Optimal Beamforming for Gaussian MIMO Wiretap Channels with Two Transmit Antennas

TL;DR

This paper derives the optimal beamforming and power allocation strategies for a Gaussian MIMO wiretap channel with two transmit antennas, achieving higher secrecy rates than previous methods.

Contribution

It determines the optimal input covariance and precoding schemes for the two-antenna transmitter to maximize secrecy capacity.

Findings

Optimal input covariance matrix is identified.

Linear precoding achieves the secrecy capacity.

Proposed schemes outperform GSVD-based precoding.

Abstract

A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. Under an average power constraint, the optimal input covariance to obtain the secrecy capacity of this channel is unknown, in general. In this paper, the input covariance matrix required to achieve the capacity is determined. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the capacity, are developed subsequently. The secrecy capacity is then compared with the achievable secrecy rate of generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed technique for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.