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YCor
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approximating Expectation Approximating expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as:

\begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}\begin{align} E[\operatorname{trace}((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{\operatorname{trace}(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}

approximating Expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as:

\begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}

Approximating expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as:

\begin{align} E[\operatorname{trace}((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{\operatorname{trace}(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}

deleted 242 characters in body; edited title
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hichem hb
hichem hb
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approximating Expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as: \begin{align} E[\frac{{\tilde A\,{{\tilde A}^H}}}{{trace(A\,{A^H})}}] \end{align} \begin{align} E[\frac{A\,{\tilde A\,{{\tilde A}^H}}A^H}{{trace(A\,{A^H})}}] \end{align}

\begin{align} E[B\tilde A\,{{\tilde A}^H}{B^H}]\end{align} and \begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({A^H}A))]\end{align}\begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}

Expectation of the of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as: \begin{align} E[\frac{{\tilde A\,{{\tilde A}^H}}}{{trace(A\,{A^H})}}] \end{align} \begin{align} E[\frac{A\,{\tilde A\,{{\tilde A}^H}}A^H}{{trace(A\,{A^H})}}] \end{align}

\begin{align} E[B\tilde A\,{{\tilde A}^H}{B^H}]\end{align} and \begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({A^H}A))]\end{align}

approximating Expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as:

\begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({B^H}B))]\end{align}

edited body
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hichem hb
hichem hb
  • 377
  • 1
  • 11

Expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix XA $(N, M)$ and $Y(N, K)$$B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as: \begin{align} E[\frac{{\tilde A\,{{\tilde A}^H}}}{{trace(A\,{A^H})}}] \end{align} \begin{align} E[\frac{A\,{\tilde A\,{{\tilde A}^H}}A^H}{{trace(A\,{A^H})}}] \end{align}

\begin{align} E[B\tilde A\,{{\tilde A}^H}{B^H}]\end{align} and \begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({A^H}A))]\end{align}

Expectation of the trace of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix X $(N, M)$ and $Y(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as: \begin{align} E[\frac{{\tilde A\,{{\tilde A}^H}}}{{trace(A\,{A^H})}}] \end{align} \begin{align} E[\frac{A\,{\tilde A\,{{\tilde A}^H}}A^H}{{trace(A\,{A^H})}}] \end{align}

\begin{align} E[B\tilde A\,{{\tilde A}^H}{B^H}]\end{align} and \begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({A^H}A))]\end{align}

Expectation of the of inverse of a Gaussian random matrix combination

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particular case that is defined as. For a given random complex gaussian matrix A $(N, M)$ and $B(N, K)$ Gaussian matrix and constant parameter $\alpha$, where ${\tilde A}$ indicate the Moore–Penrose inverse of $A$. The problem consists to find the expectations defined as: \begin{align} E[\frac{{\tilde A\,{{\tilde A}^H}}}{{trace(A\,{A^H})}}] \end{align} \begin{align} E[\frac{A\,{\tilde A\,{{\tilde A}^H}}A^H}{{trace(A\,{A^H})}}] \end{align}

\begin{align} E[B\tilde A\,{{\tilde A}^H}{B^H}]\end{align} and \begin{align} E[trace((aI + \frac{{\tilde A\,B{B^H}{{\tilde A}^H}}}{{trace(\tilde A\,B{B^H}{{\tilde A}^H})}})({A^H}A))]\end{align}

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hichem hb
hichem hb
  • 377
  • 1
  • 11
Source Link
hichem hb
hichem hb
  • 377
  • 1
  • 11