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On the Secrecy Performance of Continuous-Aperture Arrays Over Fading Channels

Xuan Yang, Chongjun Ouyang, Dongming Li, Yuanwei Liu

Abstract

The secrecy performance of continuous-aperture array (CAPA)-based wiretap channels in terms of secrecy rate and secrecy outage probability (SOP) is analyzed. First, the system models of CAPA systems with maximum-ratio transmission under a Rayleigh fading channel are established, and approximate probability density functions for the legitimate user Bob's signal-to-noise ratio (SNR) and the eavesdropper Eve's SNR are derived using Mercer's theorem and Landau's eigenvalue theorem. Three scenarios are considered, including a single Eve, multiple independent Eves, and multiple collaborative Eves. Next, the expressions of the secrecy rate and SOP under these three scenarios are derived, and the high-SNR slope, high-SNR power offset, diversity order, and array gain in Bob's high-SNR region are obtained. It is then theoretically proven that, in all three scenarios, the CAPA system achieves the same high-SNR slope and the same diversity order, with the latter being equal to the spatial degrees of freedom. Moreover, the CAPA system with a single Eve has the smallest high-SNR offset and the highest array gain, whereas the CAPA system with multiple collaborative Eves exhibits the largest high-SNR offset and the lowest array gain. Finally, the theoretical analyses of secrecy rate, SOP, high-SNR performance are validated by the simulation results, and a higher secrecy rate and a lower SOP are achieved by the CAPA systems compared to the spatially-discrete array systems with half-wavelength antenna spacing.

On the Secrecy Performance of Continuous-Aperture Arrays Over Fading Channels

Abstract

The secrecy performance of continuous-aperture array (CAPA)-based wiretap channels in terms of secrecy rate and secrecy outage probability (SOP) is analyzed. First, the system models of CAPA systems with maximum-ratio transmission under a Rayleigh fading channel are established, and approximate probability density functions for the legitimate user Bob's signal-to-noise ratio (SNR) and the eavesdropper Eve's SNR are derived using Mercer's theorem and Landau's eigenvalue theorem. Three scenarios are considered, including a single Eve, multiple independent Eves, and multiple collaborative Eves. Next, the expressions of the secrecy rate and SOP under these three scenarios are derived, and the high-SNR slope, high-SNR power offset, diversity order, and array gain in Bob's high-SNR region are obtained. It is then theoretically proven that, in all three scenarios, the CAPA system achieves the same high-SNR slope and the same diversity order, with the latter being equal to the spatial degrees of freedom. Moreover, the CAPA system with a single Eve has the smallest high-SNR offset and the highest array gain, whereas the CAPA system with multiple collaborative Eves exhibits the largest high-SNR offset and the lowest array gain. Finally, the theoretical analyses of secrecy rate, SOP, high-SNR performance are validated by the simulation results, and a higher secrecy rate and a lower SOP are achieved by the CAPA systems compared to the spatially-discrete array systems with half-wavelength antenna spacing.
Paper Structure (27 sections, 97 equations, 3 figures, 1 table)

This paper contains 27 sections, 97 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model Under MRT
  4. Channel Model
  5. Channel Statistics
  6. Statistical Equivalence
  7. Autocorrelation
  8. PDFs of Bob's and Eve's SNRs under Different Scenarios
  9. PDF of Bob's SNR
  10. PDF of the SNR for a Single Eve
  11. PDF of the SNR for Multiple Independent Eves
  12. PDF of the SNR for Multiple Collaborative Eves
  13. Secrecy Rate and SOP of CAPA Systems
  14. Secrecy Rate and SOP Under a Single Eve
  15. Secrecy Rate and SOP Under Multiple Independent Eves
  16. ...and 12 more sections

Figures (3)

  • Figure 1: CAPA system model with eavesdropping.
  • Figure 2: Secrecy rate varying with (a) SNR of Bob, (b) SNR of Eve, (c) array length, and (d) the number of Eves.
  • Figure 3: SOP varying with (a) SNR of Bob, (b) SNR of Eve, (c) array length, and (d) the number of Eves.