# BER Aided Energy and Spectral Efficiency Estimation in a Heterogeneous Network
## 3 Test Results  
The above presented analytical model is implemented in software by using an ns3 network simulator. The goal of the preliminary tests' results is just the verification of the presented concept, whereas the comprehensive follow-up tests can be repeated as many times as needed. Five rounds of according simulations were made, with the \(BER\) results, in particular, enhanced by statistical data averaging. Both \"native\" SINR and the BER-based one were estimated by simulation.  
The three considered scenarios were tested, with the following parameters each:  
* single-tier, 5 macro BSs, BS power: 40 W;
* single-tier 250 pico BSs, BS power: 0.25 W;
* two-tier 5 macro and 250 pico BSs.  
The set-up data for the simulation are presented in Table 1.  
The obtained simulation results for BER, SINR, SE, and EE are presented in Table 2, giving rise to the SE graphs presented in Figure 6 as a function of the instantaneous transmit powers \(P_{1}^{\text{tx}}\) and \(P_{2}^{\text{tx}}\) ratio for the various exemplar scenarios considered here.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Value** \\ \hline Maximal size (\(L\)) of LTE code-block & 6144 Bytes \\ Count of macro cell BSs & 5 \\ Maximal output transmit power of macro-cell BS & 40 W \\ Maximal output transmit power of small-cell BS & 250 mW \\ Count of small-cell BSs & 250 \\ Population density per m\({}^{2}\) & 3.8\(\cdot 10^{-4}\) \\ Maximal distance between BSs in macro cell & 500 m \\ Maximal distance between BSs in small cell & 50 m \\ Count of resource blocks with LTE 5 MHz channel bandwidth & 25 \\ Center of frequency operating band & 2.1 GHz \\ LTE channel bandwidth & 5 MHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters in ns3 simulations.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(BER\) & SINR & \(SE\) [b/s/Hz] & \(EE\) [b/J] \\ \hline
0.0378 & 11.98 & 17.28 & 0.53 \\
0.0550 & 11.06 & 15.96 & 1.04 \\
0.0659 & 10.55 & 15.22 & 1.65 \\
0.0813 & 9.86 & 14.22 & 3.09 \\
0.0921 & 9.45 & 13.63 & 4.45 \\
0.0996 & 9.16 & 13.22 & 5.75 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation results (after averaging).  
Figure 6: Spectral efficiency vs. relative transmitted power and cell range expansion bias (theta).  
Coming out of the presented curves, it is evident that the SE of the entire HetNet of interest grows exponentially with the transmit power ratio, when small cells are implemented surrounding a typical macro cell.  
However, it is quite different when a single macro tier is to be considered, where the SE is not affected by the transmitting power ratio. Therefore, more picocells in the network necessarily imply higher spectral efficiency, which complies to the expected values coming out of the proposed analytical model.  
Accordingly, the diagrams in Figure 7a,b represent \(SE\) and \(EE\), respectively, resulting from simulations of the three above-reviewed scenarios and parameters' values in Table 1.  
In both the above diagrams, it can be seen that the two-tier setup scenario yielded the top efficiencies.  
Furthermore, the small-cell scenario (250 pico BSs) came out to be more efficient than what was achieved with macro cells (5 BSs), while still with an unchanged users' layout and count.  
Finally, considering various transmit power values within the pico tier with constant macro-tier transmit power, \(SE\) exhibits a rising trend with regard to the transmit powers.