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

doi:10.12142/ZTECOM.202603003

ZTE Communications ›› 2026, Vol. 24 ›› Issue (3): 12-17.DOI: 10.12142/ZTECOM.202603003

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

Wu Tuo¹^,², Wu Zhenguan³, Zhi Kangda⁴, Liu Baiyang⁵, Tong Kin‑Fai²^,⁵

^1.South China University of Technology, Guangzhou 510640, China
^2.Shenzhen Research Institute, Hong Kong Metropolitan University, Shenzhen 518057, China
^3.Dongguan University of Technology, Dongguan 523808, China
^4.Technical University of Berlin, Berlin 10587, Germany
^5.Hong Kong Metropolitan University, Hong Kong SAR, China

Received:2026-07-04 Online:2026-09-20 Published:2026-09-20
About author:Wu Tuo received his BE degree in telecommunication engineering from South China Normal University, in 2017, MS degree in radio physics from Sun Yat-sen University, China in 2021, and PhD degree from the School of Electronic Engineering and Computer Science, Queen Mary University of London, UK in 2024. He was a postdoctoral researcher with Nanyang Technological University, Singapore from 2024 to 2025, and a research fellow with City University of Hong Kong, China from 2025 to 2026. He is currently an associate professor with the School of Electronic and Information Engineering, South China University of Technology. His research interests include fluid antenna systems, reconfigurable intelligent surfaces, wireless localization, and sensing. He has published extensively in wireless communications and serves on the editorial boards of several IEEE journals.
Wu Zhenguan received his BE degree in communication engineering from Zhaoqing University, China in 2025. He is currently a graduate student at Dongguan University of Technology, China. His research interests include fluid antenna systems and reconfigurable intelligent surfaces.
Zhi Kangda received his BE degree from Shanghai University, China in 2017, ME degree from the University of Science and Technology of China in 2020, and PhD degree from Queen Mary University of London, UK in 2023. He is currently a Marie Curie Research Fellow with the Technical University of Berlin, Germany. His research interests include next-generation MIMO systems, reconfigurable intelligent surfaces, sensing and estimation, and near-field communications. He received the 2026 IEEE ComSoc CTTC Andrea Goldsmith Young Scholars Award, the 2025 IEEE ComSoc Heinrich Hertz Award for Best Communications Letter, the 2025 IEEE ComSoc EMEA Outstanding Young Researcher Award, and the 2024 Marie Curie Postdoctoral Fellowship. He serves as an editor for several IEEE journals and as a Guest Editor for IEEE Network and EURASIP Journal on Wireless Communications and Networking.
Liu Baiyang received his BS degree in wireless communication from Guangdong University of Technology, China, and his PhD degree in communication and information systems from South China University of Technology in 2018. He is currently an assistant professor with the College of Artificial Intelligence, Shenzhen Technology University, China. He has held research fellow positions at Hong Kong Metropolitan University, China; City University of Hong Kong, China;Queen Mary University of London, UK; Southern University of Science and Technology, China; and Shenzhen University, China. His research interests include reconfigurable intelligent surfaces, fluid antenna systems, orbital angular momentum multiplexing, and integrated sensing and communication. He has published extensively in antennas and wireless communications, and received the Best Paper Award at GSMMW 2024 and the 2024 Best Reviewer Awards from IEEE Transactions on Antennas and Propagation and IEEE Antennas and Wireless Propagation Letters.
First author contact:Tong Kin-Fai (ktong@hkmu.edu.hk) is currently a Chair Professor of antennas and applied electromagnetics at Hong Kong Metropolitan University, China. His research interests include wideband antennas, circularly polarized patch antennas, microwave and millimeter-wave techniques, fluid antennas, surface waves, and wideband mmWave transducers for future wireless communications systems. He has made significant contributions to research translation through industrial collaboration, patents, commercialization, and public engagement. His Innovate UK project was rated “outstanding” and featured in the Parliamentary Review. He received the UCL Knowledge Transfer Business of the Year Award in 2015 and the UCL Provost’s Spirit of Enterprise Award in 2017. He is a Chartered Engineer (UK), a Fellow of the Electromagnetics Academy, and serves as an editor for several leading journals in antennas, electromagnetics, and wireless propagation.
Supported by:
the Shenzhen Research Institute, Hong Kong Metropolitan University;DON/2026/01 SZ

Abstract

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 develops 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 available 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 decisive security resource is Bob’s aperture-induced EDoF advantage rather than the raw number of selectable ports.

