Traffic simulation and losses estimation in stratospheric drone network

The use of stratospheric drones for data transmission requires reliable two-way communication. In this regard, it is necessary to explore the possibilities of combining existing air and ground networks for effective interaction with stratospheric drones during heavy data traffic. This article focuses on calculating the packet loss and the impact of traffic parameters on communication with drones. For the first time, traffic characteristics of the complex network “Base Station—Stratospheric Drone – Remotely Piloted Air System—Ground Cellular Network” are obtained. The original models are created based on MATLAB Simulink and NetCracker software. Packet loss dependences on the transaction size for different numbers of cellular users are estimated using NetCracker software. Average load dependences on the size of the transaction are obtained. Channels with different throughput are considered and the influence of channel loading on the bit error rate is studied. Data transmission is simulated using MATLAB Simulink depending on the signal-to-noise ratio, nonlinearity levels of the base station amplifier, types of signal modulation and diameters of base station antennas. Data obtained make it possible to predict the operation of stratospheric drones.


Introduction
High-Altitude Platform Station (HAPS) according to Article 1.66A of the ITU Radio Regulations is defined as "a station on an object at an altitude of 20 to 50 km and at a specified, nominal, fixed point relative to the Earth". Stratospheric Remotely Piloted Air Systems (RPASs) or Unmanned Stratospheric Vehicles (USVs) are attracting more and more attention (Fig. 1), since they can be used for both military and civilian missions. Therefore, a significant number of publications have been devoted to these issues. To implement applications using stratospheric drones, it is important to develop new structures for communication and information transfer in real time [1][2][3].
In the existing literature on HAPS and stratospheric drones, there is no quantitative information on the loss of data packets when communicating with drones. How is packet loss related to an increase in the number of cellular network users? How does the message size affect the percentage of losses? How does nonlinearity, modulation type, and antenna size affect packet loss? Our article is devoted to the development of these issues.
Many countries are researching and developing their own USVs that can be used as platforms for intelligence and communications, thereby replacing space-based communications satellites. Currently, the development of USVs has moved to a new stage in connection with the possibility of their use as geostationary satellites, but much cheaper and easily replaceable. Their economic efficiency in combination with the use of new technologies for long-term stay in one place determines their commercial value, especially in those regions that have not developed terrestrial infrastructure for cellular communications. USVs can land on the surface for maintenance and energy replenishment, making them cost effective. They can create communication and navigation systems, carry out thermal and aerial photography, monitor the environmental situation, support the work of emergency and rescue services [4]. The acquisition by Google and Facebook of companies that produce USVs has the same goalto provide Internet coverage to remote regions of the Earth.
The novelty of this work is as follows: 1) for the first time, the traffic parameters of a complex network for data transmission through a stratospheric drone and a low-altitude RPAS to a terrestrial cellular network are calculated, which are currently not available in the world literature; 2) for the first time, models with five cellular network users have been developed that have no analogues in the literature, which are first comprehensively studied on the basis of MATLAB Simulink and NetCracker software; 3) for the first time, the effects of strong nonlinearity in the communication channels of RPASs/UAVs for two signal modulations and different antenna sizes are considered.
This work has been done in paradigm of using stratospheric drones as HAPS for transmitting data to users of cellular networks through a low-altitude RPAS. Stratospheric drones require reliable communication channels with minimal packet loss. Currently, there is not enough research in this area, and in the literature there is generally no data on the loss of data when exchanging information with stratospheric drones. In fact, the first estimate of the data loss in the drone's communication channel was published in the article [5].
Our article studies the centralized two-way line-of-sight channel for the ground Base Station (BS) with a stratospheric drone, which is connected through low-altitude RPAS to cellular network users. To predict the behavior of such a system, the following was done in the work: -original models were created for simulating data exchange using MATLAB Simulink and NetCracker software; -data traffic in the stratospheric drone network was first modeled using NetCracker software and packet loss was estimated for a different number of cellular network users; dependences of "Base Station-Stratospheric Drone" channel average load on the size of transmitted packets and data transfer rate were obtained; -data transmission in a stratospheric drone network was investigated for the first time using the MATLAB Simulink software depending on the Signal-to-Noise Ratio (SNR), nonlinearity of the BS High-Power Amplifier (HPA), the type of signal modulation and diameters of the BS antenna; -obtained data are of practical importance and allow predicting the behavior of the network in critical conditions. The rest of the paper is organized as follows. Section 1 covers related work. Section 2 presents the architecture and parameters of the model "Base Station-Stratospheric Drone -RPAS-Cellular Users", the simulation algorithm, the calculation method, the description of data traffic and results obtained using the NetCracker software. In Sect. 3, the model "Base Station-Stratospheric Drone -RPAS-Cellular Users" is considered using the MATLAB Simulink software and the influence of nonlinearity, modulation and diameters of the BS antenna is studied. Results are discussed in Sect. 4, and Conclusions are given at the end of the article.

