# On Mathematical Modelling of Automated Coverage Optimization in Wireless 5G and beyond Deployments
## 4 Numerical Simulations and Results Discussion
### gNodeB Parameters Settings  
To prepare the datasets, we need to consider the parameters taking into account the expected user connection growth, maximal available throughput (capacity) of gNodeB node, and gNodeB coverage range for selected the deployment use-cases. For the sake of simplification, we consider  
Figure 4: The basic concept of producing the optimal solution (SC: service centre, CL: customer location and ES: existing services).  
that a single gNodeB represents a single mobile cell. All the parameters are further discussed in the next paragraphs.  
To estimate the expected connection growth and required throughput, we used the parameters from the white paper [5] from Cisco company and the 5G reference guide for network operators [104]. In [5], we see that the fastest-growing device and connections category is Machine-to-Machine (M2M) (see Figure 5) that can grow to reach 14.7 billion connections by 2023. Here, it is important to track the changing mix of devices and connections and growth in multi-device ownership as it affects traffic patterns. Video devices, in particular, can have a multiplier effect on traffic. An Internet-enabled High Definition (HD) television that draws two hours of content per day from the Internet would generate, on average, as much Internet traffic as an entire household today. The impact of devices with video on the network traffic is more pronounced because of the introduction of Ultra-High-Definition (UHD), or 4K, video streaming. The expected user thresholds are for Downlink (DL) 100 Mbit/s and for Uplink (UL) it is 50 Mbit/s. This high data rate demanded by end-users is based on the situation that in the 5G systems, there is a high expectation for emerging high-end user applications such as AR or VR, that require data rates in the range of several hundreds of Mbit/s [5; 104]. Based on this information, we used the values from [5] that expect the significant growth of M2M devices and other devices in 2023 that can produce a workload close to 43.9 Mbit/s. This value was estimated in the [5; 104] based on the wide usage of AR, VR and such applications. In the presented scenario, it represents the upper limit that the network operator will allocate for one user. We used that value to design the network to handle such borderline scenario [104].  
On the other hand, based on the specification presented in [105], the expected capacity limits of a single gNodeB node are as follows: (i) DL peak data rate 20 Gbit/s and; (ii) UL peak data rate is 10 Gbit/s. These requirements are further specified for selected deployment use-cases (urban, suburban, rural) [106]. In practice, the capacity of gNodeB node is dependent on a variety of configuration parameters as-is: hardware setup, class of radio interface, duplex mode, number of sector carriers/baseband unit, number of users/baseband unit, number of users/sector carrier, data radio bearers, scheduling entities per slot DL/UL--cell, maximum sector carrier bandwidth, maximum throughput per connected user DL/UL, maximum throughput per radio node DL/UL and Single User (SU) Multiple-Input Multiple-Output (MIMO) layers. All of these can be further optimized based on the actual requirements after the deployment is complete. For the sake of generalization, the average base station coverage range (cell range) is most commonly set to 0.5 km in urban, 1 km in suburban and 8 km in rural areas [107]. Further, in the numerical simulations, we used the parameters to set the  
Figure 5: Global device and connection growth.  
SUI model that is typically used in practical applications. The settings for each gNodeB node were as follows \(a=4\), \(b=0.0065\), \(c=17.1\), \(h_{b}\) ranging from 5 to 35 m, \(f\) was under 5 GHz, \(X_{f}\), \(X_{h}\) and \(s\) were calculated using the antenna height and frequency parameters).  
The summarized list of parameters of gNodeB and users is shown in Table 5.