# Energy Efficient Access Point Placement for Distributed Massive MIMO
###### Abstract  
Distributed massive multiple-input multiple-output (D-mMIMO) is one of the key candidate technologies for future wireless networks. A D-mMIMO system has multiple, geographically distributed, access points (APs) jointly serving its users. First of all, this paper reports on where to position these APs to minimize the overall transmit power in actual deployments. As a second contribution, we show that it is essential to take into account both the radiation pattern of the antenna array and the environment information when optimizing AP placement. Neglecting the radiation pattern and environment information, as generally assumed in the literature, can lead to a power penalty in the order of 15 dB and 20 dB, respectively. These results have been obtained by formulating the AP placement optimization problem as a combinatorial optimization problem, which can be solved with different approaches where different channel models are applied. The proposed graph-based channel model drastically lowers the computational time with respect to using an ray-tracing simulator (RTS) for channel evaluation. The performance of the graph-based approach is validated via the RTS, showing that it achieves 5 dB power saving on average compared with a Euclidean distance-based approach, which is the most commonly used approach in the literature. distributed massive MIMO; energy efficiency; access point placement; shortest path; ray-tracing simulator +
Footnote †: journal: Network  
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It includes information regarding the objects, e.g., buildings, impacting the channel gain (the average signal power received at a given user when considering unit transmit power and including a potential antenna gain). Regarding the first aspect, in practical scenarios, e.g., urban areas, APs are conveniently deployed on the walls along the streets or at the roofs' edges. It is unlikely that APs are deployed, for example, in the middle of a street. The importance of the environment in this perspective may be less evident when the coverage region is large, e.g., 1 km by 1 km. In that case, modifying the generated AP placement by several meters to make the deployment feasible will have little impact on the system's performance. However, in future wireless networks, the distance between APs and their users is going to shrink drastically due to the increasing AP density [6]. In this case, the system's performance becomes very sensitive to the AP placement. Therefore, taking into account the environment information regarding any feasible locations for APs deployment is important. Nevertheless, most existing work is based on assumptions neglecting environment information [5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. In [7, 10, 11], the authors considered a distributed antenna system in a cell where all the transmitters and receivers are placed on a line. Another commonly used assumption is the circular topology [8, 9, 12, 15, 17, 19, 20]. It considers that the APs are placed evenly on a circle. This assumption was initially introduced to make the analysis of the optimization problem tractable [8]. It simplifies the problem to finding an optimal radius for the circle. A few earlier studies, e.g., [14, 15, 24, 27], model the problem in a continuous way. They developed different gradient-based heuristic algorithms. Some other researchers applied [PERSON]'s algorithm or k-means clustering-based approaches [11, 18, 21, 25, 28]. To the best of our knowledge, only [29, 30] take into account the environment information. The focus of these studies, however, is on indoor and underground applications, respectively. This paper focuses on outdoor deployments and takes into account environment information about possible locations for deploying the APs. Additionally, environment information regarding the possible AP locations is an essential prerequisite when considering the radiation pattern of the arrays.