  In this paper, we address the problem of energy-efficient power allocation
for secure communications in an amplify-and-forward (AF) large-scale
multiple-input multiple-output (LS-MIMO) relaying system in presence of a
passive eavesdropper. The benefits of an AF LS-MIMO relay are exploited to
significantly improve the secrecy performance, especially the secrecy energy
efficiency (bit per Joule). We first analyze the impact of transmit power at
the relay on the secrecy outage capacity, and prove that the secrecy outage
capacity is a concave function of transmit power under very practical
assumptions, i.e. no eavesdropper channel state information (CSI) and imperfect
legitimate CSI. Then, we propose an energy-efficient power allocation scheme to
maximize the secrecy energy efficiency. Finally, simulation results validate
the advantage of the proposed energy-efficient scheme compared to the capacity
maximization scheme.
