On Secrecy Capacity of Fast Fading MIMOME Wiretap Channels With Statistical CSIT

TL;DR

This paper derives the secrecy capacity for MIMOME wiretap channels with only statistical CSIT, revealing how capacity scales with SNR under various antenna configurations and power constraints.

Contribution

It provides the first analytical secrecy capacity characterization for MIMOME channels with partial CSIT, using a novel degraded channel approach and solving complex covariance optimization problems.

Findings

Secrecy capacity scales with SNR when receiver has more antennas than eavesdropper.

The proposed degraded channel simplifies the non-concave optimization problem.

Capacity does not scale with SNR when both receiver and eavesdropper have single antennas.

Abstract

In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thank to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schuar-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.