MIMO Gaussian Channels with Arbitrary Inputs: Optimal Precoding and Power Allocation ## AbstractWe investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error. The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For nonGaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the nonGaussian input distributions, but also for the interference among inputs.
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