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Enormous Fluid Antenna Systems (E-FAS) under Correlated Surface-Wave Leakage: Physical Layer Security

Farshad Rostami Ghadi, Kai-Kit Wong, Masoud Kaveh, Mohammad Javad Ahmadi, Kin-Fai Tong, Hyundong Shin

Abstract

Enormous fluid antenna systems (E-FAS) have recently emerged as a surface-wave (SW)-enabled architecture that can induce controllable large-scale channel gains through guided electromagnetic routing. This paper develops a secrecy analysis framework for E-FAS-assisted downlink transmission with practical pilot-based channel estimation. We consider a multiple-input single-output (MISO) wiretap setting in which the base station (BS) performs minimum mean-square-error (MMSE) channel estimation and adopts maximum-ratio transmission (MRT) with artificial noise (AN). To capture the leakage of SW routing in EFAS, we introduce a correlated SW-leakage model that accounts for statistical coupling between the legitimate and eavesdropper channels caused by partially overlapping SW propagation paths. Exploiting the two-timescale nature-with slowly varying routing gain and small-scale block fading, we then derive a closed-form conditional expression for the secrecy outage probability (SOP) and a tractable characterization of the ergodic secrecy rate (ESR) in the presence of correlated quadratic forms. Our analysis yields three key insights: (i) secrecy collapses at high transmit power if and only if AN is not present, whereas any strictly positive AN can prevent asymptotic collapse; (ii) the optimal data-AN power split is achieved by a strictly interior solution; and (iii) routing gain improves both the received signal strength and the channelestimation quality, creating a nonlinear coupling that raises the signal-to-interference plus noise ratio (SINR) ceiling in the high signal-to-noise ratio (SNR) regime, and disperses secrecy across routing states. Numerical results indicate that E-FAS markedly enlarges the secure operating region significantly when compared with conventional space-wave transmission.

Enormous Fluid Antenna Systems (E-FAS) under Correlated Surface-Wave Leakage: Physical Layer Security

Abstract

Enormous fluid antenna systems (E-FAS) have recently emerged as a surface-wave (SW)-enabled architecture that can induce controllable large-scale channel gains through guided electromagnetic routing. This paper develops a secrecy analysis framework for E-FAS-assisted downlink transmission with practical pilot-based channel estimation. We consider a multiple-input single-output (MISO) wiretap setting in which the base station (BS) performs minimum mean-square-error (MMSE) channel estimation and adopts maximum-ratio transmission (MRT) with artificial noise (AN). To capture the leakage of SW routing in EFAS, we introduce a correlated SW-leakage model that accounts for statistical coupling between the legitimate and eavesdropper channels caused by partially overlapping SW propagation paths. Exploiting the two-timescale nature-with slowly varying routing gain and small-scale block fading, we then derive a closed-form conditional expression for the secrecy outage probability (SOP) and a tractable characterization of the ergodic secrecy rate (ESR) in the presence of correlated quadratic forms. Our analysis yields three key insights: (i) secrecy collapses at high transmit power if and only if AN is not present, whereas any strictly positive AN can prevent asymptotic collapse; (ii) the optimal data-AN power split is achieved by a strictly interior solution; and (iii) routing gain improves both the received signal strength and the channelestimation quality, creating a nonlinear coupling that raises the signal-to-interference plus noise ratio (SINR) ceiling in the high signal-to-noise ratio (SNR) regime, and disperses secrecy across routing states. Numerical results indicate that E-FAS markedly enlarges the secure operating region significantly when compared with conventional space-wave transmission.

Paper Structure

This paper contains 31 sections, 5 theorems, 78 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Motivation and Contributions
  3. Secure System Model
  4. Two-Timescale Channel and Routing-Gain Randomness
  5. Eavesdropper Channel with SW Leakage Coupling
  6. Uncertainty Model for Eve's Large-Scale Gain
  7. Uplink Training and Estimation of Bob's Channel
  8. Downlink Signaling with AN
  9. Secrecy Metrics and Robust SOP
  10. Statistical Characterization of SINRs
  11. Legitimate SINR Under Imperfect CSI and AN
  12. Eavesdropper SINR Under SW Leakage Correlation
  13. Robust SOP Under Correlated Leakage
  14. Outage Event Reformulation
  15. Conditional SOP Representation
  16. ...and 16 more sections

Key Result

Corollary 1

If the leakage-induced conditional mean vanishes, i.e., $\mu_X = 0$ (equivalently, $\kappa = 0$), the Poisson mixture in eq:noncentral_pdf collapses to its zeroth-order term. In this case, the conditional PDF reduces to which yields a simplified single-sum integral for $\mathcal{G}(\hat{\mathbf h}_b,\beta_e)$.

Figures (9)

  • Figure 1: The E-FAS-assisted secure communication scenario.
  • Figure 2: Conditional CDF of the eavesdropper SINR under different channel correlation coefficients $\rho$.
  • Figure 3: Conditional PDF of the eavesdropper SINR under different channel correlation coefficients $\rho$.
  • Figure 4: SOP versus transmit power $P$ for E-FAS and No-FAS transmission under correlated ($\rho>0$) and independent ($\rho=0$) leakage conditions, with different AN power fractions $\theta_a$.
  • Figure 5: ESR versus transmit power $P$ for E-FAS and No-FAS transmission under correlated ($\rho>0$) and independent ($\rho=0$) leakage conditions, with different AN power fractions $\theta_a$.
  • ...and 4 more figures

Theorems & Definitions (11)

  • Remark 1: Statistical Coupling Between $\gamma_b$ and $\gamma_e$
  • Remark 2: Derivation Outline
  • Corollary 1: Conditionally Central Case
  • Proposition 1: Elimination of Secrecy Collapse
  • Corollary 2: Routing Increases Bob's Effective SINR Ceiling
  • proof
  • Lemma 1: Non-Triviality of the Interior Secrecy Region
  • proof
  • Proposition 2: Interior Optimal Power Split with Nonzero Optimum
  • proof
  • ...and 1 more