# Energy Efficient Access Point Placement for Distributed Massive MIMO
## 4 Simulation Results
### Different Channel Models  
This section assesses Q4 and Q5. We analyze the value of environment information regarding channel gain for the AP placement optimization. We also compare our proposed channel models with the Euclidean distance-based model, which is commonly used in the literature. We consider a four-AP D-mMIMO system and four channel models discussed in Section 3. The heatmaps for the received power simulated via the RTS when using the AP placement generated by the different channel models for map 5 are illustrated in Figure 13. The heatmaps suggest that the Euclidean distance-based model, which represents the commonly applied model in the literature, generates a low-quality AP placement compared with the other models. The main reason here is that the Euclidean distance-based model ignores the building blocks when estimating the angle of departure for the arrays. Figure 13 demonstrates that environment information is very important when considering the radiation pattern of the arrays. Figure 12: Significance of considering radiation pattern for AP placement optimization. The average relative power saving when generating AP placements considering the radiation pattern compared with the situation where we do not consider the radiation pattern, using patch antennas. The average relative power saving when using the shortest path-based model, angular penalty-based model, and the RTS-based model compared with the Euclidean distance-based model over all the maps is illustrated in Figure 14. The result in Figure 14, for example, corresponds to the scenario where we use isotropic antennas. In general, the power saving in Figure 14 is higher when using patch antennas instead of isotropic antennas. This is consistent with the results in Figure 13. Additionally, Figure 14 indicates that the setup generated via the RTS-based model requires the least power compared with the setups found with other models (for all the scenarios). It saves around 20 dB compared with the Euclidean distance-based model. This is expected given that the RTS-based model is regarded as the ground truth in this paper. It accurately captures  
Figure 13: Heatmaps of the RTS-simulated received signal power at user locations when using the optimal AP placements generated using different channel models for map 5, using patch antennas. The red spots are the APs. The orange spots are the user locations that receive the overall lowest signal power. (**a**) Euclidean distance-based model; (**b**) Shortest path-based model; (**c**) Angular penalty-based model; (**d**) RTS-based model. environment information. The results further confirm the importance of considering environment information regarding channel gain for the AP placement optimization. As mentioned in Table 3, the RTS-based model requires around 1000-2000 s to evaluate all the channels for each AP placement in a simplified coverage region. Table 4 lists the average time that is required for different channel models to evaluate the channels for all the possible AP placements in a simplified coverage region. As shown in Table 4, the RTS-based model requires very long computational time. Therefore, it is interesting to consider the other models for the AP placement optimization. The two graph-based models: the shortest path-based model and the angular penalty-based model are proposed in this work. These models take around one minute to generate the average channel gain \(\widehat{\beta}_{il}\) for all the possible AP locations. As suggested by Figure 14, using the AP placements generated via the two graph-based models, particularly, the angular penalty-based model, power saving is achieved compared with the Euclidean distance-based model in most situations. The average relative power saving of using the angular penalty-based model is around 5 dB compared with the Euclidean distance-based model. This is consistent with the fact that the two graph-based models contain more environment information than the Euclidean distance-based model.