Secure Communication in the Low-SNR Regime: A Characterization of the Energy-Secrecy Tradeoff

TL;DR

This paper analyzes the secrecy capacity of multiple-antenna wiretap channels in low-SNR conditions, deriving key derivatives, optimal transmission strategies, and energy efficiency metrics, including the effects of fading.

Contribution

It provides the first and second derivatives of secrecy capacity at zero SNR, identifies optimal transmission eigenspaces, and quantifies energy efficiency under secrecy constraints.

Findings

Optimal transmission in maximum-eigenvalue eigenspace at low SNR

Derived expressions for secrecy capacity derivatives at zero SNR

Quantified minimum bit energy and wideband slope under secrecy constraints

Abstract

Secrecy capacity of a multiple-antenna wiretap channel is studied in the low signal-to-noise ratio (SNR) regime. Expressions for the first and second derivatives of the secrecy capacity with respect to SNR at SNR = 0 are derived. Transmission strategies required to achieve these derivatives are identified. In particular, it is shown that it is optimal in the low-SNR regime to transmit in the maximum-eigenvalue eigenspace of H_m* H_m - N_m/N_e H_e* H_e where H_m and H_e denote the channel matrices associated with the legitimate receiver and eavesdropper, respectively, and N_m and N_e are the noise variances at the receiver and eavesdropper, respectively. Energy efficiency is analyzed by finding the minimum bit energy required for secure and reliable communications, and the wideband slope. Increased bit energy requirements under secrecy constraints are quantified. Finally, the impact of fading is investigated.