Simulation of Data Losses, Nonlinearity and Modulation Impact in RPAS/UAV Swarms

Intelligence of Remotely Piloted Air System (RPAS) swarms depends on reliable communications. The parallelism and distributed characteristics of swarm intelligence provide self-adapting and reliable capabilities. This article is devoted to the calculation of packet losses and the impact of trac parameters on the data exchange with swarms. Original swarm models were created with the help of MATLAB and NetCracker packages. Dependences of data packet losses on the transaction size are calculated for different RPAS number in a swarm using NetCracker software. Data trac with different parameters and statistical distribution laws was considered. The effect of different distances to drones on the base station workload has been simulated. Data transmission in a swarm was studied using MATLAB software depending on the signal-to-noise ratio, nonlinearity levels of base station amplier, signal modulation types, base station antenna diameters, and signal phase offsets. The data obtained allows foresee the operation of RPAS communication channels in swarms.

The article [16] provides an overview of typical Swarm Intelligence (SI) algorithms and summarizes their application in the Internet of Things (IoT). The focus is on analyzing SI-enabled applications for the WSN and discussing research issues at WSN. Authors generally divide the UAV-aided wireless network into three categories according to their principles, and their applications based on SI are analyzed.
When using UAVs, there are many problems that need to be solved, and the main one is communication. The review [17] explores the latest UAV communication technologies by examining suitable task modules, antennas, resource processing platforms, and network architectures. Explored techniques such as machine learning and path planning. Encryption methods to ensure long-term and secure communication are discussed. Applications of UAV networks are investigated for a variety of contextual purposes, from navigation to surveillance, URLLC (Ultra-Reliable Low Latency Communication), edge computing and work related to arti cial intelligence. The complex interaction between UAVs, cellular communications and the IoT is one of the main topics of this article. This literature review demonstrates the need for additional research in the eld of drone-to-drone and drone-to-device communications.
There are many complex issues in the design of UAV swarm networks, such as the integration of hardware and software for large-scale UAV network management, long distance data transmission between UAVs, swarm shape/formation control, and intelligent UAV mobility/position prediction.
Engineering developments and designs of network protocols for dynamic large-scale UAV networks are considered in the book [18]. It provides technical models/algorithms and protocol speci cations for the practical deployment of UAV swarms.
Automating swarms' management is challenging as every drone operates under uctuating wireless, networking and environment constraints. In the review [19], drone swarms are considered as Network Control Systems (NCS), in which the control of the entire system is carried out within the wireless communication network. This is based on a tight interconnection between the networking and computational systems, aiming e ciently support data collection, information exchanging, decisionmaking, and the distribution of commands. The development of self-organized drone swarms as NCS through the integration of networking and computing systems is described. Their integration is analyzed to improve the performance of drone swarms.
UAVs swarm is usually used to solve the problems of nding survivors, monitoring and tracking several targets. This requires complex mechanisms for their control, communication and coordination. However, these mechanisms are di cult to test and analyze in the context of ight dynamics. Such multi-UAV scenarios are inherently well suited to be simulated as multi-agent systems. The article [20] presents an approach for modeling the UAV as an agent in terms of multi-agent system. Sensors and communication devices allow interaction with other drones in the swarm and the environment. Proposed ight dynamics model re ects limitations and uncertainties.
Data congestion control is used to expand network capabilities, improve the reliability of VANETs by reducing packet loss and communication delays. The study [21] proposes a distributed congestion control strategy based on an intelligent swarm. This maintains channel utilization below the network failure threshold and maintains high quality of service. Experiments have shown that the proposed strategy improves network throughput, channel utilization, and link stability when compared to other competing congestion management strategies.
Due to the uncertainty of wireless links, communications between UAVs experience transmission delays that impair the swarm's ability to stabilize the system. The article [22] examines the problem of joint communication and control for a group of three UAVs connected by cellular communication. A new approach is proposed to optimize the swarm operation while taking into account the wireless network latency and the stability of the control system. The maximum allowable delay required to prevent swarm instability is determined. The simulation results help to get recommendations for the formation of a stable UAV swarm.
Tra c monitoring is considered in the paper [23] using a swarm that continuously monitors tra c in SwarmCity. It is a simulated city built on the Unity game engine, where drones and cars are modeled realistically. The swarm control algorithm is based on six modes of behavior with twenty-three parameters that are con gurable. Parameters optimization is performed using a genetic algorithm in a simpli ed and fast simulator. The best resulting con gurations are tested at SwarmCity and perform well in terms of the number of vehicles monitored versus the total number of vehicles over time windows.
Mini-UAVs should be grouped using swarm coordination algorithms to perform tasks in a scalable and reliable manner. The article [24] uses biological mechanisms to coordinate unmanned aerial vehicles searching for a target with imperfect sensors. Coordination can be achieved by combining stigmergic and ocking behavior. Stigmergia occurs when a drone releases a digital pheromone when it detects a potential target. Such pheromones can aggregate and spread between ocking drones, creating a spatially attractive potential eld. The geometric model includes an arbitrary orientation of the GS and UAV antenna elements and estimates the polarization mismatch losses that arise due to the UAV's movement and orientation. For homogeneous linear and rectangular arrays, the optimal distance between the antennas has been determined.
The data transfer from the RPAS swarm was modeled using MATLAB Simulink in our work [27]. RLOS and Beyond Radio Line of Sight (BRLOS) link models included: 1) "Base Station Transmitter"; 2) RLOS channel: "Uplink Path", "RPAS Receiver"; 3) BRLOS channel: "Uplink Path", "Satellite Transponder", "Downlink Path"; "RPAS Receiver". The dependences of the BER on the SNR were obtained for different levels of BS transmitter nonlinearity, its gain, diameters of BS and satellite transponder antennas.
Models of "Base Station -Satellite -RPASs" communication channels were built using the NetCracker Professional 4.1 software [28]. We analyzed the dependences of average utilization on the size of the transaction, satellite channels with different bandwidths and the number of RPAS, as well as the impact of the likelihood of satellite failure.
The article [29] proposes the UAV-Edge-Cloud model as a new hybrid computing platform to provide powerful resources for supporting resource-intensive applications and real-time tasks in edge networks. Potential applications of the model for smart cities and the routing problem for latency-critical applications are discussed. Simulation results show that this approach can improve Quality of Service (QoS).
The paper [30] describes experiments with small drones, a real-time big data platform, and an operating system that interacts with 4G cellular mobile services. The purpose of the experiment is to collect data for testing obstacle avoidance algorithms and to evaluate communication performance.
In the literature, there is generally no data on the loss of data packets when exchanging information with drones in swarms. In the article [31] we published the rst packet losses estimation for single drone. The article [32] is actually the rst publication containing numerical experimental data on the tra c of single drone.

