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# Secrecy Outage Probability for Two-Way Integrated Satellite Unmanned Aerial Vehicle Relay Networks with Hardware Impairments

1 College of Public Management, China University of Mining and Technology, Xuzhou, 221116, China

2 School of Space Information, Space Engineering University, Beijing, 101407, China

* Corresponding Author: Kefeng Guo. Email:

(This article belongs to this Special Issue: Recent Advances in Backscatter and Intelligent Reflecting Surface Communications for 6G-enabled Internet of Things Networks)

*Computer Modeling in Engineering & Sciences* **2023**, *135*(3), 2515-2530. https://doi.org/10.32604/cmes.2023.024857

**Received** 09 June 2022; **Accepted** 14 July 2022; **Issue published** 23 November 2022

## Abstract

In this paper, we investigate the secrecy outage performance for the two-way integrated satellite unmanned aerial vehicle relay networks with hardware impairments. Particularly, the closed-form expression for the secrecy outage probability is obtained. Moreover, to get more information on the secrecy outage probability in a high signal-to-noise regime, the asymptotic analysis along with the secrecy diversity order and secrecy coding gain for the secrecy outage probability are also further obtained, which presents a fast method to evaluate the impact of system parameters and hardware impairments on the considered network. Finally, Monte Carlo simulation results are provided to show the efficiency of the theoretical analysis.## Keywords

It is reported that satellite communication (SatCom) is considered to be a wishing way for the sixth generation (6G) and beyond next generation (BNG) wireless communication system for its special characters, such as the wide coverage and particular services [1–5]. Owing to similar reasons, it can make up for the shortage of unmanned aerial vehicle (UAV) networks along with the high data transmission and wide coverage. Based on this foundation, to both utilize the advantage of the SatCom and UAV networks, the framework for the integrated satellite UAV relay network (ISUAVRN) appears, which is considered the major part of the future wireless communication networks [6,7]. Besides, owing to the transmission beam’s wide coverage, many users or relays existed in one beam [7–11]. In [7], a selection scheme based on the threshold was provided to keep the balance between the system performance and system complexity for the considered network. Furthermore, the outage probability (OP) was studied. In [8], one partial selection scheme was utilized to enhance the system performance for the considered networks. In [9], the authors studied the OP for the cognitive networks, which combined the satellite and the terrestrial networks. In [10], the OP was researched for the considered networks along with the secondary network selection scheme under the cognitive technology. In [11], the authors gave a terrestrial and user scheduling scheme based on the maximal performance for the ISUAVRNs in the presence of many terrestrial relays and many users. In [12], the ergodic capacity for the ISUAVRNs with a selection scheme and multiple terrestrial relays was researched. In [13], the OP was investigated for the ISUAVRNs with multiple users and an opportunistic user scheduling scheme. To enhance the spectrum efficiency and time utilization, a two-way relay technique is proposed for the ISUAVRNs [14]. In [15], the OP was researched for the ISUAVRNs with hardware impairments (HIs) and the two-way terrestrial relay. In [16], the OP was analyzed for the ISUAVRs in the presence of many two-way terrestrial relays and a partial selection scheme. In [17], the OP was investigated for the considered ISUAVRNs with multiple terrestrial relays and an opportunistic selection scheme under the non-orthogonal multiple access scenario. However, due to the inherent characters of wireless communications particularly for the SatCom, the secrecy issue has been regarded as the major point for the SatCom [18]. The physical layer security (PLS) is considered as the hopeful method to investigate the difference between the eavesdroppers’ and legitimate channels, which is a popular research issue over recent years [19,20]. In [19], a proposed beamforming (BF) scheme was utilized for the cognitive ISUAVRNs to enhance the secrecy performance. In [21], the authors researched the secrecy-energy efficient hybrid BF scheme for the ISUAVRNs. In [22], the non-ideal channel state information (CSI) and cognitive technology were both investigated for the secrecy ISUAVRNs along with secrecy performance. In practical systems, all nodes are not often ideal, which means they always suffer the I/Q imbalance, phase noise, and amplifier non-linearities [23–25], which results in the HIs in the transmission nodes. In [26], all the HIs issues are concluded, which leads to a general HIs model, widely utilized for many former works [27–31]. Above all, to the authors’ best effort, the investigation for the effects of two-way terrestrial relays on the secrecy ISUAVRNs with HIs is still not published, which motivates our paper.

From the former discussions, by considering the two-way UAV relay and an eavesdropper into our sight, we investigate the secrecy performance for the considered network. The contributions of this paper are presented in the following:

• By utilizing the two-way UAV relay and an eavesdropper into consideration, the framework for the secrecy ISUAVRN is founded. Besides, the decode-and-forward (DF) mode is used in the UAV to help the source to transmit the signals. Due to the heavy fading and other obstacle reasons, no direct link is assumed for the legitimate transmission link for the two sources. In addition, all the nodes are assumed to suffer from the HIs.

• Based on the considered system model, the detailed analysis for the secrecy outage probability (SOP) is obtained, which gives the easy method to investigate the SOP. Besides, these theoretical results can direct the engineering guide.

