# A Practical Resource Management Scheme for Cellular Underlaid D2D Networks
## 5 Numerical Results
It is shown that the average sum-rates of the proposed scheme approach the optimal values for entire SNR values and they are almost optimal in a practical region of SNR such as \(0\text{--}20\ \text{dBm}\). Figure 4: Average sum-rates when all channels are _i.i.d._, \(N=10\), and \(I^{\prime}_{\text{th}}=0\) or 5 dB. Figure 3: Average sum-rates when all channels are _i.i.d._, \(N=5\), and \(I^{\prime}_{\text{th}}=0\) or 5 dB. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(N=5\)} & \multicolumn{6}{c}{\(N=10\)} \\ \cline{2-13}
**SNR (dB)** & \multicolumn{3}{c}{\(I^{\prime}_{\text{th}}=0\) dB} & \multicolumn{3}{c}{\(I^{\prime}_{\text{th}}=5\) dB} & \multicolumn{3}{c}{\(I^{\prime}_{\text{th}}=0\) dB} & \multicolumn{3}{c}{\(I^{\prime}_{\text{th}}=5\) dB} \\ \cline{2-13}  & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** \\ \hline \(-10\) & 0.47 & 0.48 & 99.5\% & 0.48 & 0.48 & 99.8\% & 0.75 & 0.79 & 94.7\% & 0.77 & 0.78 & 98.3\% \\ \(-6\) & 0.75 & 0.82 & 91.3\% & 0.86 & 0.86 & 99.1\% & 1.03 & 1.24 & 82.8\% & 1.24 & 1.30 & 95.3\% \\ \(-2\) & 0.93 & 1.09 & 85.5\% & 1.25 & 1.34 & 93.8\% & 1.24 & 1.58 & 78.2\% & 1.61 & 1.90 & 84.8\% \\ \(2\) & 0.96 & 1.12 & 86.0\% & 1.44 & 1.66 & 86.6\% & 1.31 & 1.66 & 79.1\% & 1.80 & 2.29 & 78.5\% \\ \(6\) & 0.78 & 0.86 & 91.6\% & 1.38 & 1.63 & 84.9\% & 1.16 & 1.37 & 84.8\% & 1.77 & 2.27 & 77.9\% \\ \(10\) & 0.48 & 0.51 & 94.8\% & 1.07 & 1.20 & 89.0\% & 0.81 & 0.89 & 90.7\% & 1.52 & 1.87 & 81.1\% \\ \(14\) & 0.21 & 0.22 & 98.1\% & 0.67 & 0.72 & 93.6\% & 0.45 & 0.47 & 95.4\% & 1.03 & 1.18 & 86.9\% \\ \(18\) & 0.10 & 0.10 & 97.8\% & 0.32 & 0.33 & 98.6\% & 0.22 & 0.22 & 99.8\% & 0.57 & 0.60 & 95.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average sum-rates when all channels are _i.i.d._  
Figure 5: Optimal threshold in the proposed scheme when all channels are _i.i.d._, \(N=5\), and \(I^{\prime}_{\text{th}}=0\) or \(5\) dB. Figure 6: Optimal threshold in the proposed scheme when all channels are _i.i.d._, \(N=10\), and \(I^{\prime}_{\text{th}}=0\) or \(1\) dB. Figure 8: Average sum-rates when all channels are non-_i.i.d._ and \(N=10\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(N=5\)} & \multicolumn{6}{c}{\(N=10\)} \\ \cline{2-13}
**P (dBm)** & \multicolumn{2}{c}{\(I_{\text{th}}=-80\) dBm} & \multicolumn{2}{c}{\(I_{\text{th}}=-50\) dBm} & \multicolumn{2}{c}{\(I_{\text{th}}=-80\) dBm} & \multicolumn{2}{c}{\(I_{\text{th}}=-50\) dBm} \\ \cline{2-13}  & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** & **Prop** & **Opt** & **Ratio** \\ \hline
0 & 1.74 & 1.75 & 99.7\% & 1.75 & 1.75 & 99.7\% & 3.25 & 3.29 & 98.7\% & 3.20 & 3.24 & 98.8\% \\
4 & 2.39 & 2.41 & 99.4\% & 2.41 & 2.42 & 99.4\% & 4.32 & 4.41 & 98.0\% & 4.29 & 4.38 & 98.1\% \\
8 & 3.14 & 3.17 & 99.1\% & 3.17 & 3.20 & 99.0\% & 5.46 & 5.62 & 97.3\% & 5.46 & 5.62 & 97.2\% \\
12 & 3.92 & 3.98 & 98.5\% & 3.96 & 4.03 & 98.4\% & 6.54 & 6.80 & 96.2\% & 6.59 & 6.85 & 96.2\% \\
16 & 4.59 & 4.70 & 97.8\% & 4.71 & 4.83 & 97.6\% & 7.42 & 7.82 & 94.9\% & 7.55 & 7.94 & 95.2\% \\
20 & 5.07 & 5.26 & 96.4\% & 5.34 & 5.52 & 96.6\% & 8.05 & 8.57 & 93.9\% & 8.29 & 8.82 & 94.0\% \\
24 & 5.30 & 5.59 & 94.8\% & 5.80 & 6.07 & 95.5\% & 8.15 & 8.97 & 90.8\% & 8.79 & 9.46 & 92.9\% \\
28 & 5.10 & 5.62 & 90.7\% & 6.10 & 6.46 & 94.4\% & 7.73 & 8.95 & 86.4\% & 9.09 & 9.89 & 92.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average sum-rates when all channels are non-_i.i.d._  
Figure 7: Average sum-rates when all channels are non-_i.i.d._ and \(N=5\).