# Energy Efficient Underlaid D2D Communication for 5G Applications
## 3 Proposed Modified Derivative Algorithm
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline K (no of bands) & 5 \\ Wi (bandwidth of ith band) & 25 MHz \\ \(\alpha\) (Path loss exponent) & 4.1 \\ e\({}_{\text{c}}\),i (cellular probability for ith band) & 0.1 \\ e\({}_{\text{d}}\),i (D2D probability for ith band) & 0.1 \\ Tc\({}_{\text{c}}\),i (cellular threshold for ith band) & 0 dB \\ Td\({}_{\text{i}}\) (D2D threshold for ith band) & 0 dB \\ \([\text{R}_{\text{c,00,1}}\,,\,\text{R}_{\text{c,00,2}}\,,\ldots,\text{R}_{\text {c,00,5}}]\) & [60,80,100,120,140] m \\ \([\text{R}_{\text{d,00,1}}\,,\,\text{R}_{\text{d,00,2}}\,,\ldots,\text{R}_{\text {d,00,5}}]\) & [20,20,20,20,20] m \\ \([\lambda_{\text{c,1}}\,,\,\lambda_{\text{c,2}}\,,\ldots,\lambda_{\text{c,5}}]\) & [10,1,10,10,10]\(\times\)\(\lambda_{\text{c,ref}}\) \\ \([\lambda_{\text{d,1}}\,,\,\lambda_{\text{d,2}}\,,\,\ldots,\,\lambda_{\text{d,5}}]\) & [10,1,10,10,10]\(\times\)\(\lambda_{\text{d,ref}}\) \\ D\({}_{\text{p}}\) (total transmission power of D2D users) & 65 mW \\ D\({}_{\text{p,i,up}}\) & 25 mW \\ \(\epsilon\) (tolerance) & \(1.5\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters by using the modified derivative algorithm. Figure 4: The energy efficiency of D2D users with the reference density of cellular users by using the derivative algorithm. Figure 6 shows the energy efficiency of D2D users versus the reference density of cellular users by using the modified derivative algorithm. We assumed an uplink environment where 5 multiple bands of the spectrum with a bandwidth 25 MHz are shared by cellular and device users and \(\lambda_{\text{d,ref}}=10^{-4}\), \(\lambda_{\text{c,ref}}=10^{-5}\). We were able to observe that EE decreases with an increase in the reference density of cellular users if the D2D user's reference distances of 15 m, 20 m, and 25 m are fixed. We were aware that the severity of the channel fading worsens with distance, causing a fall in signal-to-interference ratio. As a result, the average sum rate declines, which lowers the EE. Figure 5: The energy efficiency of D2D users versus the reference density of D2D users by using the modified derivative algorithm. Figure 6: The energy efficiency of D2D users against the reference density of cellular users by using the modified derivative algorithm. Table 3: Simulation parameters by using the modified derivative algorithm with different parameters. Figure 7 shows the energy efficiency of D2D users versus the reference density of cellular users by using the modified derivative algorithm with different parameters. From Figure 7 we assumed an uplink environment where 8 multiple bands of the spectrum with a bandwidth of 25 MHz are shared by cellular and devices users and \(\lambda_{\text{d,ref}}=10^{-4}\), \(\lambda_{\text{c,ref}}=10^{-5}\); we were able to observe that EE decreases with an increase in the reference density of cellular users if the D2D user's reference distances of 15 m, 20 m, and 25 m are fixed. We were aware that the severity of the channel fading worsens with distance, causing a fall in signal-to-interference ratio. As a result, the average sum rate declines, which lowers the EE. Figure 8 shows the energy efficiency of D2D users versus the reference density of D2D users by using the modified derivative algorithm with different parameters. We assumed an uplink environment where 8 multiple bands of the spectrum with a bandwidth of 25 MHz are shared by cellular and device users and \(\lambda_{\text{d,ref}}=10^{-4}\), \(\lambda_{\text{c,ref}}=10^{-5}\). As the