Key words: equivalent degrees of freedom, fluid antenna system, physical-layer security, secrecy outage probability, wiretap channel

Wu Tuo, Wu Zhenguan, Zhi Kangda, Liu Baiyang, Tong Kin‑Fai. Equivalent Degrees of Freedom Based Secrecy Outage Analysis for Fluid Antenna Wiretap Channels[J]. ZTE Communications, 2026, 24(3): 12-17.

Figures/Tables 5

Table 1 Parameters and their denotation

Parameter	Denotation
q∈{B, E}	Receiver index (Bob/Eve)
N_q	Number of candidate ports
W_q =L_q /λ	Aperture length normalized by carrier wavelength
g_q and R_q	Channel vector and spatial correlation matrix
η_q	Average channel power
$γ ¯$ _q and X_q	Average SNR and normalized selected gain
$m i n N q, 2 W q + 1$	Effective dominant-mode count
R_s and θ (2 raised to the power R_s )	Target secrecy rate and its threshold factor
P_so	Secrecy outage probability

Table 1 Parameters and their denotation

Parameter	Denotation
q∈{B, E}	Receiver index (Bob/Eve)
N_q	Number of candidate ports
W_q =L_q /λ	Aperture length normalized by carrier wavelength
g_q and R_q	Channel vector and spatial correlation matrix
η_q	Average channel power
$γ ¯$ _q and X_q	Average SNR and normalized selected gain
$m i n N q, 2 W q + 1$	Effective dominant-mode count
R_s and θ (2 raised to the power R_s )	Target secrecy rate and its threshold factor
P_so	Secrecy outage probability

Figure 1 Secrecy outage probability versus Bob’s average SNR for WE=1, γˉE=0 dB, and Rs=0.5 bit/s/Hz

Figure 2 Secrecy outage probability versus Bob’s normalized aperture for γˉB=15 dB, γˉE=5 dB, and different Eve apertures

Figure 3 EDoF and refined-WIM secrecy outage validation against exact Monte Carlo simulation for NB=40, NE=30, WB=3, WE=2, and γˉE=0 dB

Figure 4 High-SNR secrecy outage floor versus the relative Eve link quality α for different EDoF pairs (KB*,?KE*) and Rs=0.5 bit/s/Hz

