Secrecy performance analysis on spatial modeling of wireless communications with unmanned aerial vehicle and ground devices

ABSTRACT


INTRODUCTION
Unmanned aerial vehicles (UAVs) have used popularity in the world, in which superiorities of quad-copter UAVs, which were well introduced in recently published studies, included: adaptive altitude flight control, vertically moving and landing on moving targets via disturbance observer-based controllers.Furthermore, UAVs have become a vital link between the internet of things (IoT) and cellular systems in 5G communication technologies [1], [2].The preference for UAVs in emerging IoT communications can be attributed to the dominant line-of-sight (LoS) links and mobility; therefore, making UAV-aided communication very desirable [3], [4].However, the prevalence of these strong LoS links makes UAV-aided communications vulnerable to ground/aerial eavesdroppers, consequently ensuring privacy and data security becomes very crucial [5].
Several research works such as [6], [7], have proposed different solutions for securing various kinds of UAV-assisted networks.In [5], the secrecy outage analysis of UAV-aided two-hop decode and forward (DF) relay cognitive transmission with energy harvesting under Nakagami-m channel conditions was investigated.On the basis of closed-form expressions of non-zero secrecy capacity probability and optimal secrecy outage probability (SOP), the study examined where there is no channel state information (CSI) for eavesdropper.Furthermore, in the simulation results, it was proved that the system secrecy capacity commits to be increased by optimizing the power dividing factor and other parameters simultaneously.Differently in Ji et al. [6] analyzing the functions was employed to derive the closed-form expressions of the system SOP and the Int J Elec & Comp Eng ISSN: 2088-8708  Secrecy performance analysis on spatial modeling of wireless communications … (Cuu Ho Van) 6411 probability of non-zero secrecy capacity for a cognitive network DF UAV-assisted relay transmission with energy harvesting.Li et al. [7] studied the secrecy energy efficiency maximization problem in full-duplex (FD) UAV-assisted wireless sensor networks (WSNs) with eavesdroppers without CSI.The result depends on the restrictions of connection outage probability (COP), SOP, safely collected bits, and flight trajectory.To deal with the non-convex difficulty, two important steps were taken.In the first step, the optimal code word ratio and the redundancy ratio in closing expressions were inferred.In the next step, an algorithm with low complication was established utilizing block coordinate reduction (BCD) method to develop the replacement of sensor nodes (SNs) scheduling, SN transmitter power, UAV transmit power and UAV trajectory.Moreover, the research [8]- [11] investigated the impact of multiple eavesdroppers on SOP.Liu et al. [8] examined the SOP obtained by forwarding it to a low-altitude UAV large stable transmission system with the existence of numerous UAV eavesdroppers utilizing maximum ratio combining for intercepting legitimate UAV-transmitter and UAV-relay transmissions.The authors derived closed-form expressions for the SOP in regarding the UAV participation, backhaul dependability, eavesdropping probability, and Nakagami-m fading parameters.The possibility of asymptotic secret loss is also inferred in the area with a high signal-to-noise rate.It is found that the secrecy variety obtained by forwarding is collectively concluded by the UAV cooperation and structure elements of Nakagami-m fading links in the main channel.Bao et al. [9], the SOP of a UAV-aided relay communication system, where the UAV relay transmits information from a ground base station (GBS) to legitimate ground users in the presence of multiple aerial and ground eavesdroppers.The links are considered to operate under the general κ-μ shadow channel fading model.To improve the secrecy performance efficiency, the GBS and UAV relays adopt beam-oriented communication while deploying safety zones around their expected accepting targets.Consequently, the almost exact closing expressions of the SOP are obtained under varied aerial and ground eavesdroppers' conditions.The SOP over Rayleigh fading as an extraordinary situation is also obtained.The simulation results demonstrated that UAV eavesdroppers impact the system performance more than ground eavesdroppers.Wu et al. [10] considered the impact of random UAV vibration interference and various non-colluding unintentional walk eavesdroppers on the security efficiency of the air-to-ground (A2G) eavesdropping system.Secrecy coverage probability (SCP) and ergodic secrecy capacity (ESC) expressions are acquired with features for the signal-to-noise ratio (SNR) received at legitimate receivers and eavesdroppers.Simulation results showed that UAV vibration interference can be employed to improve security efficiency of A2G eavesdropping system with applicable UAV height and beamwidth.In research [11]- [13], the study investigated UAV-assisted IoT communication systems operating in a completely incidental environment regarding the number of eavesdroppers and their positions around the earth source.
Moreover, to improve the system's security, we inspect the secrecy efficiency of the UAV IoT system with a favorable UAV that produces interference to confuse the eavesdroppers in [14].By using stochastic geometry theory, the increasing allocation functions for the signal-to-noise plus-noise ratio of the main and eavesdropping links are obtained.After that, the analytical expressions of the SOP and the average secrecy rate (ASR) are achieved in [15], [16].Ye et al. [17], [18] have studied UAVs and their rapid advancement to supply wider signal coverage and more comprehensive observation power in military and civil activities.The integration of UAVs into macrocellular networks is attracting remarkable attention to complement terrestrial cellular networks [19]- [21].As an aerial base station, UAV is a progressive technology to supply wireless networks to users quickly.With the versatility and portability of UAVs, a major issue is how to better UAVs distribution to best meet immediately the needs of wireless network in a region.Azari et al. [22], Wang et al. [23], Wang et al. [24], Hayat et al. [25] have optimized the travel distance of the UAV in the selected area to optimize the average throughput and the probability of advantageous communication when the user density is low and the travel distance is small.The movement of the UAV becomes light when the user density is high.
In this paper, our main contributions can be outlined as follows: to look at the diversity performance of the considered network, we propose the system model and analytical expressions to indicate performance metrics such as the secrecy outage probability (SOP) and intercept probability (IP) of the proposed system, which is applicable to evaluate UAV-aided reliability.
The paper is organized as follows: section 2 describes the system model of mobile UAV-aided spatial distributions for secure communication.Section 3 provides for security performance analysis of ground users.Section 4 numerical results.Section 5 concludes of paper.

