The compound secrecy capacity of a class of non-degraded MIMO Gaussian channels

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.