References 24

[1]	Wyner A D. The wire-tap channel [J]. The Bell system technical journal, 1975, 54(8): 1355–1387. DOI: 10.1002/j.1538-7305.1975.tb02040.x
[2]	Bloch M, Barros J. Physical-layer security: from information theory to security engineering [M]. Cambridge, UK: Cambridge University Press, 2011. DOI: 10.1017/cbo9780511977985
[3]	Wong K K, Shojaeifard A, Tong K F, et al. Fluid antenna systems [J]. IEEE transactions on wireless communications, 2021, 20(3): 1950–1962. DOI: 10.1109/TWC.2020.3037595
[4]	Wong K K, Shojaeifard A, Tong K F, et al. Performance limits of fluid antenna systems [J]. IEEE communications letters, 2020, 24(11): 2469–2472. DOI: 10.1109/LCOMM.2020.3006554
[5]	New W K, Wong K K, Xu H, et al. A tutorial on fluid antenna system for 6G networks: encompassing communication theory, optimization methods and hardware designs [J]. IEEE communications surveys & tutorials, 2025, 27(4): 2325–2377. DOI: 10.1109/COMST.2024.3498855
[6]	New W K, Wong K K, Wang C, et al. Fluid antenna systems: redefining reconfigurable wireless communications [J]. IEEE journal on selected areas in communications, 2026, 44: 1013–1044. DOI: 10.1109/JSAC.2025.3632097
[7]	Hong H J, Wong K K, Chae C B, et al. A contemporary survey on fluid antenna systems: fundamentals and networking perspectives [J]. IEEE transactions on network science and engineering, 2026, 13: 2305–2328. DOI: 10.1109/TNSE.2025.3613225
[8]	Wu T, Zhi K D, Yao J T, et al. Fluid antenna systems enabling 6G: principles, applications, and research directions [J]. IEEE wireless communications, 2026, 33(4): 100–108. DOI: 10.1109/MWC.2025.3629597
[9]	Tong K F, Liu B Y, Wong K K. Designs and challenges in fluid antenna system hardware [J]. Electronics, 2025, 14(7): 1458. DOI: 10.3390/electronics14071458
[10]	Shen Y J, Tang B Y, Gao S, et al. Design and experimental validation of mmWave surface-wave-enabled fluid antennas for future wireless communications [J]. IEEE antennas and wireless propagation letters, 2026, 25(4): 1467–1471. DOI: 10.1109/LAWP.2026.3657059
[11]	Liu B Y, Wu T, Wong K K, et al. Wideband pixel-based fluid antenna system: an antenna design for smart city [J]. IEEE Internet of Things journal, 2026, 13(4): 6850–6862. DOI: 10.1109/JIOT.2025.3637319
[12]	Huang J W, Meng H, Liu B Y, et al. Multi-activation fluid antenna system with a single RF chain for fast multi-user access [C]//Proceedings of International Symposium on Antennas and Propagation (ISAP). IEEE, 2025: 1–2. DOI: 10.23919/ISAP63122.2025.11362065
[13]	Liu B Y, Tong K F, Wong K K, et al. Programmable meta-fluid antenna for spatial multiplexing in fast fluctuating radio channels [J]. Optics express, 2025, 33(13): 28898. DOI: 10.1364/oe.567923
[14]	Chai Z, Wong K K, Tong K F, et al. Port selection for fluid antenna systems [J]. IEEE communications letters, 2022, 26(5): 1180–1184. DOI: 10.1109/LCOMM.2022.3152451
[15]	Tang B Y, Xu H, Wong K K, et al. Fluid antenna enabling secret communications [J]. IEEE communications letters, 2023, 27(6): 1491–1495. DOI: 10.1109/LCOMM.2023.3264634
[16]	Rostami Ghadi F, Wong K K, López-Martínez F J, et al. Physical layer security over fluid antenna systems: secrecy performance analysis [J]. IEEE transactions on wireless communications, 2024, 23(12): 18201–18213. DOI: 10.1109/TWC.2024.3463488
[17]	New W K, Wong K K, Xu H, et al. Fluid antenna system: new insights on outage probability and diversity gain [J]. IEEE transactions on wireless communications, 2024, 23(1): 128–140. DOI: 10.1109/TWC.2023.3276245
[18]	Wong K K, Tong K F, Chen Y, et al. Closed-form expressions for spatial correlation parameters for performance analysis of fluid antenna systems [J]. Electronics letters, 2022, 58(11): 454–457. DOI: 10.1049/ell2.12487
[19]	Khammassi M, Kammoun A, Alouini M S. A new analytical approximation of the fluid antenna system channel [J]. IEEE transactions on wireless communications, 2023, 22(12): 8843–8858. DOI: 10.1109/TWC.2023.3266411
[20]	Vega-Sánchez J D, Urquiza-Aguiar L F, Mora H R C, et al. Fluid antenna system: secrecy outage probability analysis [J]. IEEE transactions on vehicular technology, 2024, 73(8): 11458–11469. DOI: 10.1109/TVT.2024.3376475
[21]	Slepian D, Pollak H O. Prolate spheroidal wave functions, Fourier analysis and uncertainty: I [J]. The bell system technical journal, 1961, 40(1): 43–63. DOI: 10.1002/j.1538-7305.1961.tb03976.x
[22]	Landau H J, Pollak H O. Prolate spheroidal wave functions, Fourier analysis and uncertainty: II [J]. The bell system technical journal, 1961, 40(1): 65–84. DOI: 10.1002/j.1538-7305.1961.tb03977.x
[23]	Jakes W C. Microwave mobile communications [M]. New York: Wiley, 1974
[24]	Wu T, Luk K M, Tang J, et al. Variable block-correlation modeling and optimization for secrecy analysis in fluid antenna systems [PP/OL]. arXiv.(2025-10-04) [2026-06-06].

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

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