On the Fast Fading Gaussian Wiretap Channel With Statistical Channel State Information at the Transmitter

In this paper, we investigate the ergodic secrecy capacity of the fast fading Gaussian wiretap channel when only the statistics of the channel state information are known at the transmitter. We derive conditions for the existence of degradedness and a positive ergodic secrecy capacity under the usual stochastic order, the convex order, and the increasing convex order between the legitimate and eavesdropper channels. For more general orders, we prove the secrecy capacity of layered erasure wiretap channels and propose a layered signaling for the achievable scheme, and we derive an upper bound on the capacity for fast fading Gaussian wiretap channels. Finally, the numerical results show that under Nakagami-m fast fading channels, the proposed layered signaling outperforms the Gaussian codebook in several cases. In particular, in certain cases, the Gaussian codebook can achieve only a zero secrecy rate, whereas the proposed scheme achieves positive secrecy rates. Therefore, the connectivity of wireless networks can be significantly improved by the proposed scheme.