Equivalent Degrees of Freedom Based Secrecy Outage Analysis for Fluid Antenna Wiretap Channels

Abstract: Fluid antenna systems (FAS) improve wireless reliability by selecting the strongest port within a compact aperture, but the same port- selection capability also changes the physical-layer security behavior of a wiretap channel. Exact secrecy outage analysis is difficult because the legitimate and eavesdropping links each contain many spatially correlated ports, leading to high-dimensional joint distributions. This paper de⁃ velops a closed-form secrecy outage framework for FAS wiretap channels using the equivalent degrees of freedom (EDoF) principle. Under the Jakes spatial correlation model, the many correlated physical ports are represented by a much smaller set of aperture-limited dominant spatial modes. The resulting model converts the correlated wiretap channel into a tractable competition between the effective selection branches avail ⁃ able to Bob and Eve. An eigenvalue-weighted refinement further captures unequal dominant-mode powers. Closed-form and asymptotic results reveal how Bob’s aperture determines secrecy diversity, how Eve’s aperture strengthens the eavesdropping link, and why proportional Bob-Eve signal-to-noise ratio scaling produces a nonzero secrecy outage floor. Numerical simulations verify the analytical trends and show that the deci⁃ sive security resource is Bob’s aperture-induced EDoF advantage rather than the raw number of selectable ports.

Keywords: equivalent degrees of freedom; fluid antenna system; physical-layer security; secrecy outage probability; wiretap channel