Robust Capacity for Additive Colored Gaussian Uncertain Channels

This paper is concerned with the definition and computation of channel capacity of continuous time additive Gaussian channels, when the channel is subject to uncertainty, the noise power spectral density is known and the input signal is wide-sense stationary and constrained in power. The uncertainty description of the channel transfer function is described by the set of all channels which belong to a ball in a normed linear space, known as H space. Two uncertainty models are used that are borrowed from the control theory, additive, and multiplicative. The channel capacity, that we call robust capacity, is then defined as a maxi-min of mutual information rate in which the minimization is over the uncertainty set while the maximization is over all transmitted signals having finite power. An exact formulae for the robust capacity is derived. Part of the results include a modified version of the water-filling equation, describing how the optimal transmitter power depends on the channel uncertainty. The conditions are introduced under which the robust capacity is equivalent to operational capacity. Finally, an example is worked out to show the effect of uncertainty in case of the second order system. Copyright c ©2005 IFAC