Physical Layer Security for Continuous-Aperture Array (CAPA) Systems

TL;DR

This work presents a CAPA-based framework for physical-layer security, formulating secure transmission in terms of a continuous current distribution over a planar or arbitrary aperture. It derives closed-form expressions for the maximum secrecy rate under a power constraint and the minimum power required for a target secrecy rate, along with the exact optimal current distributions. The analysis reveals that MRT beamforming is optimal at low SNR while ZF beamforming dominates at high SNR for MSR, and that ZF is asymptotically optimal for achieving large secrecy targets in terms of MRP. Asymptotic results confirm energy-conserving limits as aperture size grows, and numerical results show CAPAs outperform conventional SPDAs in secrecy rate and power efficiency. Overall, CAPAs emerge as a powerful platform for secure wireless communications with tangible gains over traditional discrete arrays.

Abstract

A continuous-aperture array (CAPA)-based secure transmission framework is proposed to enhance physical layer security. Continuous current distributions, or beamformers, are designed to maximize the secrecy transmission rate under a power constraint and to minimize the required transmission power for achieving a specific target secrecy rate. On this basis, the fundamental secrecy performance limits achieved by CAPAs are analyzed by deriving closed-form expressions for the maximum secrecy rate (MSR) and minimum required power (MRP), along with the corresponding optimal current distributions. To provide further insights, asymptotic analyses are performed for the MSR and MRP, which reveals that i) for the MSR, the optimal current distribution simplifies to maximal ratio transmission (MRT) beamforming in the low-SNR regime and to zero-forcing (ZF) beamforming in the high-SNR regime; i) for the MRP, the optimal current distribution simplifies to ZF beamforming in the high-SNR regime. The derived results are specialized to the typical array structures, e.g., planar CAPAs and planar spatially discrete arrays (SPDAs). The rate and power scaling laws are further analyzed by assuming an infinitely large CAPA. Numerical results demonstrate that: i) the proposed secure continuous beamforming design outperforms MRT and ZF beamforming in terms of both achievable secrecy rate and power efficiency; ii) CAPAs achieve superior secrecy performance compared to conventional SPDAs.

Figures (9)

• Figure 1: Illustration of a CAPA-based wiretap channel.
• Figure 2: Illustration for a planar CAPA.
• Figure 3: Illustration for Planar SPDA.
• Figure 4: Secrecy rates versus power budget $P$.
• Figure 5: MSRs versus aperture size $\left| \mathcal{A}\right|$.

Theorems & Definitions (24)

• Lemma 1
• Lemma 2
• Theorem 1
• Lemma 3
• Lemma 4
• Theorem 2
• Theorem 3
• Remark 1
• Lemma 5
• Theorem 4