  Strong secrecy capacity of compound wiretap channels is studied. The known
lower bounds for the secrecy capacity of compound finite-state memoryless
channels under discrete alphabets are extended to arbitrary uncertainty sets
and continuous alphabets under the strong secrecy criterion. The conditions
under which these bounds are tight are given. Under the saddle-point condition,
the compound secrecy capacity is shown to be equal to that of the worst-case
channel. Based on this, the compound Gaussian MIMO wiretap channel is studied
under the spectral norm constraint and without the degradedness assumption.
First, it is assumed that only the eavesdropper channel is unknown, but is
known to have a bounded spectral norm (maximum channel gain). The compound
secrecy capacity is established in a closed form 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. More general uncertainty sets are
considered and the existence of a maximum element is shown to be sufficient for
a saddle-point to exist, so that signaling on the worst-case channel achieves
the compound capacity of the whole class of channels. The case of
rank-constrained eavesdropper is considered and the respective compound secrecy
capacity is established. Subsequently, the case of additive uncertainty in the
legitimate channel, in addition to the unknown eavesdropper channel, is
studied. Its compound secrecy capacity and the optimal signaling are
established in a closed-form as well, revealing the same saddle-point property.
