# Energy Efficient Access Point Placement for Distributed Massive MIMO
## 5 Conclusions  
In this paper, we focus on reducing the transmit power of a D-mMIMO system by optimizing the AP placement. Although we have only considered the downlink, given the reciprocity between downlink and uplink, the optimized AP placement will also relax transmit power requirements for the users. We formulate the AP placement problem as a combinatorial optimization problem. A simplified coverage region is applied, which results in significantly less computational time while having little impact on the solutions. With this approach, we have analyzed the performance of the D-mMIMO using an RTS-based model for optimizing the AP placement. Different antenna types and signal coverage levels are considered. Our results have demonstrated the significance of environment information, feasible locations for deploying APs and radiation patterns, which are commonly neglected in the existing studies. The consideration of the radiation pattern leads to a power saving of around 15-24 dB. Furthermore, using four APs instead of one or two APs in the system brings a power saving of more than 22 dB and 9 dB, respectively. Additionally, a power saving of around 20 dB is achieved by evaluating the channels with perfect environment information. The RTS-based model precisely captures environment information and generates a very good AP placement, however, it is computationally intensive and not scalable. For this reason, we have introduced a graph-based approach to effectively approximate the channel gain. The performance of this approach has been evaluated via the RTS. The results show that the graph-based approach saves around 5 dB power compared with the Euclidean distance-based approach, which represents the commonly applied model in the literature.  
Nevertheless, this work has some limitations which can be addressed in future work. The gap between the transmit power when using the graph-based approach and using the RTS-based model is still large. Therefore, the graph-based approach requires further improvement. This may be achieved by applying some ideas from existing geometric models, e.g., [43]. In addition, we assume that all the system's APs jointly serve each user. However, this is computationally intensive in practice. It would be necessary to investigate the tradeoff between computational effort and energy efficiency regarding the total number of APs that jointly serve each user out of all the APs in the system. Other than these, we assume the signals from different APs are combined coherently at each user location, which is an ideal case. It is also worthwhile to check the performance of the graph-based approaches in the worst case where signals are combined non-coherently at each user location. Finally, this work does not focus on the solver development for the AP placement optimization problem, yet has formed a bridge between the problem and the combinatorial optimization. Combinatorial optimization techniques can be explored in the future to develop an efficient solver for the problem.  
Conceptualization, L.V.d.P. and F.R.; methodology, Y.-H.Z. and F.R.; software, Y.-H.Z. and G.C.; validation, Y.-H.Z. and G.C.; formal analysis, Y.-H.Z.; writing--original draft preparation, Y.-H.Z.; writing--review and editing, Y.-H.Z., G.C., H.C., L.V.d.P. and F.R.; visualization, Y.-H.Z. and G.C.; supervision, L.V.d.P. and F.R.; project administration, L.V.d.P. and F.R.; funding acquisition, L.V.d.P. and Y.-H.Z. All authors have read and agreed to the published version of the manuscript. This research was partly funded by Huawei Technologies (Sweden)--DASPOP project. [PERSON] is supported by the Chinese Scholarship Council (CSC).  
Not applicable.  
**Acknowledgments:** The authors would like to thank Huawei Technologies (Sweden) for providing the ray-tracing simulator and the NVIDIA for providing the GPU, which has been instrumental in running the RTS. The authors are also grateful to [PERSON] (KU Leuven) for his comments and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.