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On the fading Gaussian wiretap channel with statistical channel state information at transmitter

In this paper we partially characterize the relation between the ergodic secrecy capacity of fast fading wiretap channels and the stochastic orders including the usual stochastic orders, the convex orders, and the increasing convex orders, of the main and eavesdropper's channels. We assume that there is only statistical channel state information of both channels at transmitter and both fading channels can be with arbitrary distributions. We derive the sufficient conditions for the existence of the positive ergodic secrecy capacity under these three orders. For more general orders we also derive capacity lower and upper bounds. To achieve it, we apply the concept of channel enhancement to the continuous fading wiretap channel and derive an upper bound. Motivated by the upper bound, we also derive the lower bound of the ergodic secrecy capacity by the layered signaling. Finally numerical results show that under Nakagami-m channels, the proposed achievable scheme outperforms Gaussian signaling in several cases. More specifically, the proposed scheme may result in positive secrecy rate while Gaussian signaling only lead to zero. Thus when we apply the proposed scheme to the wireless network, the connectivity can be significantly improved.