Timeline for Expectation of $\left| \frac{\textbf{x}^{H} \textbf{y} }{\| \textbf{x} \|^2} \right|^2$, where $\textbf{x}$ and $\textbf{y}$ are complex Gaussians?
Current License: CC BY-SA 4.0
6 events
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| Feb 20, 2019 at 20:34 | comment | added | Synia | If you look for a random variable $Z_N$ s.t. $\mathbb{E}(Z_N^p) = {N\choose p}^{-1}$ for $p\leq N$ and undefined for $p \geq N+1$, you can have it with the ratio of an independent $ \boldsymbol{e}\sim $Exp(1) random variable and $ \gamma_{N + 1}\sim$Gamma($N + 1$) random variable. You can check that $ \mathbb{E}((\boldsymbol{e}/\gamma_{N + 1})^p ) = 1/{N\choose p} $. | |
| Feb 17, 2019 at 15:43 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 17, 2019 at 7:10 | vote | accept | Felipe Augusto de Figueiredo | ||
| Feb 16, 2019 at 18:54 | vote | accept | Felipe Augusto de Figueiredo | ||
| Feb 17, 2019 at 7:10 | |||||
| Feb 16, 2019 at 18:48 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2019 at 18:42 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |