Multiple-input multiple-output Gaussian channels: Optimal covariance for non-Gaussian inputs

Miguel R. D. Rodrigues, Fernando Perez-Cruz, Sergio Verduy
2008 2008 IEEE Information Theory Workshop  
We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleoutput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixedpoint equation involving key system quantities, including the MMSE matrix. We also
more » ... e the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr.
doi:10.1109/itw.2008.4578704 dblp:conf/itw/RodriguesPV08 fatcat:udwms5bqonazpc36o5pupafg6i