PaperlayerView exact revision on arXiv

Source-linked AI summary

Covert Communications over Enormous Fluid Antenna Systems (E-FAS): Impact of Channel Hardening on Detection

Farshad Rostami Ghadi, Damoon Shahbaztabar, Kai-Kit Wong, Wei-Ping Zhu

arXiv:2609.34668v1cs.ITmath.IT

TL;DR

E-FAS propagation creates random channel-scale fluctuations that affect both a legitimate link and a passive warden’s ability to detect transmission. The paper models covert communication over this channel using an effective-mode representation and an energy-detector test. For finite observation intervals, finite-mode channels improve covertness relative to the fully hardened Rayleigh limit, while hardening has different effects at Bob and Willie.

  • Problem

    The paper asks how E-FAS channel-scale fluctuations and hardening affect covert communication, where a passive warden tries to distinguish transmission from its absence.

    Source: §I · p. 1

  • Method

    An equal-power effective-mode representation characterizes the channel-power distribution and supports an energy-detector test and covert-throughput analysis.

    Source: §I · p. 1, B. Effective Mode Representation · p. 2, E. Achievable Covert Throughput · p. 3

  • Results

    For the same average channel power, smaller mw yields larger minimum detection error; finite-mode covertness gains diminish as observation length N increases.

    Source: §IV · p. 4

  • Takeaways & Limitations

    Hardening can improve reliability at Bob, whereas retaining channel-scale fluctuations at Willie can improve finite-observation covertness.

    Source: F. Role of E-FAS Channel Hardening · p. 3, §IV · p. 4

Abstract

from arXiv · show

Enormous fluid antenna systems (E-FAS) enable guided surface wave (SW) propagation and induce an end-to-end channel that is conditionally complex Gaussian with a random covariance scale. This paper investigates the impact of this channel structure on covert communication in the presence of a passive warden. Under an equal power effective mode representation, the random channel scale follows a Gamma distribution, leading to a Bessel-K distribution for the effective channel power. We show that the optimal likelihood ratio test at the warden reduces to an energy detector and derive the corresponding false alarm and missed detection probabilities. These results are then used to characterize the achievable covert throughput under a prescribed detection error constraint. Numerical results show that, for finite observation intervals, finite mode E-FAS channels improve covertness relative to the fully hardened Rayleigh limit with the same average channel power. They further reveal an asymmetric role of channel hardening: stronger hardening can improve the legitimate link, whereas retaining channel scale fluctuations at the warden can enhance finite observation covertness.

I. INTRODUCTION

E-FAS creates a compound propagation channel whose random scale makes channel hardening relevant to both link reliability and detection by a passive warden. The paper studies covert transmission over this channel and models the route from surface excitation through guided-wave propagation to radiation toward Bob and Willie.

A. E-FAS Channel Model

  • Guided surface waves travel along structures before reradiating toward the receiver, producing a conditionally complex Gaussian channel with a random covariance scale.The scale fluctuations depend on the effective number of contributing radiation modes.Source: §I · p. 1, A. E-FAS Channel Model · p. 2

I. INTRODUCTION

  • E-FAS channel hardening has an asymmetric covert-communication tradeoff: more effective modes can improve Bob’s reliability, while retaining scale fluctuations at Willie can improve finite-observation covertness.The effective number of contributing modes governs scale fluctuations; Willie observes unintended radiation from the surface route configured for Bob.Source: §I · p. 1, A. E-FAS Channel Model · p. 2

II. SYSTEM MODEL

  • The system is an E-FAS-assisted downlink from an M-antenna transmitter to Bob, with Willie observing unintended radiation from the same configured surface aperture.Direct links to both terminals are assumed severely blocked, so the E-FAS-assisted component dominates.Source: §II · p. 1, A. E-FAS Channel Model · p. 2

A. E-FAS Channel Model

  • The channel model uses a calibrated transfer matrix for Bob’s configured route, with guided-wave propagation and surface reradiation, and includes terminal-specific radiation gain and distance factors.The radiation gain toward Willie describes unintended radiation, not a route intentionally configured for him.Source: A. E-FAS Channel Model · pp. 1–2

B. Effective Mode Representation

The effective mode representation models the random channel scale through equal-power modes and yields an effective channel-power distribution. It also supports a moment-matching approximation for general eigenvalue profiles and recovers Rayleigh fading in the fully hardened limit.

B. Effective Mode Representation

  • With equal nonzero eigenvalues, the channel power is represented as a sum of independent exponential contributions; for general eigenvalue profiles, moment matching preserves its mean and variance.The approximation defines the effective mode number μ from the eigenvalue profile.Source: B. Effective Mode Representation · p. 2
  • The instantaneous effective channel power is defined as Zu = |hu|^2, and the paper derives its distribution by averaging over the random channel scale.The resulting density involves the modified Bessel function of the second kind.Source: B. Effective Mode Representation · p. 2
  • In the fully hardened E-FAS limit, the conventional Rayleigh channel is recovered.As the effective mode number increases, the channel scale concentrates around its mean.Source: B. Effective Mode Representation · p. 2

C. Covert Transmission Model

The covert-transmission model uses Gaussian signaling over an observation interval during which the channels remain constant. Willie tests whether transmission is absent or present, with known noise power but no instantaneous E-FAS channel knowledge.