• To derive the further results of the system parameters on the SOP for the system, the asymptotic behaviors for the SOP are derived, which provide the secrecy diversity and order secrecy coding gain.

The remaining of this paper is shown in the following. A detailed illustration for the considered system is given in Section 2. The analysis for the secrecy OP is derived in Section 3. Some computer simulations namely Monte Carlo (MC) results are given in Section 4 to show the efficiency of the analytical results. The conclusion of the work is provided in Section 5.

Notations:

As plotted in Fig. 1, we consider an ISUAVRN with HIs in this paper, which contains a satellite source

It will use two time slots for the whole transmission. During the first time slot,

where

Since E and R are located in the same transmission beam, the overhear signal at E in the first time slot is shown as

where

In the second time slot, owing to the utilized DF protocol, the UAV relay will use some techniques to decode the signals received and then re-transmit the re-encoded signal to

where

As the same assumption, R and E are located in the similar transmission beam. Thus, the obtained signal at E in the second time slot is represented as

where

By utilizing Eqs. (1) and (3), the obtained signal-to-interference-plus-noise ratio (SINR) at R from the p-th source is obtained as

where

The derived signal-to-noise ratio (SNR) at

where

With the help of Eqs. (2) and (4), the obtained SNR at E is, respectively, obtained as

where

According to [32], the capacity for secrecy performance has the definition which is shown as the difference between the capacity of the legitimate users’ channel and the eavesdroppers’ channel. By utilizing Eqs. (5)–(9), the secrecy capacity for the considered network is represented as

where

The detailed analysis for the SOP will be obtained in this part. At first, the channel model for the transmission link is presented.

3.1.1 The Terrestrial Transmission Link

The channel model for the terrestrial transmission link is modeled as independent and identically distribution (i.i.d) Rayleigh fading. From [33], the PDF and CDF of

and

where

3.1.2 The Satellite Transmission Link

The geosynchronous Earth orbit (GEO) satellite is taken for the analysis. In addition, we also consider the satellite having multiple beams for the considered system model. Particularly, time division multiple access (TDMA) [34] scheme is utilized in the considered model, which means that only one UAV R is suitable to forward the information signal at the next time slot.

The channel coefficient

where

where

With help of [35],

where

where

For

With the help of [8], the PDF for

where

Relied on Eq. (17) and utilizing [11], the CDF of

3.1.3 Secrecy Outage Probability

From [18], the SOP defined as

where

For

For

Firstly, with the help of

From Eq. (22), the first consideration is to obtain the CDF for

Then by utilizing Eq. (5), the CDF for

With the help of Eq. (17) with

Then, after some mathematic steps,

Next, with the help of [39],

Then, recalling Eq. (22), Eq. (22) can be re-written as

Then, it should be mentioned that in Eqs. (23) and (24), y should be satisfied with the following condition, which is

where

However, try the authors’ best efforts, it is too hard to obtain the closed-form expression of Eq. (29), then by utilizing [35] and utilizing the Gaussian-Chebyshev quadrature [40], by inserting Eqs. (24) and (23) into Eq. (29), it can be derived as

where

and

By utilizing the similar ways, the closed-form expressions for the

where

and

where

and

where

and

Then, by substituting Eqs. (30)–(33) into Eqs. (19)–(21), respectively. The closed-form expression for the SOP will be obtained, which is omitted here.

In what follows, the asymptotic behaviors for the SOP is obtained. When

and

Then by substituting Eqs. (34)–(37) into Eqs. (19)–(21), the asymptotic expression will be derived.

Then from the final asymptotic SOP expression, the secrecy diversity order and secrecy coding gain are respectively derived as

During this part, some representative MC simulations are provided to prove the efficiency of the theoretical analysis. Through these results, the impacts of channel parameters are evaluated. Without loss of any generality, we set

Fig. 2 examines the SOP vs.

Fig. 3 represents the SOP vs.

Fig. 4 plots the SOP vs.

This paper investigated the SOP for an integrated satellite UAV relay network with HIs. Especially, the closed-form and asymptotic behaviors for the SOP were derived. Firstly, it was derived that the SOP would have worse performance with threshold being larger; Secondly, it was found that the SOP would be larger with a larger

Acknowledgement: The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.

Funding Statement: This work is supported by the Natural Science Foundation of China under Grant No. 62001517.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

1We should know that, during this paper, only one antenna is assumed, however the derived results are still fit for the case with many antennas.

2Although this paper just considers one eavesdropper, the derived results are still fit for the model with multiple eavesdroppers. Besides, the model with multiple eavesdroppers will be investigated in our near future.

3Owing to some reasons, direct transmission link between two sources is not available.

4It should be mentioned that, the SR channel is a famous channel model [8,10], which comes from the practical estimation date [37,38].

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## Cite This Article

Ren, X., Guo, K. (2023). Secrecy Outage Probability for Two-Way Integrated Satellite Unmanned Aerial Vehicle Relay Networks with Hardware Impairments.*CMES-Computer Modeling in Engineering & Sciences, 135(3)*, 2515–2530.