Related works
The review [6] is devoted to the history of HAPs and the current state of affairs without taking into account the aspects of the telecommunications sphere, which are among the main in this issue.
Airborne Communications Networks (ACNs) have received great attention as heterogeneous networks designed to use satellites, HAPs, and Low-Altitude Platforms (LAPs) as communication access. ACNs, unlike terrestrial wireless networks, are characterized by changing network topology and more vulnerable communication links. The review [7] covers communication networks based on LAPs, HAPs and integrated networks ACNs.
RPASs will become a component of 5G communication systems (and not only) to achieve global access to the Internet for everyone. The paper [8] proposes a new hierarchical network architecture that integrates inter-layer platforms for high and low altitudes into conventional terrestrial cellular networks. This provides additional bandwidth and expands coverage of underserved areas. Comparison and overview of various RPASs types for the provision of communication services are presented in the paper. An integrated architecture of an air-heterogeneous network is proposed and its characteristics are described.
RPASs need to effectively interact with each other and using the existing network infrastructure. The requirement for reliable communication is caused by errors in navigation, guidance and control systems that are introduced at each stage. The foundations of our approach to modeling drone communication channels were developed in works and monographs [5,9,10].
RPASs deployment is seen as an alternative complement to existing cellular communications to achieve higher transmission efficiency with increased coverage and capacity. The article [11] provides an overview of advances in integrating 5G communications into wireless networks supported by RPASs. A taxonomy is given to classify existing research problems. Based on the proposed taxonomy, current issues and solutions for this newly emerging area are discussed.
The study [3] provides an overview of HAPS wireless service delivery in rural or remote areas using the cellular radio spectrum and focuses on the potential of using HAPS as an alternative to terrestrial systems. The feasibility of expanding the achievable wireless coverage using HAPS was investigated. This takes into account the coexistence of HAPS with terrestrial systems using intelligent techniques to dynamically manage radio resources and mitigate interference. The study has shown that effective intelligent radio resource and topology management can reduce intersystem interference. Potential techniques for extending coverage are discussed, such as using the spatial characteristics of lattice antennas, radio environment maps and inter-device communication.
With new technologies in autonomous avionics, antenna arrays, solar panel efficiency and battery energy density, HAPS has become an indispensable component of nextgeneration wireless networks. The review [12] presents the structures of future HAPS networks, proposes the integration of the emerging reconfigurable smart surface technology into the communication payload of HAPS systems, and discusses radio resource management in HAPS systems. The contribution of artificial intelligence to HAPS is noted, including machine learning in aspects of design, topology management, handover and resource allocation.
Terrestrial and satellite communication systems often face certain disadvantages and problems that can be solved by complementing them with HAPS systems. The article [4] considers HAPS as a base station for providing connectivity in a variety of applications. In contrast to conventional HAPS, which aims to reach a wide range of remote areas, it is expected that the next HAPS generation will have the necessary capabilities to meet the requirements for high throughput, low latency and compute resources. It focuses on the potential opportunities, target use cases, and challenges that are associated with the design and implementation of a future wireless access architecture.
In the review [13], RPAS networks are classified and the topology, control and behavior of the client server are investigated. Important aspects of self-organization and automated operations using Software-Defined Networks (SDN) are highlighted. The requirements of routing protocols for SDN networks and the need to create networks resistant to violations are discussed.
The review [14] outlines functions and requirements that are important to ensure reliable, efficient and energy efficient communications in basic UAV systems. The various UAVto-UAV (U2U) and UAV-to-Infrastructure (U2I) network architectures and the various communication protocols that can be used at the network model layers are provided. A classification of data traffic that may be present in U2U and U2I communications is described. Various communication protocols and technologies are discussed that can be used for different channels and levels of the UAV-based network architecture. Efficient and uninterrupted communication in UAV-based networks is essential for their safe deployment and operation.
The book [15] focuses on the communication and networking aspects of UAVs and the fundamental knowledge required to conduct research in this area. The basic concepts and state of affairs in the field of UAV networks are outlined. Deployment procedures and risk analysis are discussed.
UAVs can be connected to cellular networks as a new type of user equipment, providing operators with significant revenues and guaranteeing service requirements. It is possible to upgrade UAV-based flying base stations that can move dynamically to increase coverage and spectral efficiency. Standards bodies are currently exploring the possibility of servicing commercial UAVs over cellular networks. The industry is testing prototypes of base stations and user equipment. Mathematical and algorithmic solutions for new problems arising in flying nodes in cellular networks are investigated. The article [16] provides an overview of developments that facilitate the integration of UAVs into cellular networks: types of consumer UAVs available off-the-shelf; interference problems; possible solutions for servicing aeronautical users with existing ground base stations; communication with flying repeaters and base stations created using UAVs.
The use of drone-based flying platforms is growing rapidly due to mobility, flexibility and adaptive altitude, which enables them to be used in wireless systems. UAVs can be used as aerial base stations to increase the coverage, capacity, reliability and energy efficiency of wireless networks. Drones can act as flying mobile terminals within a cellular network. These drones, connected to a cellular network, can use several applications, ranging from live video streaming to delivering goods. The article [17] provides detailed guidance on the UAVs use in wireless communications: 3D deployment, performance analysis, channel modeling and energy efficiency. Analytical foundations and mathematical tools such as optimization theory, machine learning, stochastic geometry, transport theory and game theory are described. The basic recommendations for the analysis, optimization and design of wireless communication systems based on UAVs are presented.
The main problem that needs to be solved for the successful introduction of drones in all areas is communication [18]. This review aims to outline the latest UAV communication technologies through research on suitable task modules, antennas, resource processing platforms, and network architectures. Methods such as machine learning and path planning are considered to improve existing communication methods with drones. Encryption and optimization techniques are discussed to ensure long-term and secure communications as well as power management. Applications of UAV networks are investigated for a variety of contextual purposes, from navigation to surveillance, ultra-reliable low latency communications, edge computing, and works related to artificial intelligence. The complex interaction between UAVs, advanced cellular communications and the Internet of things are the main topics of this article.
The best example of high-altitude RPAS with multisensory synthesis technology is the Global Hawk [19], which is equipped with an integrated surveillance and reconnaissance system HISAR (Hughes Integrated Surveillance & Reconnaissance). Such devices belong to the class HALE (High-Altitude Long Endurance), fly at an altitude of 20,000 m and conduct strategic reconnaissance and target designation. The complex includes synthetic aperture radar and a moving target indicator, as well as optical and infrared sensors. All three subsystems can work simultaneously, and one processor works on their data. Digital data can be transmitted to the ground in real time with line-of-sight or over a satellite link at speeds up to 50 Mbps. RPASs such as the Global Hawk are expensive to manufacture and operate, which leads to the search for cheaper HAPS counterparts to provide Internet coverage in remote regions, target detection and recognition. There is interest in the development of low-cost UAVs networks, which together provide reliable communications, sufficient performance and have increased autonomy.