Swarm Model Architecture
Swarm model architecture is based on ICAO documents [1,2] and is designed using Professional NetCracker 4.1 software. Models with different numbers of RPASs (N = 1 -4) are built and considered. Models' parameters are given in Table 1

Algorithm
The algorithm for modeling channel characteristics is described in our paper [Modelling]. Characteristics are divided into internal (obtained using mathematical modeling tools) and external (on which the internal characteristics depend). The internal characteristics were the average channels utilization (load), the packets travel time, and the number of dropped packets. The external characteristics are the transaction size, the time between transactions, the bit error rate, and the link bandwidth. During simulation, it is possible to calculate internal characteristics using speci ed external characteristics.
NetCracker as analytical simulator provides real-time "what-if" simulation using mathematical equations. Its core is written in Java EE, the native application server is Weblogic, and Oracle is used as a database.

Calculation Methods
The models' parameters were simulated taking into account different statistical distributions for TS and TBT parameters, the BER, the links bandwidth and the data transfer protocols. The following probability distribution laws were used: Const law -ω (x) = Const, Exponential law -, and LogNormal law -Formulas for the average length of the transmitted packets, the average time interval between two adjacent packets, the average utilization of the communication link, and the average packet travel time are given in our paper [33].

Data Tra c
A tra c with Local Area Network peer-to-peer protocol is speci ed for the created models with the topology according to Figure 2. This means decentralized network based on the equal rights of participants. There are no dedicated servers in such a network, and each peer is both a client and acts as a server. Such an organization allows maintaining the network's operability for any number and any combination of available RPASs. Swarm communication tra c is performed as two-way communication.

