A Note on Functional Averages over Gaussian Ensembles
We find a new formula for matrix averages over the Gaussian ensemble. Let H be an n×n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n×n positive definite matrix A and a continuous function f:ℝ+→ℝ such that ∫0∞e-αt|f(t)...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2013/941058 |
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| author | Gabriel H. Tucci Maria V. Vega |
| author_facet | Gabriel H. Tucci Maria V. Vega |
| author_sort | Gabriel H. Tucci |
| collection | DOAJ |
| description | We find a new formula for matrix averages over the Gaussian ensemble. Let H be an n×n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n×n positive definite matrix A and a continuous function f:ℝ+→ℝ such that ∫0∞e-αt|f(t)|2dt<∞ for every α>0, we find a new formula for the expectation
𝔼[Tr(f(HAH*))]. Taking f(x)=log(1+x) gives another formula for the capacity of the MIMO communication channel, and taking f(x)=(1+x)-1 gives the MMSE achieved by a linear receiver. |
| format | Article |
| id | doaj-art-2c4c8f516bb14199aa211f381beddae7 |
| institution | OA Journals |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-2c4c8f516bb14199aa211f381beddae72025-08-20T02:38:49ZengWileyJournal of Probability and Statistics1687-952X1687-95382013-01-01201310.1155/2013/941058941058A Note on Functional Averages over Gaussian EnsemblesGabriel H. Tucci0Maria V. Vega1Bell Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USAWilliam Paterson University, Mathematics Department, 300 Pompton Road, Wayne, NJ 07470, USAWe find a new formula for matrix averages over the Gaussian ensemble. Let H be an n×n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n×n positive definite matrix A and a continuous function f:ℝ+→ℝ such that ∫0∞e-αt|f(t)|2dt<∞ for every α>0, we find a new formula for the expectation 𝔼[Tr(f(HAH*))]. Taking f(x)=log(1+x) gives another formula for the capacity of the MIMO communication channel, and taking f(x)=(1+x)-1 gives the MMSE achieved by a linear receiver.http://dx.doi.org/10.1155/2013/941058 |
| spellingShingle | Gabriel H. Tucci Maria V. Vega A Note on Functional Averages over Gaussian Ensembles Journal of Probability and Statistics |
| title | A Note on Functional Averages over Gaussian Ensembles |
| title_full | A Note on Functional Averages over Gaussian Ensembles |
| title_fullStr | A Note on Functional Averages over Gaussian Ensembles |
| title_full_unstemmed | A Note on Functional Averages over Gaussian Ensembles |
| title_short | A Note on Functional Averages over Gaussian Ensembles |
| title_sort | note on functional averages over gaussian ensembles |
| url | http://dx.doi.org/10.1155/2013/941058 |
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