arXiv:0709.3541 · IEEE Transactions on Information Theory

Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel

Shabnam Shafiee, Nan Liu, Sennur Ulukus

Published Aug 24, 2009• 234 citations

Abstract

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.

DOI: 10.1109/tit.2009.2025549

Related papers

Secrecy capacity of the 2-2-1 gaussian MIMO wire-tap channel

Shabnam Shafiee, Nan Liu, Şennur Ulukuş

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.

International Symposium on Communications, Control and Signal ProcessingMar 1, 200812 citations

Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: The 2-2-1 channel

Shabnam Shafiee, Nan Liu, Şennur Ulukuş

Abstract—We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary. Index Terms—Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, secrecy capacity,

Jan 1, 2007267 citations

Optimal Beamforming for Gaussian MIMO Wiretap Channels With Two Transmit Antennas

Mojtaba Vaezi, Wonjae Shin, H. Vincent Poor

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. The input covariance matrix that achieves the secrecy capacity is determined. In particular, it is shown that the secrecy capacity of this channel can be achieved by linear precoding. Precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the secrecy capacity, are developed. 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.

arXiv:1707.06271IEEE Transactions on Wireless CommunicationsJul 25, 201728 citations

MIMO Gaussian wiretap channels with two transmit antennas: Optimal precoding and power allocation

Mojtaba Vaezi, Wonjae Shin, H. Vincent Poor +1 more

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. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes achieving the secrecy capacity are developed subsequently, and the secrecy capacity is compared with the generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed precoding for this problem. Numerical results show that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 20178 citations

Optimality of beamforming and closed form secrecy capacity of MIMO wiretap channels with two transmit antennas

Jiangyuan Li, Athina P. Petropulu

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.

International Symposium on Wireless Personal Multimedia Communications (WPMC)Jun 24, 20132 citations

On the optimal precoding for MIMO Gaussian wire-tap channels

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

Jan 1, 20130 citations