Sums of correlated Wishart Random Matrices

Mario Kieburg1

  • 1Universität Bielefeld

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14:00 - 16:00 | Wed 15 Mar | Main Room | S1

Random matrix theory and statistical physics in the analysis and design of MIMO systems

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Abstract

Random matrix theory of Wishart ensembles are a good model to describe the white noise of the channel when transmitting signals due to either the irregular shape (chaotic dynamics) of the channel or the fact that the system is open (coupling to an environment). A more advanced approach of this description is the introduction of correlations at the receivers and emitters. When we have only one emitter and one receiver with several channels the model becomes a doubly correlated Wishart random matrix ensemble. However when we have several emitters the situation drastically changes. We have to consider the spectral statistics of a sum of correlated Wishart ensembles. I will report on a very explicit result for the spectral density of a sum of two correlated Wishart matrices and what its generalization to an arbitrary sum is. This work was done together with Gernot Akemann and Tomasz Checinski.

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