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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Rank property of the MIMO Gaussian wiretap channel with an average power constraint

S. Ali. A. Fakoorian, Jing Huang, Arnold Lee Swindlehurst

Published Nov 1, 2012• 2 citations

Abstract

This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. In particular, we study the rank of the optimal input covariance matrix that achieves the secrecy capacity of the multiple antenna MIMO Gaussian wiretap channel under an average power constraint. The rank and other properties of the optimal solution are derived based on certain relationships between the channel matrices for the legitimate receiver and eavesdropper. Such properties are useful steps towards characterizing the general solution to the MIMO wiretap problem with an average power constraint.

DOI: 10.1109/acssc.2012.6489038

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A Gaussian multiple-input multiple-output (MIMO) wiretap channel model is considered, where there exists a transmitter, a legitimate receiver and an eavesdropper each equipped with multiple antennas. The problem of finding the optimal input covariance matrix that achieves secrecy capacity subject to a power constraint is studied. In particular, it is shown that when the difference between the Grams of legitimate and eavesdropper channel matrices has all negative eigenvalues except one positive eigenvalue, beamforming is optimal. For that case, the secrecy capacity is obtained.

A Gaussian multiple-input multiple-output (MIMO) wiretap channel model is considered. The input is a two-antenna transmitter, while the outputs are the legitimate receiver and an eavesdropper, both equipped with multiple antennas. All channels are assumed to be known. The problem of obtaining the optimal input covariance matrix that achieves secrecy capacity subject to a sum power constraint is addressed, and a closed-form expression for the secrecy capacity is obtained. The sufficient and necessary condition for beamforming to be optimal is also given.