Open AccessArticle

Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios

Xiwen Zhang

^1,*,

Shanghong Zhao

¹,

Yuan Wang

¹,

Hang Hu

¹,

Guangmingzi Yang

Xinkang Song

¹,

Xin Li

and

Jianjia Li

Institute of Aeronautics Engineering, Air Force Engineering University, Xi’an 710043, China

China Mobile System Integration Co., Ltd., Xi’an 710077, China

Author to whom correspondence should be addressed.

Drones 2024, 8(12), 729; https://doi.org/10.3390/drones8120729

Submission received: 4 November 2024 / Revised: 20 November 2024 / Accepted: 27 November 2024 / Published: 2 December 2024

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Abstract

Free-space optical (FSO) communication with unmanned aerial vehicles (UAVs) as relays is a promising technology for future aeronautical communication systems. In this paper, a multiple UAV-based aeronautical communication system is proposed, wherein a hybrid FSO/radio frequency (RF) link is established to connect the Airborne Warning and Control System (AWACS) with the mobile ground station (GS). Initially, we consider the velocity variance of both AWACS and the mobile GS, along with the influence of the Doppler effect. Furthermore, four relay selection modes are proposed, and exact closed expressions are derived for the end-to-end outage probability and bit error rate (BER) of the considered system. Numerical simulations demonstrate the impact of velocity variance variation on system performance. Additionally, we analyze the applicability of these four relay modes under different platform mobility characteristics through simulation results, while discussing the optimal numbers and the deployment altitude of UAVs. Finally, effective design guidelines that can be useful for aeronautical communication system designers are presented.

Keywords:

UAV relay; FSO/RF; aeronautical communication; relay selection mode

1. Introduction

In recent years, the application of free-space optical (FSO) technology to aeronautical communication systems has received significant attention. In contrast to traditional radio frequency (RF) aeronautical communication in short-wave or ultra-short-wave frequency bands, FSO communication overcomes bandwidth limitations, low transmission capacity, and susceptibility to interference. Hence, FSO communication has become a viable and promising solution to gratify enormous data transmission requirements.

It is widely acknowledged that the FSO signal is affected by three significant factors—attenuation, turbulence, and pointing errors (PEs)—all of which are distance-dependent [1]. Furthermore, FSO transceivers are constrained by the strict requirement of line-of-sight (LoS) alignment. In addition, the aeronautical communication network exhibits the characteristics of a complex atmospheric environment and strong node mobility. Consequently, aerial relay (AR)-aided communication has emerged as the key to influencing the application and development of FSO airborne communication [2,3].

Unmanned aerial vehicles (UAVs) are flexible and highly maneuverable and can operate as flying base stations, providing perfect LoS connectivity to ground users and other aircraft. For the UAV-based FSO system, accurate channel modeling is very important. In [4,5,6], several channel models based on hovering UAVs were proposed. In [4], a new closed-form statistical channel model was proposed by using a log-normal turbulence model and considering the effect of non-zero pointing error. A simpler and tractable channel model over a log-normal atmospheric turbulence environment under weak turbulence conditions was proposed in [5]. In [6], a multi-rotor UAV-based FSO link in the presence of atmospheric turbulence by considering angle-of-arrival (AOA) fluctuations was considered. Moreover, UAV relays are flexible enough to maneuver and adjust their positions based on channel conditions [7,8,9], such as cloud obstacles. In addition, extensive research has been conducted on the combined utilization of serial and parallel UAV relays to achieve significant performance enhancements by reducing hops in multi-hop systems [10,11,12].

Therefore, the main motivations of our paper can be summarized as follows:

The current literature extensively studies the use of UAV relay-assisted communication. However, these studies are rarely studied in aeronautical communication systems and the mobility of source and destination nodes is neglected.
To the best of our knowledge, existing research almost ignores the impact of varying velocity variance among mobile platforms on system performance.
Currently, extensive research has been conducted on relay selection modes; however, there is a lack of performance comparison and applicability analysis for various modes in mobile scenarios.
In aeronautical communication scenarios, a single FSO link is susceptible to platform movement and atmospheric interference, thereby compromising information transmission reliability. Therefore, incorporating an RF backup link is crucial for enhancing the overall system performance.