Results
Packet losses during exchanging data between a base station and drones is a critical factor, as it can     In the "Base Station Transmitter" the Bernoulli Binary Generator block 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).
The model uses forward error correction coding in the form of convolutional encoding with Viterbi decoding [34]. A model uses a rate 3/4, constraint length 7, (r=3/4; K=7) convolutional code on both transmission and reception.
BPSK/QPSK Baseband Modulator block modulates a signal using the binary phase shift keying method.
The HPA block applies Saleh model [35]. The following backoff is used to set the input and output gain of the Memoryless Nonlinearity block: 30 dB -the average input power is 30 decibels below the input power that causes ampli er saturation; and 1 dB -severe nonlinearity.
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 e ciency. For calculations (here η = 1), the following parameters in the model were set up: RPAS antenna gain was 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).
"AWGN Channel" blocks add white Gaussian noise to the input signal. In the previous paragraph, the modeling of different distances between the BS and RPASs was carried out by setting different BER values for different communication channels of the RPAS with the BS (see Figure 6). In the case of the In "RPAS Receivers", signals are decoded and the BER is determined. The Viterbi Decoder block decodes input symbols to produce binary output symbols. Unquantized decision type parameter was used.

Results
The calculations were carried out using the MATLAB R2014a package. Figures 8-11 show data for BPSK modulation, Figure 12 compares data for BPSK and QPSK modulations, and Figures 13-16 illustrate QPSK modulation. An important problem in communication with RPASs is related to the nonlinearity of the BS HPA, which is associated with the small size of the drone antennas and the need to maximize the range of the drones. Therefore, the key issue is to compare the cases of negligible and severe nonlinearities (Figures 8, 9 for BPSK modulation and Figures 14, 15 for QPSK modulation). Figure 8 shows data for BPSK modulation with negligible HPA nonlinearity. When the SNR in AWGN Channel 1 changes from -34 dB to -30 dB, the BER decreases from ≈ ≈ 3.9•10 −2 to ≈ 1.1•10 −6 . In this case, for each next channel, the BER values turn out to be large due to long distances and worse SNR values. With E s /N 0 = -30 dB, the BER value for AWGN Channel 2 is ≈ 5.0•10 −6 , for AWGN Channel 3 is ≈ 4.0•10 −5 , and for AWGN Channel 4 is ≈ 1.9•10 −4 . This means that AWGN Channel 4 will be closed, and AWGN Channel 3 may be unstable.
In the case of strong HPA nonlinearity, the situation changes dramatically (Figure 9). For the operation of RPAS communication channels in these conditions, much higher SNR values are required. When the SNR in AWGN Channel 1 changes from -13 dB to -10 dB, the BER decreases from ≈ 4.8•10 −3 to ≈ 1.1•10 −6 .
The BER for AWGN Channel 2 reaches a value of ≈ 1.4•10 −6 at E s /N 0 = -8 dB, and for AWGN Channels 3 and 4 at the same time ≈ 2.0•10 −5 and ≈ 9.0•10 −5 respectively. The distance between the graph of AWGN Channel 1 and the curves for the remaining channels increased compared to the negligible HPA nonlinearity (see Figure 8), although for the latter the SNR "shift" remained the same. This means that with an increase in the level of nonlinearity, communication with the RPAS at large distances suffers rst of all. This is a seemingly obvious conclusion, but the data obtained allow us to quantify the degree of such deterioration.
The plots in Figures  The prede ned M-ary Gray-coded signal constellation assigns the binary representation to the Mth phase.
The zeroth phase in the constellation is the phase offset parameter. If the block input is the natural binary representation, the block output has phase jθ + j2πm/M, where θ is the phase offset parameter and m is an integer between 0 and M-1. Figure 11 (BPSK modulation) and Figure 15 (QPSK modulation) show the dependences of the BEP on the SNR for different phase offset parameters with a high degree of HPA nonlinearity (in both cases, for simplicity, data are given only for the rst two RPASs). Phase offset values equal to 0 radians lead to the least number of bit errors. In the case of QPSK modulation, higher SNR values are required for the communication channels compared to BPSK modulation.
A comparison of the differences between BER versus SNR dependences for the rst two RPASs for BPSK and QPSK modulations is shown in Figure 12. The AWGN Channel 1 is open for BPSK modulation at E s /N 0 = -13 dB, and at E s /N 0 = -11 dB, the second is also open. For QPSK modulation both considered channels are closed in this case.
Comparison of negligible and severe HPA nonlinearities for BPSK modulation is considered above in Figures 8 and 9. Figure 14 shows the data for QPSK modulation with negligible HPA nonlinearity. When the SNR in AWGN Channel 1 changes from -33 dB to -28 dB, the BER decreases from ≈ 9.5•10 −2 to ≈ In the case of severe HPA nonlinearity, the situation is shown in Figure 15. High SNR values are required for RPAS communication links operation under these conditions. When the SNR in AWGN Channel 1 changes from -13 dB to -8 dB, the BER decreases from ≈ 7.0•10 −2 to ≈ 5.1•10 −6 . The BER for AWGN Channel 2 reaches a value of ≈ 4.1•10 −3 at E s /N 0 = -8 dB, and for AWGN Channels 3 and 4 at the same time, respectively, ≈ 1.3•10 −2 and ≈ 1.8•10 −2 . The distance between AWGN Channel 1 graph and the curves for the remaining channels increased compared to the negligible HPA nonlinearity (see Figure 14).
An increase in the level of nonlinearity leads to a deterioration in communication with the RPAS over long distances.

