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arXiv · 1701.02013

Numerically Stable Evaluation of Moments of Random Gram Matrices with Applications

Khalil Elkhalil·Abla Kammoun·Tareq Y. Al-Naffouri·Mohamed-Slim Alouini
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Abstract

This paper is focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

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Khalil Elkhalil, Abla Kammoun, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini. 2017-01-08. Numerically Stable Evaluation of Moments of Random Gram Matrices with Applications. https://doi.org/10.1109/lsp.2017.2731373

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