Robust Capacity for Additive Colored Gaussian Uncertain Channels

This paper is concerned with the computation of channel capacity of continuous additive Gaussian channel, when the latter is subject to uncertainty, the noise power spectrum is known and the input is wide-sense stationary and constrained in power. The uncertainty description is represented by a ball in the H-infinity space. Two uncertainty models known as addtive and multiplicative are used. The channel capacity, called robust capacity, is defined as a maxi-min of the mutual information rate, in which the minimization is over the uncertainty set while the maximization isover all transmitted signals having finite power. An exact formulae for the robust capacity is derived. A modified version of the water-filling formulae, and a condition under which the robust capacity is equivalent to the operation capacity, are obtained. An example for second-order systems is included.