C. Covert Transmission Model

  • Alice transmits N independent Gaussian symbols x[n] with power P, and the channel remains constant during those N symbols.Channels vary independently across transmission blocks.Source: C. Covert Transmission Model · p. 2
  • Willie tests between hypotheses H0 and H1 using his received observations.Source: C. Covert Transmission Model · p. 2
  • Willie knows P, σ²w, N, and the statistical distribution of Zw, but not its instantaneous realization; the noise power is assumed perfectly known.Thus, the modeled covertness advantage comes from E-FAS propagation statistics rather than uncertainty in receiver noise power.Source: C. Covert Transmission Model · p. 2

A. Optimal Detection at Willie

After integrating over Willie’s random channel power, the likelihood ratio is increasing in received energy. Consequently, the optimal test can be implemented by comparing received energy with a scalar threshold.

A. Optimal Detection at Willie

  • The likelihood ratio is formed from Willie’s received-signal vector after conditioning on the random channel power and then integrating that power out.Source: A. Optimal Detection at Willie · p. 2
  • The optimal likelihood ratio test reduces to an energy detector because the likelihood ratio increases with the received energy.Willie decides H1 when the energy statistic Tw exceeds a scalar threshold τ.Source: A. Optimal Detection at Willie · p. 2
  • For every positive channel-power value, the conditional likelihood-ratio integrand increases with the squared norm of Willie’s observation vector.Averaging over the nonnegative channel-power distribution preserves this monotonicity.Source: A. Optimal Detection at Willie · p. 2

B. Detection Error Probability

The section characterizes Willie’s detection error under equal prior probabilities and uses the resulting detection criterion to specify covert transmission and threshold optimization.

B. Detection Error Probability

C. Finite-Observation Nature of the E-FAS Gain

The E-FAS covertness benefit is a finite-observation effect: scale fluctuations alter the hypotheses’ statistical overlap, but do not make persistent transmission fundamentally undetectable.

C. Finite-Observation Nature of the E-FAS Gain

D. Legitimate Link Reliability

The legitimate-link reliability analysis defines outage using the target spectral efficiency and derives Bob’s transmission success probability.

D. Legitimate Link Reliability

E. Achievable Covert Throughput

The section defines achievable covert throughput around Bob’s successful reception probability and explains how effective mode numbers affect hardening. Numerically, finite-mode fluctuations at Willie improve finite-observation covertness, while hardening at Bob improves reliability.

E. Achievable Covert Throughput

  • Effective covert throughput is target spectral efficiency multiplied by Bob’s successful-reception probability, and its maximum is characterized subject to the covert constraint.For each transmit power, the optimal rate is found by a one-dimensional search; the allowable power range follows from the covert constraint.Source: E. Achievable Covert Throughput · p. 3

F. Role of E-FAS Channel Hardening

  • Increasing the effective mode number suppresses received-power scale fluctuations toward the Rayleigh limit; this can aid Bob’s reliability but facilitate Willie’s detection.The section suggests configurations with more effective modes toward Bob and fewer in unintended observation directions may benefit covert transmission.Source: F. Role of E-FAS Channel Hardening · p. 3

IV. NUMERICAL RESULTS

  • The numerical evaluation uses N = 20 and ε = 0.1 by default, with normalized average Willie channel power and Bob-to-Willie average channel power ratio of 10 dB for throughput.The throughput target rate is optimized at each operating point, and the transmit power is limited by the covertness constraint.Source: §IV · p. 3
  • For the same average channel power, smaller Willie mode number yields larger minimum detection error, with the finite-mode advantage approaching the Rayleigh limit as modes increase.The additional random channel-scale fluctuations broaden the H1 distribution and increase its overlap with the noise-only distribution.Source: §IV · p. 4
  • The maximum Willie SNR allowed by the covertness constraint decreases with observation length, while smaller Willie mode number permits a slightly larger SNR at each finite length.The gap between finite-mode cases and the Rayleigh limit becomes less significant as observation length increases.Source: §IV · p. 4
  • Higher optimized covert throughput occurs when Bob has more effective modes and Willie fewer, as Willie-side hardening reduces concealment while Bob-side hardening improves reliability.For fixed Bob mode number, throughput decreases as Willie’s mode number increases; for fixed Willie mode number, increasing Bob’s mode number improves throughput.Source: §IV · p. 4, Figure 1 · p. 4

V. CONCLUSION

The paper analyzes covert communication over the compound Gaussian channel induced by E-FAS propagation. It derives detection and throughput quantities and finds that channel hardening has different implications at Bob and Willie.

V. CONCLUSION

  • The analysis characterizes the random channel scale and Bessel-K received channel power, then derives energy detection error probabilities, Bob’s outage probability, and achievable covert throughput.Source: §V · p. 4
  • A larger effective mode number can improve Bob’s reliability, whereas retaining channel-scale fluctuations at Willie can improve finite-observation covertness.Source: §V · p. 4
  • Covert E-FAS design may benefit from jointly accounting for legitimate-link quality and the effective modal structure observed in unintended directions.Source: §V · p. 4
Loading 2609.34668v1…