Secure communication in the low-SNR regime: A Characterization of the energy-secrecy tradeoff

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 Phi = H_m ^dagger H_m - N_m/N_e H_e ^dagger 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.