a note on functional averages over gaussian ensembles
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2013
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Abstract
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.
| Reference Key |
tucci2013journala
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|---|---|
| Authors | ;Gabriel H. Tucci;Maria V. Vega |
| Journal | nature protocols |
| Year | 2013 |
| DOI |
10.1155/2013/941058
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| URL | |
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