On the Finite-SNR Diversity-Multiplexing Tradeoff of Zero-Forcing Transmit Scheme under Secrecy Constraint

In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secret multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secret diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secret diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secret diversity gain of the Multiple-Input Multiple-Output (MIMO) wiretap channel.

[1]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[2]  Sennur Ulukus,et al.  The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel , 2009, IEEE Transactions on Information Theory.

[3]  Shlomo Shamai,et al.  A Note on the Secrecy Capacity of the Multiple-Antenna Wiretap Channel , 2007, IEEE Transactions on Information Theory.

[4]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[5]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[6]  A. Robert Calderbank,et al.  Applications of LDPC Codes to the Wiretap Channel , 2004, IEEE Transactions on Information Theory.

[7]  Frédérique E. Oggier,et al.  The secrecy capacity of the MIMO wiretap channel , 2008, ISIT.

[8]  Guanding Yu,et al.  On the Secrecy Capacity of Fading Wireless Channel with Multiple Eavesdroppers , 2007, 2007 IEEE International Symposium on Information Theory.

[9]  Roy D. Yates,et al.  Secret Communication via Multi-antenna Transmission , 2007, 2007 41st Annual Conference on Information Sciences and Systems.

[10]  Shlomo Shamai,et al.  Secure Communication Over Fading Channels , 2007, IEEE Transactions on Information Theory.

[11]  Catherine Douillard,et al.  Finite-SNR Diversity-Multiplexing Tradeoff for , 2013 .

[12]  Gregory W. Wornell,et al.  Secure Broadcasting Over Fading Channels , 2008, IEEE Transactions on Information Theory.

[13]  Hesham El Gamal,et al.  On the Secrecy Capacity of Fading Channels , 2007, ISIT.

[14]  Mustafa Cenk Gursoy.  Secure communication in the low-SNR regime: A Characterization of the energy-secrecy tradeoff , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  François Gagnon,et al.  Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications , 2009, IEEE Transactions on Information Theory.

[16]  Elza Erkip,et al.  Diversity-Multiplexing Tradeoff for the Multiple-Antenna Wire-tap Channel , 2011, IEEE Transactions on Wireless Communications.

[17]  H. Vincent Poor,et al.  On the Throughput of Secure Hybrid-ARQ Protocols for Gaussian Block-Fading Channels , 2007, IEEE Transactions on Information Theory.

[18]  Richard E. Blahut,et al.  Secrecy capacity of SIMO and slow fading channels , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[19]  Gregory W. Wornell,et al.  Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel , 2010, IEEE Transactions on Information Theory.