Stratospheric drone network architecture
Network models with different numbers of cellular users are based on ICAO documents [1,2] and are designed using Professional NetCracker 4.1 software [20]. The number of cellular users N varied from one to five (N = 1-5) but results in the article are given only for N = 1, 3, 5. Models parameters are given in Table 1. The network model "BS -Stratospheric Drone -RPAS -Cellular Users" (Fig. 2) contains the BS, the high-altitude Stratospheric Drone (30 km from the BS), the low-altitude RPAS (50 km from the Stratospheric Drone) and Cellular Users (CUs) each on the distance 10 km from the RPAS.

Algorithm and calculation method
The algorithm for traffic modeling using NetCracker software is described in the paper [5]. NetCracker is a real-time analytical simulator using mathematical equations. Its core is written in Java EE, its own application server is WebLogic, and Oracle is used as a database. We tested the capabilities of NetCracker software for realistic data traffic modeling in our article [21]. In this paper the data were calculated, which were subsequently confirmed. The model of the "Aircraft-Satellite-Ground Station" communication channel was built to simulate the transmission of ADS-B messages using the low-orbit satellite complex Iridium. The resulting dependences of the message transit time (1.4-1.9 s) on the number of satellites and aircraft were experimentally confirmed in 2017 by Aireon [22]. By tracking multiple aircraft with ADS-B 1090 Extended Squitter receivers for Iridium NEXT satellites, the system was able to deliver data to air traffic control centers with a delay of less than 1.5 s [23]. In our approach, the characteristics are divided into internal, which are obtained by mathematical modeling, and external, on which the internal characteristics depend. Channel load, data transfer time and the number of lost transactions were selected as internal characteristics. External characteristics included the size of the data packet, the time between messages, bit errors and the data transfer rate in the channel. The simulation made it possible to calculate the internal characteristics using the specified external characteristics.
This algorithm uses an analytical simulator that uses mathematical equations to predict the behavior of the model. The essence of the applied algorithm is as follows. Let us denote the internal characteristics of the communication channel, which are calculated at the time t k , as V 1 (t k ), …, V n (t k ); external characteristics at the same moment of time influencing them as W 1 (t k ), …, W r (t k ), and the average rate of change of internal characteristics in the time interval [t k , By specifying the values of the internal and external characteristics at the moment t k , it is possible to calculate the values of the internal characteristics at the moment (t k + 1).
To do this, the segment [t 0 , T] is divided into P parts by the points t 0 , t 1 , …, t k , …, t P = T. If the values of internal characteristics at time t 0 and average rates of the internal characteristics change on each segment [t k , t k + 1] are known, then using the following relations it is possible calculating the values of internal characteristics for all t k , k = 1, …, P: where i = 1, n; k = 0, 1, …, P-1.
Internal characteristics are obtained from the simulation and external characteristics are given. Internal characteristics include the average channel load, the message travel time, the number of lost packets, etc. External characteristics are the transaction size, the Time Between Transactions (TBT), the Bit Error Rate (BER), and the channel bandwidth. Net-Cracker is an analytical simulator based on mathematical equations for simulating network operation.
If we consider the functions Y 1 (t), …, Y n (t) continuous and having derivatives, then to describe the process, equations are used that have the following form where i = 1,…, n. Here, the functions F i (t, V 1 , …, V n , W 1 , …, W r ) represent the "instantaneous" rates of change of the corresponding internal characteristics.
