Further results on optimal signaling over secure MIMO channels

Optimal signalling over the wire-tap MIMO Gaussian channel is studied under the total transmit power constraint. The recent results are extended in several directions, including a rank-deficient solution for the optimal covariance, lower and upper capacity bounds for the general case, and characterization of optimality of the isotropic signaling. An isotropic eavesdropper model is studied, which provides (tight) upper and lower capacity bounds for the non-isotropic case and also serves as the worst-case scenario. The optimal signaling for this model is obtained in an explicit form and its properties are studied, including the high and low-SNR behavior, the conditions for the eavesdropper to be negligible and the capacity saturation effect.

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

[2]  Shlomo Shamai,et al.  An MMSE Approach to the Secrecy Capacity of the MIMO Gaussian Wiretap Channel , 2009, 2009 IEEE International Symposium on Information Theory.

[3]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[4]  David W. Lewis,et al.  Matrix theory , 1991 .

[5]  Gregory W. Wornell,et al.  Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel , 2007, IEEE Transactions on Information Theory.

[6]  Hesham El Gamal,et al.  On the Secrecy Capacity of Fading Channels , 2006, 2007 IEEE International Symposium on Information Theory.

[7]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[8]  Charalambos D. Charalambous,et al.  On optimal signaling over secure MIMO channels , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[9]  Jan Brinkhuis,et al.  Optimization Insights and Applications , 2010 .

[10]  Tetsunao Matsuta,et al.  国際会議開催報告:2013 IEEE International Symposium on Information Theory , 2013 .

[11]  Athina P. Petropulu,et al.  Transmitter Optimization for Achieving Secrecy Capacity in Gaussian MIMO Wiretap Channels , 2009, ArXiv.

[12]  Frédérique E. Oggier,et al.  The secrecy capacity of the MIMO wiretap channel , 2007, 2008 IEEE International Symposium on Information Theory.

[13]  Shlomo Shamai,et al.  Information Theoretic Security , 2009, Found. Trends Commun. Inf. Theory.

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