\documentclass[border=5pt]{standalone}
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\usepackage{tikz}
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\usepackage{xcolor}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
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ymode=log,
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height = 0.4\columnwidth,
scale only axis,
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table[row sep=crcr]{
1 2\\
};\label{plot1}
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table[row sep=crcr]{
1 2\\
};\label{plot2}
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y filter/.code={\pgfmathparse{\pgfmathresult-0}\pgfmathresult}]
table[row sep=crcr]{
1 2\\
};\label{plot_UBMSEP_BB}
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y filter/.code={\pgfmathparse{\pgfmathresult-0}\pgfmathresult}]
table[row sep=crcr]{
1 2\\
};\label{plot_UBMSEP_Ex}
\node [draw,fill=white,font=\tiny,anchor= south west] at (axis cs: -10,1.8e-3) {
\setlength{\tabcolsep}{0.5mm}
\renewcommand{\arraystretch}{.8}
\begin{tabular}{l}
\ref{plot1}{Exhaustive Search using the MMDDT criterion} \\
\ref{plot2}{Exhaustive Search using the MMSE criterion}\\
\ref{plot_UBMSEP_BB}{Proposed UBMSEP B\&B}\\
\ref{plot_UBMSEP_Ex}{Exhaustive Search using the UB-MSEP criterion}\\
\end{tabular}
};
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\end{tikzpicture}
\end{document}