# Energy Efficient Access Point Placement for Distributed Massive MIMO
## 4 Simulation Results
### Reducing Potential User Locations  
The generated user locations are one meter apart, as mentioned in Section 2. The total number of the generated user locations is large. Considering a 100 m by 100 m coverage region, for example, the total number of the user locations within the coverage region is more than 5000, which results in a long computational time when running the RTS to validate the AP placements. This motivates us to find a way of reducing the total number of user locations. We hypothesize that, for a given user location that is fully surrounded by eight user locations, the user location will surely receive sufficient power if the other eight locations have received sufficient power. This implies that we only need to consider the signal coverage for locations that are not fully surrounded by other locations. The user locations, which are either next to a building or on a boundary of the considered coverage region, are the essential user locations. To test this hypothesis, we calculate the total required transmit power via the RTS-based model using a four-AP D-mMIMO system for 10 randomly generated AP placements. Two antenna types and two maps are considered. The targeted signal coverage level is 100%. The result of this simulation is illustrated in Figure 8, where a full coverage region means that all the user locations are included, while a simplified coverage region only includes essential user locations. Figure 9 gives an example for the heatmaps of the average received signal power \(\widetilde{p}_{\tt R_{i}}\) in dBm at each location when considering an AP placement on map 1. The red spots in Figure 9 represent the APs, and the orange spot indicates the user \begin{table}
\begin{tabular}{l l l} \hline \hline \multirow{3}{*}{General:} & Minimum required transmit power (\(P_{\tt MIN}\)) & \(-94\) dBm \\  & Center frequency & \(2.6\) GHz \\  & Total number of antennas in the system & 128 \\  & Signal coverage levels (\(V\)) & \(100\%\),..., 91\% and 90\% \\ \hline \multirow{3}{*}{RTS:} & Height of each AP & \(30\) m \\  & Height of each user location & \(1.5\) m \\ \cline{1-1}  & Bandwidth & \(100\) MHz \\ \cline{1-1}  & Total number of sub-carrier frequencies & \(10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings. Figure 7: The procedure for executing the experiments with different channel models. location that receives the overall lowest power. The results in Figures 8 and 9 confirm that the total transmit power and the user location that receives the overall lowest power for each AP placement remain very similar when we consider a full coverage region or simplified coverage region. This implies that most of the essential locations have been included in the simplified coverage regions. The required computational time is given in Table 3, demonstrating that the simplified coverage region results in a 4 to 8 times lower computational time compared to the full one. Therefore, we use the simplified coverage regions approach in RTS experiments and when solving Formulations (6)-(9). Figure 8: Comparison between the full coverage region and simplified coverage region regarding the total required transmit power. When considering a full coverage region or a simplified one, the total transmit power simulated via the RTS is very similar. This confirms that the simplified coverage region contains the user locations which receive the overall lowest channel gain. (**a**) Map 1; (**b**) Map 5. Figure 9: Comparison between the full coverage region and simplified coverage region regarding the heatmaps of the average received signal power at user locations. The red spots are the APs. The orange spots are the user locations that receive the overall lowest signal power. (**a**) Full; (**b**) Simplified. Figure 10 illustrates the simplified coverage regions for the five maps, generated as follows. The data of a selected region is exported from OpenStreetMap. The RTS is used to generate the coverage region, adding 2 m's padding around each map for easier processing of the buildings on the map.