Discussion
There are practically no theoretical studies devoted to the development of predictive analysis methods in the eld of RPAS/UAV swarms data synthesis. There are no methods for assessing the e ciency and tra c parameters for swarms. Our research focuses on the development of such methods. To understand the ways to ful ll the requirements for drone swarms delay, reliability, bandwidth, and QoS this study was undertaken.
It is possible to conclude that in a swarm for "small" packets up to 4 Kbits it is "more pro table" (less losses) to use Exponential law for TBT parameter (≈ 25% losses compared to ≈ 42% for Const and LogNormal laws), but for "large" packets (4 -9) Kbits is more pro table to use the LogNormal law (≈ 42% losses).
The nonlinearity in the communication channel is critical for wireless communication systems in general, and for drones in particular. Therefore, the obtained data allow quantitatively compare the features of data transmission using the dependences of the BER on the SNR for different levels of BS transmitter nonlinearity (Figures 8-16). It is shown that data transmission with an increase in the nonlinearity and the transition to QPSK modulation requires an increase in the SNR. So, for BPSK modulation (phase offset pi/8 rad, BS antenna diameter 1 m) with the negligible nonlinearity BER ≈ 1.0 • 10 -6 at E s /N 0 = -30 dB, and with the severe nonlinearity BER ≈ 1.0 • 10 -6 at E s /N 0 = -10 dB. For QPSK modulation (phase offset pi / 4 rad, BS antenna diameter 1 m) with the negligible nonlinearity BER ≈ 4.8 • 10 -6 at E s /N 0 = -28 dB, and with the severe nonlinearity BER ≈ 5.1. • 10 -6 at E s /N 0 = -8 dB.
The given dependences of the BER on the diameter of the BS antenna for the severe nonlinearity allow analyzing and predicting the behavior of communication channels for various signal modulations during data transmission.
It should be noted such aspects in our article as the original architecture of channel models and the possibility of using the results to assess the quality of data transmission. The study is a continuation of our work and expands it to modeling RPAS communication channels in swarms. In the future, we plan to include an estimate of packet loss and parameters of telecommunication channels in RPAS swarms with satellite radio access networks.

Conclusions
This work is the rst study with the calculation of data packet losses and the effect of nonlinearity for RPASs in a swarm. Results can be considered as a way to estimate the parameters of such channels using the MATLAB Simulink and NetCracker packages.
The signi cance of the results obtained lies in the ability not only to identify problems at the early stages of designing RPAS channels, but also to minimize errors, reduce time, costs and ensure scalability in new projects. It is already clear to many that such calculations are becoming a necessary tool for a researcher and developer of RPAS communication systems in clusters.

Declarations
Availability of data and materials: All data generated or analysed during this study are included in this published article.      Dependences of BER on SNR for different BS antenna diameters (QPSK modulation, phase offset pi/4 rad)