SYSTEM MODEL
As seen in Figure 1, we assume that the UAV is stationary and that the ground users (D) is placed in a circle, with  serving as the circle's center.More specifically, the ground users were deployed in the inner circle with a radius of  1 meters to assess the users' performance at various distances from the UAV.Several randomly placed eavesdroppers (E) with the radius  2 and  1 meters were also deployed in the outer ring.The wireless connectivity between the UAV and the ground users is considered insignificant in the presence of natural or artificial impediments like trees or tall buildings.Thus, it is estimated that the UAV-to-D and UAV-to-E link follow the Rayleigh fading distributions, respectively.The homogeneous poisson point process (HPPP) model is used to simulate the geographic locations of the ground users and the listeners.We exploit homogeneous poisson point processes to model the locations of the users [26].Hence, the ground users and eavesdroppers are uniformly distributed within their areas, and the probability density functions (PDF) of the distances from a user and eavesdroppers to the center are derived as Figure 1.
where ℎ  and ℎ  denote the Rayleigh fading channel between UAV-to-D and UAV-to-E.The channel power gains |ℎ  | 2 and |ℎ  | 2 are assumed to be exponentially distributed random variables (RVs) with the parameters   ,  ∈ {, }, respectively.  and   are the transmit power at the UAV and E,  refers to the path-loss factor while   indicates the distance between UAV-to-D link and UAV-to-E link,   and   are the superimposed signal vector satisfying the total power constraint {|  2 | 2 } = {|  2 | 2 } = 1 with {.} is the expectation.  denotes the additive white Gaussian noise (AWGN) with   ~(0,  0 ) in which (, ) complex normal distribution with average  and variance .

SECURITY PERFORMANCE ANALYSIS
In this part, we analyze the secrecy performance for ground users' metrics using the SOP and IP expressions.With the analysis of SOP, by observing (8), it contains many RVs.Hence, the exact closed-form of SOP expression is very hard to obtain.By applying Gaussian-Chebyshev quadrature, the approximation SOP expression can be claimed while still assessing the physical significance of the system's characteristic parameters.The detailed analysis is given as follows.

