The secrecy capacity of a compound MIMO Gaussian channel

The compound MIMO Gaussian wiretap channel is studied, where the channel to the legitimate receiver is known and the eavesdropper channel is not known to the transmitter but is known to have a bounded spectral norm (channel gain). The compound secrecy capacity is established without the de-gradedness assumption and the optimal signaling is identified: the compound capacity equals the worst-case channel capacity thus establishing 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.