MIMO Gaussian channels with arbitrary inputs: optimal precoding and power allocation

  • Authors:
  • Fernando Pérez-Cruz;Miguel R. D. Rodrigues;Sergio Verdú

  • Affiliations:
  • Electrical Engineering Department, Princeton University, Princeton, NJ and Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Leganes, Madrid, Spain;Instituto de Telecomunicações and the Department of Computer Science, University of Porto, Porto, Portugal;Electrical Engineering Department, Princeton University, Princeton, NJ

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

In this paper, we 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 (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian 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 non-Gaussian input distributions, but also for the interference among inputs.