Full Rank Solutions for the MIMO Gaussian Wiretap Channel with an Average Power Constraint

TL;DR

This paper investigates the conditions under which the optimal input covariance matrix for the MIMO Gaussian wiretap channel is full-rank, providing theoretical characterizations and numerical illustrations for secrecy capacity optimization.

Contribution

It establishes necessary and sufficient conditions for the optimal covariance matrix to be full-rank in MIMO wiretap channels, advancing understanding of secure MIMO communication strategies.

Findings

Identifies conditions for full-rank optimal covariance matrices.

Provides a complete characterization of the optimal covariance matrix.

Includes numerical results validating theoretical insights.

Abstract

This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. In this paper, we first revisit the rank property of the optimal input covariance matrix that achieves the secrecy capacity of the multiple antenna MIMO Gaussian wiretap channel under the average power constraint. Next, we obtain necessary and sufficient conditions on the MIMO wiretap channel parameters such that the optimal input covariance matrix is full-rank, and we fully characterize the resulting covariance matrix as well. Numerical results are presented to illustrate the proposed theoretical findings.