The models parameters were simulated taking into account the Const probability distribution law (ω (x) = Const, ω (t) = Const) as statistical distributions for the Transaction Size (TS) and TBT. Formulas for the average length of the transmitted packets, the average time interval between two adjacent packets, the Average Utilization (AU) of the communication link, and the average packet travel time are given in the paper [5].

Data traffic
Data transmission of drones in accordance with the ICAO requirements [1] is carried out in the form of C3 (Command, Control and Communication) traffic (Fig. 1), which consists of the Tactical Control Data (TCD) channel for flight control and the Common Data (CD) channel (for transmitting data from users of cellular networks, information from radars, optical, infrared systems, etc.).

s with Const distribution law) and interLAN profile (Local Area Network) for the Common Data (TS and TBT with
Const distribution law, TBT = 1 s) was set for our models. Command, control and communication traffic is carried out as two-way communication.

Results
The dependences of the average channel utilization on the transaction size and data transfer rate, the dependences of the bit errors number on the average channel utilization and the number of lost packets on the number of cellular users were investigated. Quantitatively packets loss is estimated as the percentage of packets lost in relation to sent packets. The numerical range of traffic parameters was chosen based on the experimental data presented in the work [24].  Kbits. This increase in the AU parameter turns out to be greater the more users there are in the network. At TS values more than 100 Kbps, the channel is closed. This is due to the large amount of specified data transmitted in both channels. The increase in the number of cellular users naturally leads to an increase in the channel load. However, the important thing here is the order of such an increase. It follows from the graphs that an increase in the number of users from N = 1 to N = 5 leads to an increase in the AU parameter by about 3 times over the entire range of packet sizes. The values of the AU parameter for N = 5 vary from ≈ 17% to ≈ 44%.
Dependences of the AU parameters for "BS-Stratospheric Drone" channel on bandwidth for different number of cellular users are shown in Fig. 4 (Traffic: TCD -FTP, TS = 100 Kbits and TBT = 1 s-with Const distribution law, CD -interLAN, TS = 100 Kbits and TBT = 1 s-with Const distribution law). The bandwidth varied from T1 (1,544 Mbps) and E1 (2,048 Mbps) to E3 (34,368 Mbps) and T3 (44,736 Mbps). The transfer of fixed-size packages in both channels was considered. Channel AU increase with a decrease in data rate and with T1 bandwidth reaching ≈ 13% for N = 1 and ≈ 37% for N = 3.
The sensitivity of the stratospheric drone's communication system to bit errors is critical for the communication reliability. Figure 5 (Traffic: TCD -FTP, TS = 10 Kbits and TBT = 1 s-with Const distribution law, CD -interLAN, TS = 10 Kbits and TBT = 1 s-with Const distribution law) shows the dependences of the BER on the AU parameter for the "BS-Stratospheric Drone" channel with a different number of cellular users. Dependences are given for TS = 10 Kbps for both TCD and CD traffic parameters. The data presented in Fig. 5 indicate a fairly high sensitivity of the channel to bit errors. It says about the need to encode the signal, which will be studied further using the MATLAB Simulink software. Figure 6 (Traffic: TCD -FTP, TS = 10 Kbits and TBT = 1 s-with Const distribution law, CD -interLAN, TS and TBT-with Const distribution laws, TBT = 1 s) demonstrates the dependences of dropped packets number on the TS parameter for CD traffic. As the TS parameter increases from 10 bits to 1000 Kbits, the number of lost packets increases and reaches: for N = 1 approximately ≈ 12%, for N = 3 approximately ≈ 30%, for N = 5 approximately ≈ 51%. In general, the nature of all dependencies is similar, however, with the growth of users, packet losses increase more than 4 times with a fivefold increase in the number of users.

