Variable Block-Correlation Modeling and Optimization for Secrecy Analysis in Fluid Antenna Systems

Fluid antenna systems (FAS) are emerging as a transformative enabler for sixth-generation (6G) wireless communications, providing unprecedented spatial diversity through dynamic reconfiguration of antenna ports. However, the inherent spatial correlation among ports poses significant challenges for accurate analysis. Conventional models such as Jakes are analytically intractable, while oversimplified constant-correlation models fail to capture the true behavior. In this work, we address these challenges by applying the variable block-correlation model (VBCM) -- originally proposed by Ram\'{i}rez-Espinosa \textit{et al.} in 2024 -- to FAS security analysis, and by developing comprehensive optimization methods to enhance analytical accuracy. We derive new closed-form expressions for average secrecy capacity (ASC) and secrecy outage probability (SOP), demonstrating that the VBCM framework achieves simulation-aligned accuracy, with relative errors consistently below $5\%$ (compared to $10$--$15\%$ for constant-correlation models). To maximize ASC, we further design two algorithms: a grid search (GS) method and a gradient descent (GD) method. Numerical results reveal that the VBCM-based approach not only provides reliable insights into FAS security performance, but also yields substantial gains -- ASC improvements exceeding $120\%$ in high-threat scenarios and $18$--$19\%$ performance enhancements for compact antenna configurations. These findings underscore the practical value of integrating VBCM into FAS security analysis and optimization, establishing it as a powerful tool for advancing 6G communication systems.