## 5 Performance Evaluation and Comparison
### Optimal Value of L and Performance Comparison with 5G Mobile Network Requirements  
We define an optimal value of L as the value of L that can satisfy both the spectral efficiency and energy efficiency requirements for 5G networks, which can be found as follows. Let for any spectrum sharing technique \(SS\in\left[\text{DedA},\text{DySP},\text{ StSR},\text{ LSA},\text{ LAA}\right]\), \(\sigma_{L}^{\text{SE}}\) and \(\sigma_{L}^{\text{EE}}\), respectively, denote the spectral efficiency and the energy efficiency for any value of \(L\in_{>0}\). Let \(\sigma_{\text{5G}}^{\text{SE}}\) and \(\sigma_{\text{5G}}^{\text{EE}}\) denote the minimum spectral efficiency and energy efficiency requirements for 5G mobile systems. An optimal value of L can be found for any spectrum sharing technique \(SS\) by solving the following optimization problem:  
\[\begin{array}{ll}\min&L\\ \text{subject to:}&\text{(a)}\ \forall L\sigma_{L}^{\text{SE}}\geq\sigma_{ \text{5G}}^{\text{SE}}\\ &\text{(b)}\ \forall L\sigma_{L}^{\text{EE}}\leq\sigma_{\text{5G}}^{\text{EE}} \end{array} \tag{60}\]  
An optimal value of \(L\), i.e., \(L^{*}\), for all \(SS\) can be found as follows:  
\[L^{*}=\begin{cases}56,&\text{for}\ SS=\text{DedA}\\ 30,&\text{for}\ SS=\text{DySP}\\ 54,&\text{for}\ SS=\text{StSR}\\ 28,&\text{for}\ SS=\text{LSA}\\ 5,&\text{for}\ SS=\text{LAA}\end{cases} \tag{61}\]  
For the 5G mobile system, it is expected that an average spectral efficiency of \(\sigma_{\text{5G}}^{\text{SE}}=24-\ 37\text{bps}/\text{Hz}\)[32] and energy efficiency of \(\sigma_{\text{5G}}^{\text{EE}}=3\ \text{\mu J}/\text{b}\)[32; 33] need to be satisfied. Now, using Figure 10, Table 4 shows the minimum values of \(L\) for any \(SS\in\left[\text{DedA},\text{DySP},\text{ StSR},\text{ LSA},\text{ LAA}\right]\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Spectrum Sharing Technique (SS)**} & \multicolumn{2}{c}{**\(L\) (To Meet the 5G Mobile System Requirements)**} \\ \cline{2-4}  & **Spectral Efficiency** & **Energy Efficiency (\(\text{\mu J}/\text{b}\))** & **Both Spectral and** \\  & **(bps/Hz/cell)** & **Energy Efficiency (\(\text{\mu J}/\text{b}\))** & **Energy Efficiencies (\(L^{*}\))** \\ \hline Dedicated access & 56 & 2 & 56 \\ \hline CoPSA (DySP) & 30 & 1 & 30 \\ \hline CoPSA (StSR) & 54 & 2 & 54 \\ \hline LSA & 28 & 1 & 28 \\ \hline LAA & 5 & 1 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Minimum values of \(L\) to satisfy 5G mobile system requirements.  
Hence, from Table 4, it can be found that an optimal value of \(L\) that can satisfy both \(\sigma_{\rm{SG}}^{\rm{SE}}\) and \(\sigma_{\rm{SG}}^{\rm{EE}}\) for any \(SS\in[\rm{DedA},\rm{DySP},\)\(\rm{StSR},\)\(\rm{LSA},\rm{LAA}]\) are given respectively by 56, 30, 54, 28, and 5.  
So, based on the above solution and proof to find an optimal value of \(L\) for all \(SS\), the spectral efficiency and energy efficiency requirements for 5G mobile systems (i.e., \(\sigma_{\rm{SG}}^{\rm{SE}}=24-37\rm{bps}/\rm{Hz}\)[32] and \(\sigma_{\rm{SG}}^{\rm{EE}}=3\)\(\rm{\upmu}/\rm{b}\)[32; 33] respectively) can be easily met by employing each of the realized spectrum sharing technique. More specifically, unlike the spectral efficiency (SE) requirement, the EE requirement for the 5G can be easily met with a low value of \(L\) such that the density of small cells, i.e., an optimal value of \(L\) can be defined solely by the spectral efficiency requirement for the 5G mobile networks to satisfy both the spectral efficiency and energy efficiency requirements.