## 5 Simulation Results and Discussion  
This section shows and discusses the results of extensive computer simulations which are conducted in accordance with the system setup explained in Section 2. The simulation parameters are shown in Table 1.  
Obviously, as the half duplex systems suffer less interference, and hence requires less transmit power for achieving certain SINR, the full duplex; on the other hand, it requires less bandwidth to achieve the same SINR. Therefore, a general metric that measures the overall performance is required for a fair comparison between full duplex based system and half duplex based system. The energy efficiency (EE) in terms of bits per Hz per joule (bits/Hz/J) measures the overall performance of a given system as it simultaneously takes into account both the effect of the bandwidth and the effect of the transmit power. Figures 3 and 4 show the cumulative density function (CDF) of EE for half duplex based system and full duplex based system with the two schemes introduced in this paper, FD system with separate power constraint and FD system with joint power constraint. All systems have been tested under different target SINR averages in two network sizes; 12-cell network and 36-cell network. Looking carefully at the figures, the following are remarkable:  
* In all cases, the EE of the full duplex schemes outperforms that of the half duplex scheme. In fact, the 97% confidence interval of the EE average in (bits/Hz/J) for all tested schemes are (when the target SINR is 100 in a 12-cell network. ):
* FD scheme with separate power constraint: \((1.1187,1.8324)\)\(10^{8}\),
* FD scheme with joint power constraint: \((1.1222,1.8360)\)\(10^{8}\),
* hald duplex scheme: \((0.7071,1.1342)\)\(10^{8}\). * There is no significant difference between the two kinds of full duplex schemes introduced in this paper due to the fact that they both operate in intense interference dominant regime. * As the average target SINR increases, the gap between the full duplex EE and half duplex EE diminishes. This is because each transmitter is likely to radiate more power to be able to achieve higher SINR, and hence decreasing the EE. Figures 5 and 6 show the CDF of the average transmit power under different average target SINRs in a 12-cell network and a 36-cell network, respectively. In Figure 6, for example, the average transmitted power exceeds 0.1 Watt %40 of the time when the average target SINR is 100. On the other hand, when the average target SINR is 8, the average transmitted power exceeds 0.1 Watt only %3 of the time. Therefore, the phenomenon of diminishing EE can be further justified as follows. As illustrated in Figures 5 and 6, when the system tries to achieve a set of higher SINRs, the transmit power of all transmitters tend to increase. This will increase the amount of interference in the whole network, which in turn causes the actual SINR growth to diminish. * Comparing Figures 5 and 6, it is observable that, as the network size increases, the average transmit power increases as well. This can be interpreted as follows. The intercell interference amount increases with the number of cells, which in turn shifts the equilibrium point (the best vector of the transmit powers) into a higher profile. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Unit** \\ \hline System frequency & 2 & GHz \\ System bandwidth & 5 & MHz \\ No. of data subchannels & 300 & – \\ Subchannel bandwidth & 15 & KHz \\ small cell radius & 20 & m \\ \(p_{max}^{d}\) and \(p_{max}^{u}\) & 30 & dBm \\ Noise power spectral density & \(-174\) & dBm/Hz \\ Path loss model & \(37.1+30\text{log}(d)\) & dB \\  & \(d\): distance in \(m\) & \\ Shadow fading deviation & 8 & dB \\ Small scale fading & Rayleigh fading & – \\ Number of replications & 350 & – \\ \(\kappa\) and \(\beta\) & \(-80\) & dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters.