On the capacity of a class of MIMO channels subject to normed uncertainty

Abstract

The compound capacity of uncertain MIMO channels is considered, when the channel is modeled by a class described by an induced norm constraint. Within this framework, two types of classes are investigated, namely, additive and multiplicative uncertainties subject to a spectral norm constraint, using partial channel state information at the transmitter side. The compound capacity is defined as a maxmin of the mutual information, corresponding to the capacity of the class, in which the minimization is done over the class of channels while the maximization is done over the transmit covariance. Closed form solutions for the compound capacity of the classes are obtained while several properties related to transmit and received eigenvectors are presented. It is also shown that capacity of the class of channels is equal to the worst-case channel capacity, while establishing a saddle-point property. Additionally, explicit closed-from solutions are given for the capacity-achieving Tx covariance matrix and the worst-case channel uncertainty. The effect of uncertainty is shown to be equivalent to an SNR loss which is proportional to the size of the uncertainty of the channel matrix measured by the spectral norm.