# On Mathematical Modelling of Automated Coverage Optimization in Wireless 5G and beyond Deployments
## 1 Introduction
### Literature Review
#### 1.1.2 Base Station Optimization and Deployment  
Since the deployment of gNodeB nodes is a very complex task, the papers published on that topic vary a lot (Based on the Scopus database, there were 4405 papers published on wireless networks deployment in the area of computer science, engineering or multidisciplinary sciences (5 November 2020)). The papers touching that topic are mostly focused on specific parts of the deployment. From the authors' point of view, the papers are mostly targeting the problem of dynamically modifying the gNodeB parameters as-is: downtilt, the collection of three azimuths, mechanical downtilt, electrical downtilt, heigh of gNodeB and transmit power [46; 47]. Further, the papers are targeting the deployment algorithms to determine the most suitable positions of gNodeB nodes. In [48], a pico gNodeB deployment problem was formulated as an additional task to meet the increasing data exchange requirements, which assures the performance of coverage and quality of services; besides, ref. [49] proposed several gNodeB deployment algorithms including region-based, grid-based and greedy algorithms to determine the most suitable positions of micro gNodeB nodes. However, these works only consider the impact of location, where other parameters that affect the performance indicators are not taken into consideration. Moreover, those algorithms optimize only one variable in each iteration and are performed in an exhaustive manner, which is inefficient with poor performance [47]. The overview of the recent literature in gNodeB optimization and deployment is shown in the Table 3. Additionally, the literature review of gNodeB deployment is presented in the following surveys in more detail [50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61].  
In this paper, the target contribution is mainly on the gNodeB location optimization but, as opposed to the literature presented, we consider more aspects that are essential in the real-world scenarios.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Authors** & **Description** & **Published** \\ \hline [PERSON], [PERSON], et al. [46] & This paper proposes a gNodeB parameters optimization with regret minimization and a low number of iterations in the presence of uncertainties due to the stochastic response of KPI metrics & 2019 \\ \hline [PERSON], [PERSON], [PERSON] and [PERSON] [62] & Authors propose a two-stage stochastic optimization model to investigate the problem of gNodeB selection. They found that the genetic algorithms may be an adequate avenue for a solution. & 2019 \\ \hline [PERSON], [PERSON] and [PERSON], [PERSON] and [PERSON] [63] & The paper provides a case study in Uttarakhand to develop a new model for placement of the optimal number of base stations. The paper compares different models and concludes them with their pros and cons. & 2019 \\ \hline [PERSON], [PERSON] and [PERSON], [PERSON] [64] & The paper presents an evolutionary firefly algorithm and compares it to the standard firefly algorithm and uses it to deploy gNodeB stations. The authors conclude that enhanced algorithm can provide slightly better solutions in terms of the final coverage. & 2019 \\ \hline [PERSON] and [PERSON] [47] & This paper is mainly focused on the deployment of algorithms with the focus on the research of optimal machine learning (ML) model to deploy gNodeB nodes. It has found that multi-layer perceptron outperforms other ML algorithms. & 2020 \\ \hline \hline \end{tabular}
\end{table}
Table 3: An overview of recent papers targeting the deployment of gNodeB nodes.