Motivated by the aforementioned discussions, we consider a parallel UAV relay-assisted aeronautical communication system from an Airborne Warning and Control System (AWACS) to a mobile ground station (GS). In order to reduce the impact of complex atmospheric conditions on air-to-ground links, we adopted a hybrid FSO/RF link and activated an RF backup link when the FSO link failed to meet the requirement of quality of service (QoS). The key contributions of this paper are summarized as follows:

First, we propose a novel air-to-ground aeronautical communication system model based on multiple parallel UAV relays. To ensure reliable communication, we consider employing a hybrid RF/FSO communication link between the AWACS and the mobile GS.
Next, the mobility of the AWACS platform, UAV relays, and mobile GS is considered. The impacts of velocity variance variation of the AWACS and GS on the outage and average BER performance in the aeronautical communication system are analyzed in detail. Additionally, the influence of the Doppler effect is also discussed.
Moreover, four relay selection modes are proposed, and the exact closed-form expressions for end-to-end outage probability under different modes are derived. In addition, unlike other research, we do not make direct comparisons to determine the advantage of any mode. Instead, we consider the complexity of each case and the mobile characteristics of the platform in order to analyze the applicability of different modes in mobile scenarios.
Furthermore, the optimal number of relays is determined through simulation analysis, while the numerical analysis of the impact of UAV relay deployment altitude on system performance is conducted under different relay selection modes.
Finally, a valuable design guideline is provided that is useful for aeronautical communication system designers.

The rest of this paper is organized as follows: In Section 2, the system model, the FSO/RF signal model, and the relay selection modes are described. Section 3 constructs the FSO/RF channel model. In Section 4, the exact closed-form expressions for outage probability and average BER are derived. The numerical results and design guidelines are presented in Section 5. Finally, we conclude the paper in Section 6.

2. System and Signal Model

2.1. Space Environment

As illustrated in Figure 1, we consider a multiple UAV-based hybrid FSO/RF aeronautical communication network consisting of an AWACS as the source node

S

, the mobile GS as the destination node

D

, and

N

UAVs as relay nodes operating in the decode-and-forward (DF) mode terminals, denoted by

R_{i}, i = 1, 2, \dots N

. In this setup, the direct connection between

S

and

D

is considered unavailable due to the unstable weather conditions and heavy shadowing. To ensure reliable information transmission from air to ground, the UAVs divide the link into two hops. The first hop is the AWACS–UAV link, denoted by

S R_{i}

, and the second hop is the UAV-to-GS link, denoted by

R_{i} D

. Considering the intricate atmospheric conditions in the troposphere, the hybrid FSO/RF transmission scheme is implemented for both hops, in which the FSO link serves as the primary link, and the RF backup link is activated when the SNR requirement cannot be met by the FSO link. The AWACS is assumed to maintain a constant cruising altitude

H_{A W A C S}

. Additionally, for simplicity, we assume that all UAVs have an identical altitude

H_{U A V}

and zenith angle

ξ_{U A V}

, while the zenith angle of the ground station is denoted as

ξ_{G S}

. Moreover, we assume that the channel states are slowly fading in a time-varying manner, and that the channel state information (CSI) is still up-to-date information when arriving at the AWACS and UAVs.

2.2. FSO Link

We consider that the FSO system utilizes the intensity modulation and direct detection (IM/DD) technique and the On–Off keying (OOK) modulation.

The received signal at

R_{i}

can be expressed as

y_{S R_{i}}^{F S O} = η h_{S R_{i}} x_{f s o} + n_{f},

(1)

where

x_{f s o}

represents the transmitted signal. Since the OOK modulation scheme is used

x_{f s o} \in \{0, 2 P_{f, S R_{i}}\}

P_{f, S R_{i}}

is the average transmitted optical power of the source,

η

is the detector response,

h_{S R_{i}}

indicates the channel coefficient of the first hop, and

n_{f}

is the zero-mean additive white Gaussian noise (AWGN) with variance

σ_{f}^{2}

. The instantaneous received SNR at

R_{i}

can be expressed as

γ_{S R_{i}}^{F S O} = \frac{2 P_{f, S R_{i}}^{2} η^{2}}{σ_{f}^{2}} h_{S R_{i}}^{2} = {\bar{γ}}_{S R_{i}}^{F S O} h_{S R_{i}}^{2},

(2)

where

{\bar{γ}}_{S R_{i}}^{F S O}

is the average SNR for the source-to-relay FSO link.

The relay utilizes the DF mode, meaning that the instantaneous received SNR at

D

can be expressed as

γ_{R_{i} D}^{F S O} = \frac{2 P_{f, R_{i} D}^{2} η^{2}}{σ_{f}^{2}} h_{R_{i} D}^{2} = {\bar{γ}}_{R_{i} D}^{F S O} h_{R_{i} D}^{2},

(3)

where

P_{f, R_{i} D}

is the average transmitted optical power of the relay,

h_{R_{i} D}

indicates the channel coefficient of the second hop, and

{\bar{γ}}_{R_{i} D}^{F S O}

is the average SNR for the relay-to-destination FSO link.

