Optimality of beamforming for secrecy capacity of MIMO wiretap channels

Jiangyuan Li; Athina P. Petropulu

doi:https://doi.org/10.1109/WIFS.2012.6412662

Optimality of beamforming for secrecy capacity of MIMO wiretap channels

Jiangyuan Li, Athina P. Petropulu

School of Engineering, Electrical & Computer Engineering

Rutgers, The State University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

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 optimality of beamforming for secrecy capacity subject to sum power constraint is studied, and two sufficient conditions for beamforming to be globally optimal are given. The first sufficient condition states that when the difference between the Gram matrices of legitimate and eavesdropper channel matrices has exactly one positive eigenvalue, then beamforming is globally optimal. An alternative sufficient condition, which involves convex optimization, is also provided. For the case in which beamforming is globally optimal, the secrecy capacity is obtained. Otherwise, an upper bound of the difference between the secrecy capacity and beamforming secrecy rate is provided.

Original language	American English
Title of host publication	WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security
Pages	276-281
Number of pages	6
DOIs	https://doi.org/10.1109/WIFS.2012.6412662
State	Published - 2012
Event	2012 IEEE International Workshop on Information Forensics and Security, WIFS 2012 - Tenerife, Spain Duration: Dec 2 2012 → Dec 5 2012

Publication series

Name	WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security

Other

Other	2012 IEEE International Workshop on Information Forensics and Security, WIFS 2012
Country/Territory	Spain
City	Tenerife
Period	12/2/12 → 12/5/12

ASJC Scopus subject areas

Computer Science Applications
Information Systems

Keywords

MIMO wiretap channel
Secrecy capacity
beam-forming
optimality of beamforming
wireless physical layer security

Access to Document

https://doi.org/10.1109/WIFS.2012.6412662

Cite this

Li, J., & Petropulu, A. P. (2012). Optimality of beamforming for secrecy capacity of MIMO wiretap channels. In WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security (pp. 276-281). [6412662] (WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security). https://doi.org/10.1109/WIFS.2012.6412662

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title = "Optimality of beamforming for secrecy capacity of MIMO wiretap channels",

abstract = "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 optimality of beamforming for secrecy capacity subject to sum power constraint is studied, and two sufficient conditions for beamforming to be globally optimal are given. The first sufficient condition states that when the difference between the Gram matrices of legitimate and eavesdropper channel matrices has exactly one positive eigenvalue, then beamforming is globally optimal. An alternative sufficient condition, which involves convex optimization, is also provided. For the case in which beamforming is globally optimal, the secrecy capacity is obtained. Otherwise, an upper bound of the difference between the secrecy capacity and beamforming secrecy rate is provided.",

keywords = "MIMO wiretap channel, Secrecy capacity, beam-forming, optimality of beamforming, wireless physical layer security",

author = "Jiangyuan Li and Petropulu, {Athina P.}",

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doi = "https://doi.org/10.1109/WIFS.2012.6412662",

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pages = "276--281",

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note = "2012 IEEE International Workshop on Information Forensics and Security, WIFS 2012 ; Conference date: 02-12-2012 Through 05-12-2012",

}

Li, J & Petropulu, AP 2012, Optimality of beamforming for secrecy capacity of MIMO wiretap channels. in WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security., 6412662, WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security, pp. 276-281, 2012 IEEE International Workshop on Information Forensics and Security, WIFS 2012, Tenerife, Spain, 12/2/12. https://doi.org/10.1109/WIFS.2012.6412662

Optimality of beamforming for secrecy capacity of MIMO wiretap channels. / Li, Jiangyuan; Petropulu, Athina P.
WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security. 2012. p. 276-281 6412662 (WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Li, Jiangyuan

AU - Petropulu, Athina P.

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N2 - 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 optimality of beamforming for secrecy capacity subject to sum power constraint is studied, and two sufficient conditions for beamforming to be globally optimal are given. The first sufficient condition states that when the difference between the Gram matrices of legitimate and eavesdropper channel matrices has exactly one positive eigenvalue, then beamforming is globally optimal. An alternative sufficient condition, which involves convex optimization, is also provided. For the case in which beamforming is globally optimal, the secrecy capacity is obtained. Otherwise, an upper bound of the difference between the secrecy capacity and beamforming secrecy rate is provided.

AB - 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 optimality of beamforming for secrecy capacity subject to sum power constraint is studied, and two sufficient conditions for beamforming to be globally optimal are given. The first sufficient condition states that when the difference between the Gram matrices of legitimate and eavesdropper channel matrices has exactly one positive eigenvalue, then beamforming is globally optimal. An alternative sufficient condition, which involves convex optimization, is also provided. For the case in which beamforming is globally optimal, the secrecy capacity is obtained. Otherwise, an upper bound of the difference between the secrecy capacity and beamforming secrecy rate is provided.

KW - MIMO wiretap channel

KW - Secrecy capacity

KW - beam-forming

KW - optimality of beamforming

KW - wireless physical layer security

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BT - WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security

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Li J, Petropulu AP. Optimality of beamforming for secrecy capacity of MIMO wiretap channels. In WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security. 2012. p. 276-281. 6412662. (WIFS 2012 - Proceedings of the 2012 IEEE International Workshop on Information Forensics and Security). doi: https://doi.org/10.1109/WIFS.2012.6412662

Optimality of beamforming for secrecy capacity of MIMO wiretap channels

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Keywords

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