Perturbed Laguerre unitary ensembles,Hankel determinants,and information theory |
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Authors: | Estelle Basor Yang Chen |
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Affiliation: | 1. American Institute of Mathematics, Paolo Alto, USA;2. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau |
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Abstract: | This article investigates a key information‐theoretic performance metric in multiple‐antenna wireless communications, the so‐called outage probability. The article is partly a review, with the methodology based mainly on [10], while also presenting some new results. The outage probability may be expressed in terms of a moment generating function, which involves a Hankel determinant generated from a perturbed Laguerre weight. For this Hankel determinant, we present two separate integral representations, both involving solutions to certain non‐linear differential equations. In the second case, this is identified with a particular σ‐form of Painlevé V. As an alternative to the Painlevé V, we show that this second integral representation may also be expressed in terms of a non‐linear second order difference equation. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | 15B52 34M55 |
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