plus-noise ratios (SINRs), is transformed into a deterministic form using an asymptotic expression. However, the deterministic SOP expression still poses challenges in optimization. To this end, a penalty-based stochastic zeroth-order (ZO) optimization method is proposed. Additionally, an accelerated algorithm combining ZO and manifold optimization is developed to enhance convergence and ensure solution quality. The proposed algorithms are applicable to scenarios with or without artificial noise (AN) and to both single-cell or cell-free systems, enabling multiple scenarios to be handled under a general framework. Simulation results demonstrate that the proposed methods outperform existing algorithms across various network settings. The study also reveals that cell-free systems offer superior security compared to single-cell systems, highlighting the importance of spatial diversity in countering collaborative eavesdroppers.