2.3. RF Link

The received RF signal at the relay is given by

y_{S R_{i}}^{R F} = \sqrt{P_{r, S R_{i}} G_{S R_{i}}} I_{S R_{i}} x_{r f} + n_{R F},

(4)

where

x_{r f}

is the modulated signal transmitted by the RF transmitter;

P_{r, S R_{i}}

is the transmitted RF power of the source. The RF channel coefficient of the first hop is

I_{S R_{i}}

, and

n_{R F}

is the AWGN with zero-mean and variance

σ_{r f}^{2}

G_{S R_{i}}

denotes the path loss for the source-to-relay RF link.

The instantaneous received SNR at

R_{i}

can be expressed as

γ_{S R_{i}}^{R F} = \frac{P_{r, S R_{i}} G_{S R_{i}}}{σ_{r f}^{2}} I_{S R_{i}}^{2} = {\bar{γ}}_{S R_{i}}^{R F} I_{S R_{i}}^{2},

(5)

where

{\bar{γ}}_{S R_{i}}^{R F}

is the average SNR for the source-to-relay RF link. Moreover, the instantaneous SNR expression for the relay-to-destination RF link is given by

γ_{R_{i} D}^{R F} = \frac{P_{r, R_{i} D} G_{R_{i} D}}{σ_{r f}^{2}} I_{R_{i} D}^{2} = {\bar{γ}}_{R_{i} D}^{R F} I_{R_{i} D}^{2},

(6)

where

{\bar{γ}}_{R_{i} D}^{R F}

is the average SNR for the relay-to-destination RF link, and

P_{r, R_{i} D}

is the average transmitted power of the relay;

G_{R_{i} D}

and

I_{R_{i} D}

indicate the channel coefficient and path loss of the second hop, respectively.

2.4. Mode of Relay Selection

In this work, AWACS selects one relay node among UAVs that can offer optimal channel quality based on the accurate CSI feedback. Four different relay selection modes are considered: Max-Select relaying, Source-Relay-Select relaying, Relay-Destination-Select relaying, and Dual-Distributed-Select relaying.

2.4.1. Case 1 (Max-Select)

In this mode, the best relay is selected according to the CSI from both the

S R_{i}

and

R_{i} D

links. The end-to-end SNR of the

i th

link is

γ_{S D_{i}} = \min \{γ_{S R_{i}}, γ_{R_{i} D}\}

. The relay

I_{1}

is selected according to

I_{1} = \arg \max_{i = 1, 2 \dots, N} \min \{γ_{S R_{i}}, γ_{R_{i} D}\},

(7)

where

I_{1} \in \{1, 2 \dots, N\}

denotes the best relay selected in case 1. It is worth noting that both hops require feedback channels. In this case, the source node requires the CSI of all the

S R_{i}

and

R_{i} D

links. Since the source node and the destination node may not have a direct LoS connection, it even be necessary for the relay node to feedback the CSI of the

R_{i} D

link back to the source, resulting in a highly complex system.

2.4.2. Case 2 (Source-Relay-Select)

In this mode, the relay selection is based on the

S R_{i}

channel quality, and the UAV node that achieves the highest quality of the first hop is chosen to maximize the instantaneous SNR between

S

and

R_{i}

I_{2} = \arg \max_{i = 1, 2 \dots, N} \{γ_{S R_{i}}\},

(8)

where

I_{2} \in \{1, 2 \dots, N\}

denotes the best relay selected in case 2, and the selected relay

I_{2}

is utilized for communication in the second hop. In contrast to case 1, only the first hop needs a feedback channel in case 2.

2.4.3. Case 3 (Relay-Destination-Select)

In this mode, the relay selection is based on the

R_{i} D

channel quality, and the UAV node that achieves the highest quality of the second hop is chosen to relaying between

R_{i}

and

D

I_{3} = \arg \max_{i = 1, 2 \dots, N} \{γ_{R_{i} D}\},

(9)

where

I_{3} \in \{1, 2 \dots, N\}

is the index of the best relay. In this way, only the second hop needs a feedback channel.

