# Energy-Efficient On-Off Power Control of Femto-Cell Base Stations for Cooperative Cellular Networks
## 4 Performance Evaluation  
In this section, the performance of our proposed on-off power control scheme is evaluated through a simplified system level simulator based on Matlab. In the performance evaluation, we assume that \(N\) FBSs are randomly deployed and they transmit data using CoMP to one MS which is located at the center, i.e., \(K=1\). Moreover, we assume that the maximum and the minimum distance between the FBS and MS are 50 m and 30 m, respectively. For path loss model, we used the IMT-R M.2135 urban macro model [33], i.e., \(G_{i,j}=34.5+38\log_{10}(d_{i,j})\), where \(d_{i,j}\) is the distance between MS \(i\) and FBS \(j\). Moreover, we assume that noise density is \(-174\) dBm\(/\)Hz, bandwidth is 10 MHz, \(I_{inter}=-70\) dBm, \(M=5\), and the transmit power of FBS is 23 dBm. In addition, we assume that the channel experiences the fast fading which is modeled as a CSCG with mean 0 and variance 1. The simulation parameters are summarized in Table 1.  
In Figures 4 and 5, we show the number of active FBSs, \(\mid\mathbb{A}\mid\), and the spectral efficiency of our proposed scheme by varying \(N\) and \(\epsilon\), which corresponds to the threshold for switching-off. Note that the number of active FBSs is proportional to the power consumption of GCN, i.e., more power can be saved when the number of active FBSs is small. As can be seen from Figure 4, the number of active FBSs decreases as \(\epsilon\) decreases because FBSs are easier to be turned off. However, given that more FBSs are turned off, which results in the deterioration of cooperative transmission, the spectral efficiency decreases as \(\epsilon\) decreases, as can be checked from Figure 5. It is worth noting that the spectral efficiency is high when \(N\) is high, e.g., \(N=50\), because more FBSs participate in the cooperative transmission. Finally, we can observe that the variation of performance by varying \(\epsilon\) is more abrupt when \(N\) is high. For example, the number of active FBSs when \(N=50\) decreases by 80% while that when \(N=5\) decreases by 45%. Moreover, the spectral efficiency when \(N=50\) decreases by 30% while that when \(N=5\) decreases by 20%. It is due to the fact that only a few number of FBSs dominate the performance of cooperative transmission even though a large number of FBSs participate in the transmission, such that many FBSs can be turned off without sacrificing the performance of cooperative transmission. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Transmit power of FBS & 23 dBm \\ Noise variance & \(-174\) dBm\(/\)Hz [29] \\ Channel bandwith & 10 MHz \\ \(M\) & 5 \\ \(K\) & 1 \\ Maximum distance between FBS and MS & 50 m \\ Minimum distance between FBS and MS & 30 m \\ \(I_{inter}\) & \(-70\) dBm \\ Path-loss model & \(34.5+38\log_{10}(d)\)[33] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters, FBS: femto-cell base stations; MS: mobile station. Figure 4: Number of active FBSs vs. \(\epsilon\) by varying \(N\). The relative power consumption which is the ratio of power consumption with and without our proposed scheme, and spectral efficiency of our proposed scheme are depicted in Figures 6 and 7. In the simulation, we assume that \(R_{thr}=\sigma\mathbb{E}\left[R_{i}(\mathbb{N})\right]\), such that \(\sigma\) represents the tolerable deterioration of spectral efficiency caused by FBS shutdown, i.e., more FBSs can be turned off when \(\sigma\) is low. For comparison, we have also evaluated the performance of FBS shutdown based on problem (3), which is denoted as ES. It should be noted that the performance of ES can be found by exhaustive search, which requires a huge number of computations as will be explained later. Moreover, the performance of our proposed scheme is denoted as Prop and \(R_{thr}\) is denoted as Thr. Finally, in our proposed scheme, the value of \(\epsilon\) is adjusted in order not to deteriorate the spectral efficiency of cooperative transmission below \(R_{thr}\).