Model "Base station -stratospheric drone -RPAS -cellular users" in MATLAB simulink
For drones in general, and especially for stratospheric drones, due to the large distances from the base station, it is important to study the effect of the non-linearity of the base station transmitter amplifier with various signal modulations and antenna diameters. This section discusses the effects of strong non-linearity in drone communication channels with two signal modulations and different sizes of base station antennas. The simulation was carried out on the basis of the MATLAB Simulink package, in which the model is a description of the system using mathematical equations and diagrams. Simulink is a complementary product to MATLAB with an interactive graphical environment for modeling, simulating and analyzing dynamic systems, which are the communication channels of a stratospheric drone. For simulation, Simulink provides a graphical user interface for building flowchart models (Fig. 7).
The relationship between the antenna gain, the antenna diameter and the wavelength is determined by the relation G = η(πD/λ)2, where η is the antenna efficiency. For calculations (here η = 1), the following parameters in the model were set up: for Stratospheric Drone and RPAS antenna gains were taken 1.55 (an antenna diameter ≈ 0.2 m at 1 GHz); for the BS the following antenna gains were taken-6.2, 7.8 and 9.3 (an antenna diameters ≈ 0.8 m, ≈ 1.0 m and ≈ 1.2 m correspondently at 1 GHz).
The "effect of different distances" from low-altitude RPAS to CUs was modeled by setting different SNR (Es/N0) values in AWGN Channels 2-7. In Figs. 8-11 data are given when Es/N0 values were varied only in AWGN Channel 1.  These SNR values for the channels were chosen arbitrarily from considerations of the approximate "equidistance" of the curves with negligible HPA nonlinearity for both considered modulations. In this case, it is possible to trace the influence of severe nonlinearity with an increase in the range to the RPAS. Figure 8 (BPSK modulation, phase/frequency offsets 0°/0 rad, BS antenna diameter 1.0 m) shows data for BPSK modulation with negligible HPA nonlinearity. When E s /N 0 in AWGN channel 1 changes from -32 dB to -29 dB, the BER for the CU1 decreases from ≈ 5.2 • 10 -3 to ≈ 1.1 • 10 -6 . For each subsequent CU channel, the BER values become larger due to distances increase and worse SNR values. Table 2 Model "BS -Stratospheric Drone -RPAS -Cellular Users"

