Ergodic capacity under channel distribution uncertainty

The impact of channel distribution uncertainty on the performance of fading channels is studied. The compound capacity of a class of ergodic fading channels subject to channel distribution uncertainty is obtained, for arbitrary noise and nominal channel distribution. The saddle-point property is established, so that the compound capacity equals to the worst-case channel capacity, which is characterized as 1-D convex optimization problem. The properties of worst-case mutual information and channel distribution are studied. Closed-form solutions are obtained in the asymptotic regimes of small and large uncertainty, and an error floor effect is established in the latter case. The known results for the ergodic capacity of the Gaussian MIMO channel under i.i.d. Rayleigh fading are shown to hold under the channel distribution uncertainty as well.