  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.