"Base Station" transmitter
Bernoulli Random Binary Generator Generates random binary numbers using a Bernoulli distribution with parameter p, produces "zero" with probability p and "one" with probability 1-p (the value p = 0,5 is used) Convolutional Encoder Employs forward error correction coding in the form of convolutional encoding with Viterbi decoding [25]. A model uses a rate 3/4, constraint length 7, (r = 3/4; K = 7) convolutional code on both transmission and reception. The Convolutional Encoder block is using the poly2trellis ( Decodes input symbols to produce binary output symbols. Unquantized decision type parameter was used "Error Rate Calculation" block and "Display" In the case of strong HPA nonlinearity, the situation changes dramatically as it shown on Fig. 9 (BPSK modulation, phase/frequency offsets 0° /0 rad, BS antenna diameter 1.0 m). For the operation under these conditions, much higher values of the SNR are required. When E s /N 0 in AWGN channel 1 changes from -19 dB to -15 dB, the BER for the CU1 channel decreases from ≈ 1.2 • 10 -1 to ≈ 1.1 • 10 -6 . The BER for the CU3 channel reaches ≈ 9.4 • 10 -4 and for the CU5 channel reaches ≈ 4.8 • 10 -2 at E s /N 0 =-15 dB. This means that with an increase in the level of nonlinearity, communication with cellular users at large distances suffers first. This would seem to be an obvious conclusion, but the data obtained allow us to quantify the degree of such deterioration. Figure 10 (BPSK modulation, phase/frequency offsets 0°/0 rad) shows the dependences of the BER on the SNR for different BS antenna diameters with strong HPA nonlinearity (Stratospheric Drone and RPAS antennas diameters are ≈ 0.2 m in all cases). The high sensitivity of bit errors number depending on the size of the antenna is evident. The data are given only for the CU1, and for the rest of the CUs the situation is even more critical for this SNR range. Figure 11 (QPSK modulation, phase/frequency offsets 0°/0 rad, BS antenna diameter 1.0 m) demonstrates the dependences of the BER on the SNR for severe nonlinearity in the case of QPSK modulation. Comparison with similar dependences for BPSK modulation (Fig. 9) shows that the Fig. 8 Dependences of BER on SNR for negligible nonlinearity Fig. 9 Dependences of BER on SNR for severe nonlinearity transition to higher-level modulation requires a significant increase in the SNR. So for BPSK modulation the BER ≈ 1.1 • 10 -6 , at E s / N 0 =-15 dB for the CU1, and for QPSK modulation the BER ≈ 1.2 • 10 -6 at E s / N 0 =-8 dB.

Discussion
Stratospheric drone operation is not possible without reliable communication channels with low-altitude RPASs, terrestrial cellular networks, other stratospheric drones and satellite communications systems. This is stated in almost all published works, but besides proposals for the possible network architecture, data protocols and wireless standards, no quantitative traffic characteristics can be found. In fact, apart from the work [24], there are no experimental data in the literature, with traffic parameters (the size of transactions, the time between them, the traveling time of the messages, the number of lost data packets, the rate of data transmission and its impact on the number of bit errors, the loading of channels, the impact of modulation type). There are also no theoretical studies developing methods of predictive analysis for drone's communication. There are no theoretical methods for assessing the parameters of real traffic in Fig. 10 Dependences of BER on SNR for different BS antenna diameters Fig. 11 Dependences of BER on SNR for severe nonlinearity drone channels. This study is a case in which such methods are developed.
This work is the first study to calculate packet loss, convolutional coding of signals, and reveal the effects of non-linearity and signal modulation for stratospheric drone communications. The influence of the BS antenna diameter, which can significantly change the BER, is quantified. The probability of bit errors is much lower for a BS antenna with a diameter of more than 1.2 m. The results obtained can be considered as a way to estimate the parameters of such channels using the MATLAB Simulink and NetCracker programs.
The data presented in Figs. 3-5 allow us to analyze the benefits of a certain mode of information sharing and to estimate the relative AU increase with the growth of cellular users. Figure 6 is key for understanding the conditions under which packets losses becomes unacceptable.
When using drones, the base station amplifier typically works at as much power as possible due to the small size of the drone antennas and the long distances to them. So, the inevitable nonlinearity of communication channels becomes critical. Obtained data can quantify the specifics of data transmission for different levels of the BS transmitter nonlinearity, signal modulations and the BS antenna diameters (Fig. 7-11). It was found how much you need to increase the SNR when transmitting data with an increase in nonlinearity and the transition to QPSK modulation.
It is worth noting the original models architecture for connection the stratospheric drone with the cellular network and the possibility of using the results to assess the quality of data transmission. This article is a continuation of our work on modelling drone channels operation.

Conclusions
In this article, we have developed a network architecture that includes a base earth station, a stratospheric drone, RPAS, and cellular network users. Such a network takes advantage of the integration of high-altitude platform, low-altitude platform, and ground segments to support ubiquitous communications services efficiently and costeffectively. The developed system is proposed to be used as an additional solution for expanding the use of existing terrestrial cellular networks for underserved users and hard-to-reach places. Such a network architecture, due to the potential benefits, will have a wide range of applications for solving problems of joint integration. Multilayer air platforms will find use in future wireless networks.
This article highlights the cross-layer interaction between air and ground networks and helps to accelerate the pace of development and related research of integrated air-to-ground networks. The importance of the results lies in the ability to predict channel performance, identify problems early in channel design for stratospheric drones, and reduce time, cost, and ensure scalability in new projects. Obviously, such calculations are becoming a necessary tool for developers of communication systems for stratospheric drones.