## 1 Introduction  
By September of 2019, the number of mobile subscribers worldwide was around 8 billion, and one estimation puts that number at 8.9 billion by 2025 [1]. This means that in order to maintain the network's capacity and its quality of service (QoS), one might need to deploy more equipment, increasing the risk of a chaotic network, and consequently, the amount of interference.  
Wireless cellular networks propagate electromagnetic waves to establish connectivity between base station (BS) antennas and users' mobile terminals. Multiple antennas must be deployed to provide coverage of a given service area. To operate, mobile operators have access to a set of radio channels, frequencies with specific bandwidths allowing them to establish communication with mobile terminals. The distribution of frequencies among BSs, so-called frequency planning, is a challenge, as the re-use of the same frequency by a neighboring cell may result in interference that makes it impossible to communicate.  
Usually, frequency planning and allocation is a manual, time consuming, but important task to a quality network. The reason for the complexity of this task is because of aspects such as terrain topography and urban density, where non-uniform coverage exists. The overall objective is to allocate frequencies while creating the least amount of interference--ideally, none.  
There are protocols that can be applied to help with solving this problem. Self-organizing networks (SON) are an example of that. They collect data from the network and automatically make changes to it based on that data, by analyzing a set of key performance indicators (KPIs). In our case, we would need a KPI representing interference. Interference is possible to estimate, using estimated cell powers from propagation models such as Okumura-hata and Walfish Ikegami [2].  
This idea is applied and tested for the Global System for Mobile communications protocol (GSM), a cellular system that, compared to UMTS and LTE, presents higher challenges in terms of cellular planning [3]. GSM specifies that a cell has to have both control channels (CCH) and traffic channels (TCH), responsible for transmitting network information and user traffic respectively.  
This new planning pattern was implemented and applied in a commercial tool called Metric [4]. Metric is a planning, monitoring, and optimizing tool for mobile networks, currently used by multiple operators.  
The novelty of this paper is the use of cloud services and linear programming to quickly and automatically plan or heal a network. Following the SON concept, we were able to create and implement a work pattern which estimates power, calculates possible interference, and finds a solution, outputting the best set of frequencies to allocate to each cell.  
This paper considered the possibility of mass planing new cells from different sites. New methods and materials were used, new optimization rules and evaluation tests were obtained, and the new functionalities were introduced in the Metric tool. This work was started by the work presentation in [5] considering new gaps and opportunities to plan mobile cellular networks in an efficient way assuring the accuracy and precision of results.  
The paper is organized as follows: Section 2 presents the state-of-the-art and related work, including the methods and materials used. We also mathematically explain our definition of interference, as well as other rules used in integer linear programming. In the same section we also detail all module specifications and implementations present in the working pattern. The evaluation scenario and tests results are described in Section 3. Finally, main conclusions and future work are described in Section 4.