Title :
The compound secrecy capacity of a class of non-degraded MIMO Gaussian channels
Author :
Schaefer, R.F. ; Loyka, S.L.
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
fDate :
Sept. 30 2014-Oct. 3 2014
Abstract :
Secrecy capacity of a class of non-degraded compound MIMO Gaussian channels is obtained. Earlier results established for isotropic uncertainty sets are extended to broader class of (non-isotropic) sets, which bound not only the gain but also the eigendirections of the eavesdropper channel. When a maximum element exists in the uncertainty set, a saddle-point exists so that the compound and worst-case channel capacities coincide and signaling on the worst-case channel also works for the whole class of channels. The case of additive uncertainty in the legitimate channel, in addition to the unknown eavesdropper channel of a bounded spectral norm, is also studied. Its compound secrecy capacity and the optimal signaling are established in a closed-form, revealing the saddle-point property. The optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it.
Keywords :
Gaussian channels; MIMO communication; set theory; Gaussian optimal signaling; bounded spectral norm; channel capacities; compound secrecy capacity; eavesdropper channel; eigenmode power allocation; isotropic uncertainty sets; nondegraded MIMO Gaussian channels; optimal signaling; Channel capacity; Channel estimation; Compounds; Covariance matrices; MIMO; Transmitters; Uncertainty;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2014 52nd Annual Allerton Conference on
Conference_Location :
Monticello, IL
DOI :
10.1109/ALLERTON.2014.7028564