# Maximum Transmit Power for UE in an LTE Small Cell Uplink
## 4 Performance Evaluation
### Homogenous Macro/Small Cell Deployment  
Firstly, the uniform macro cell deployment was considered as the reference case. The \(P_{\text{max}}\) limit was set to be 23 dBm. The \(P_{o}\) value for both macro and small cells was computed using Equation (2). The pathloss compensation factor \(\alpha_{\text{macro}}\) for the macro cell varied from 0.7 to 1, and the received SIR was obtained using Equation (11), as presented in Figure 5. The trend with an increase in \(\alpha_{\text{macro}}\) can be observed clearly for the UE near the eNodeB (i.e., UE with the index 1), where the received SIR decreased from 10.7 dB to 4.2 dB. Meanwhile, for the UE near the cell edge (i.e., UE with the index 6), the SIR improved from 3.2 dB to 4.2 dB. For lower value of \(\alpha_{\text{macro}}\), the UE near the eNodeB had better SIR, while the cell edge UE suffered from degradation in the SIR and vice versa. This is one of the key objectives, to use the FPC to improve the average cell performance at the cost of the degradation in the cell edge UE's performance. On the other hand, the convergence of all SIR values for \(\alpha_{macro}=1\) specifies the advantages of full pathloss compensation, where all users have the same SIR regardless of their position in the cell. The coverage of a base station is defined as the area where the received SIR by the UE reaches a certain value for a given outage probability. The generic impact of shadowing and fading on outage probability for the macro cell users with a pathloss coefficient \(\eta=3.5\) was studied by following the  
Figure 5: SIR as a function of \(\alpha_{\text{macro}}\) in the homogenous macro cell deployment. recommendations in Reference [35], as this was not the focus of our work. To see the impact of shadowing and fading on the system performance, the outage probability for the system using a fluid model is depicted in Figure 6. The outage probability was plotted as a function of received SIR at the cell edge UE in the case of the macro cell only i-e at \(r=R_{\mathrm{macro}}\). Figure 6 shows that without shadowing and fading, the received SIR of the cell edge UE reaches \(-3\) dB. As there was no random variation in the signal propagation, this value was deterministic, that is, the outage was \(0\%\) up to \(-3\) dB and \(100\%\) for higher values of received SIR. In presence of shadowing (\(\sigma=3\) dB) only, the received SIR reached \(-9\) dB with an outage probability of \(10\%\). However, when the impact of fading was also considered along with the shadowing, the received SIR reached only \(-15\) dB for the same outage probability. As the received SIR highly depends on the position and number of the UE in the cell and the environment, that is, the shadowing, power control parameters, cell dimensions, and the type of environment (e.g., urban or rural), such results are helpful for the network operators while admitting or rejecting new connections according to the specific environment for the new entering UE. As in this work our focus was to find the upper bound for the transmit power \(P_{\mathrm{max}}\) for the UE rather than the actual transmit power, therefore, the impact of shadowing and fading was not taken into consideration. However, the analysis of the impact of shadowing and fading on the system performance while setting the actual uplink transmit power for the small cell uplink will be considered in detail in our future work. Secondly, a uniform small cell deployment was considered by adopting similar conditions as in the macro cell case. The cell size reduction resulted in an increase in the interference level, as the interfering UE come closer to each other. It can be seen in Figure 7 that the performance for all UE was degraded compared to Figure 5. This indicates that the network interference was more dominant. For lower value of \(\alpha_{\mathrm{small}}\), the UE near the eNodeB could not achieve enough SIR gain while the cell edge UE suffered from a significant degradation in the SIR.