On Ergodic Secrecy Capacity of Multiple Input Wiretap Channel with Statistical CSIT

TL;DR

This paper derives a tight upper bound and fully characterizes the ergodic secrecy capacity of MISOSE channels with only statistical CSIT, showing that Gaussian inputs with uniform power allocation are optimal.

Contribution

It introduces a new secrecy capacity upper bound and proves the optimality of Gaussian inputs with uniform power allocation under statistical CSIT.

Findings

Secrecy capacity is achieved by Gaussian input without prefixing.

The optimal input covariance matrix is a scaled identity matrix.

Secrecy capacity is bounded at high SNR and large antenna regimes.

Abstract

We consider the secure transmission in ergodic fast-Rayleigh fading multiple-input single-output single-antennaeavesdropper (MISOSE) wiretap channels. We assume that the statistics of both the legitimate and eavesdropper channels is the only available channel state information at the transmitter (CSIT). By introducing a new secrecy capacity upper bound, we prove that the secrecy capacity is achieved by Gaussian input without prefixing. To attain this, we form another MISOSE channel for upper-bounding, and tighten the bound by finding the worst correlations between the legitimate and eavesdropper channel coefficients. The resulting upper bound is tighter than the others in the literature which are based on modifying the correlation between the noises at the legitimate receiver and eavesdropper. Next, we fully characterize the ergodic secrecy capacity by showing that the optimal channel input covariance matrix is a scaled identity matrix, with the transmit power allocated uniformly among the antennas. The key to solve such a complicated stochastic optimization problem is by exploiting the completely monotone property of the ergodic secrecy capacity to use the stochastic ordering theory. Finally, our simulation results show that for the considered channel setting, the secrecy capacity is bounded in both the high signal-to-noise ratio and large number of transmit antenna regimes.