Generalized Mercury/Waterfilling for Multiple-Input Multiple-Output Channels

Abstract—We determine the power-allocation policy that maxi-mizes the mutual information for general multiple-input multiple-output Gaussian channels with arbitrary input distributions, by capitalizing on the recent relationship between mutual infor-mation and minimum mean squared error (MMSE). In this context, we put forth a novel interpretation of the optimal power-allocation procedure that generalizes the mercury/waterfilling algorithm, previously proposed for parallel non-interfering chan-nels. In this generalization the mercury level accounts for the sub-optimal (non-Gaussian) input distribution and the interferences between inputs