Secure Communication in the Low-SNR Regime

TL;DR

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

Contribution

It provides new analytical expressions for secrecy capacity derivatives at zero SNR and identifies optimal transmission strategies in the low-SNR regime.

Findings

Optimal transmission in the maximal-eigenvalue eigenspace.

Fading can improve energy efficiency for secure communication.

Quantified minimum bit energy 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 maximal-eigenvalue eigenspace of Phi = 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, and the benefits of fading in terms of energy efficiency are shown.