SOP analysis
In this first analysis, the performance is an important metric to show the secure performance of the UAV-enabled system, the chance that the immediate secrecy capacity is less than the goal rate is known as the secure outage probability (SOP).Thus, channel capacities can be expressed as (6a) and (6b).
The SOP is defined as the probability that secrecy capacity is below the secrecy rate threshold, thus SOP in the proposed system can be expressed as (8).
where  ℎ is so-called the secrecy rate threshold,  = .
Lemma 1: The approximated secure outage probability of ground users closed-form statement is provided by (9).Proof: By definition,  denotes the complementary event at ground users and is calculated as (10).
Based on [28], we determined to obtain a closed-form formula  for the second integral to calculate and obtain an accurate approximation.Corresponding, we use Gaussian-Chebyshev quadrature [28], (25.4.38),  is written as (13).)  =  and applying the Gaussian-Chebyshev quadrature, we have  is computed as ( where , (  ) =  ( (  +1)
Secrecy performance analysis on spatial modeling of wireless communications … (Cuu Ho Van) 6415

Intercept probability analysis
In this second analysis, we examine the UAV system's performance regarding IP secrecy in the presence of randomly placed ground users.The IP will be occurred if and only if the information from   is accurately decoded at the ground users and the eavesdropper will be able to intercept the information of the ground users successfully.
Based on above description, user D will be intercepted if E can successfully wiretap 's signal.Then, the IP of D by E is shown as (15).
where   = where (., . ) is the lower incomplete Gamma function and Γ(. , . ) is the upper incomplete Gamma function.
Proof: We have intercept probability calculated as (17).
where we have used [27], (3.381.8),[27], (3.381.9) and [27], (3.381.10) to solve the corresponding integral.In order to do this, a few straightforward mathematical operations may be used to quickly arrive at the required Lemma 2 outcome.

MUMERICAL RESULTS
In this part, we demonstrate the outage performance by numerically simulating various theoretical findings from some figures.The primary system parameters are set at  1 = 5 m,  2 = 20 m,  ℎ = 1,   = 10 dB,   = 1 and   = 1.Additionally, data from a Monte-Carlo simulation run 10 6 times are given to confirm our analytical findings.In the following figures, we denote "Exact theory" and "Simulation" as analytical computation and Monte-Carlo computation-based simulations, respectively.In addition, the Gauss-Chebyshev parameter is selected as N=K=200 to earn the closest result.
We provide the SOP curves for various values as shown in subsection 3.1, when   is big, the SOP of the system alters, as can be seen in Figure 2. The SOP performance in this scenario solely pertains to   and   .However, since the superimposed message is transmitted to two different destinations, the systems have a higher security requirement than conventional point-to-point communication, so small values for the target rate and the average SNR of the eavesdropper link should be chosen in order to ensure reliable communication.
In Figure 3, the random ground users and random eavesdropper selection are plotted.We can see that when the rate of radius  1 grows, the outage of the ground users happens more frequently.This is due to the fact that in our suggested protocol, higher outages might occur when the user decodes the signal themselves, yet the radius is close to the eavesdropper.As a result, extending the radius  1 makes it more difficult to decode, which will result in more outages.A crucial finding is that choosing the wrong radius  1 will result in an outage probability of one.
The SOP vs. target rate for various fading parameters (  = 10; 30; 40 dB) and (  = 10; 20 dB) is shown in Figure 4 under ideal circumstances.We can observe from Figure 4 that when Rth grows, the ground users SOP also rises.The dependability of the system under consideration rises together with the average SNR of the illicit link, increasing SOP.
For various transmit SNR levels, Figure 5 shows the IP vs. the target rate.The IP of SNR=25 dB is superior to SNR=20 dB, SNR=15 dB, and SNR=10 dB, as can be shown.Additionally, we can see that the target rate has a significant influence on the ground users.

CONCLUSION
In this paper, we considered the domain of wireless communication systems in which UAVs can serve ground users.The security of wireless networks is a serious aspect of the system's performance and reliability.We have focused on security issues and mitigation techniques for the outage of the ground users in wireless with SOP and IP parameters of the system.Furthermore, all analytical results are verified by Monte Carlo simulations.Based on the analysis in the paper, we can extend to the generic framework of the UAVs mobility application to examine the efficiency of a more significant number of NOMA users in future work.

Figure 1 .
Figure 1.The system model of mobile UAV-aided spatial distributions for secure communication

Int
Secrecy performance analysis on spatial modeling of wireless communications … (Cuu Ho Van) SNR of the legal links between UAV and D,   = 's average SNR between UAV and eavesdroppers E.

Figure 2 .Figure 4 .
Figure 2. SOP versus   for different secrecy SNR taget data values (16)precise closed-form equation for the IP of D for Rayleigh fading channels is provided by(16).