2.4.4. Case 4 (Dual-Distributed-Select)

In this mode, the relay nodes are divided into two parts

N_{a}

and

N_{b}

, and

N_{a} + N_{b} = N

. The source node

S

and relay nodes

N_{a}

are equipped with CSI feedbacks, as well as the destination node

D

and relay nodes

N_{b}

. Based on the received CSI, the source node selects the highest instantaneous SNR relay

I_{a}

between

S

and

R_{i}

. Similarly,

D

selects the highest instantaneous SNR relay

I_{b}

between

R_{i}

and

D

. The relay selection mode is given as

I_{a} = \arg \max_{i = 1, 2 \dots, N_{a}} \{γ_{S R_{i}}\}, I_{b} = \arg \max_{i = 1, 2 \dots, N_{b}} \{γ_{R_{i} D}\},

(10)

where

I_{a} \in \{1, 2 \dots, N_{a}\}

and

I_{b} \in \{1, 2 \dots, N_{b}\}

are the indexes of relay. The selected two relays are simultaneously activated and cooperate to transmit information during signal transmission, and the selection combining (SC) technique is adopted in the destination node. The addition of a relay in case 4 significantly reduces the system’s CSI requirements compared to case 1.

3. Channel Model

This section presents the channel models for each transmission hop, including FSO-based AWACS-to-UAV, FSO-based UAV-to-GS, RF-based AWACS-to-UAV, and RF-based UAV-to-GS. Here, the subscript

j \in \{S R_{i}, R_{i} D\}

indicates the AWACS-to-UAV and UAV-to-GS links, respectively.

3.1. FSO Channel

The cruising altitude of the AWACS typically reaches approximately 10,000 m; thus, two hops from AWACS-to-UAV and UAV-to-GS occur within the troposphere. Consequently, we can reasonably assume that the two hops are influenced by the same atmospheric condition.

3.1.1. Atmospheric Attenuation

The propagation of an optical beam is subject to power loss due to the scattering and absorption of particles in the atmosphere. The atmospheric attenuation

h_{j}^{a}

can be described by the Beer–Lambert law [13].

h_{j}^{a} = \exp (- ω L_{j}), j \in \{S R_{i}, R_{i} D\},

(11)

where

L_{S R_{i}} = (H_{A W A C S} - H_{U A V}) / \cos ξ_{U A V}

and

L_{R_{i} D} = H_{U A V} / \cos ξ_{G S}

are the distances of

S R_{i}

and

R_{i} D

links, respectively. The attenuation coefficient

ω

can be defined by Kim’s model [14].

ω = 3.91 / V {(λ_{f s o} / 550)}^{- q},

(12)

where

V = 1.002 / {(N_{C} M_{C L W C})}^{0.6473}

is the atmospheric visibility and determined based on the cloud liquid water content value

M_{C L W C}

and cloud droplet number concentration

N_{C}

q

represents the size distribution of the scattering particles and is closely associated with

V

3.1.2. Turbulence-Induced Fading

The impact of atmospheric turbulence leads to power losses and unpredictable fluctuations in both signal intensity and phase, thereby necessitating a suitable model for characterizing turbulence, ranging from weak to strong levels. In this regard, the gamma–gamma distribution emerges as an appropriate choice. The probability density function (PDF) of turbulence

h_{j}^{t}

can be mathematically expressed [15].

f_{h_{j}^{t}} (h_{j}^{t}) = \frac{2 {(α_{j} β_{j})}^{(α_{j} + β_{j}) / 2}}{Γ (α_{j}) Γ (β_{j})} {h_{j}^{t}}^{\frac{α_{j} + β_{j}}{2} - 1} K_{α_{j} - β_{j}} (2 \sqrt{α_{j} β_{j} h_{j}^{t}}), j \in \{S R_{i}, R_{i} D\},

(13)

where

K_{v} (\cdot)

is the order-modified Bessel function of the second kind and

Γ (\cdot)

is the gamma function. Additionally, the parameters that represent large-scale fading

α_{j}

and small-scale fading

β_{j}

are expressed as

α_{j} = {[\exp (0.49 σ_{R, j}^{2} / {(1 + 1.11 σ_{R, j}^{12 / 5})}^{7 / 6}) - 1]}^{- 1},

(14)

β_{j} = {[\exp (0.51 σ_{R, j}^{2} / {(1 + 0.69 σ_{R, j}^{12 / 5})}^{5 / 6}) - 1]}^{- 1},

(15)

where

σ_{R, j}^{2} = 1.23 C_{n}^{2} K^{7 / 6} L_{j}^{11 / 6}

is the Rytov variance, which depends on the refractive index

C_{n}^{2}

;

K = 2 π / λ

is the wave number; and

λ

is the wavelength.

3.1.3. Pointing Error

The primary factors contributing to PE in this system are variations in the velocity of the AWACS and mobile GS, as well as fluctuations in the relative position and orientation of the UAV caused by random air disturbances and internal vibrations within the surrounding atmosphere.

It is worth noting that the Pointing–Acquisition–Tracking (PAT) system on UAVs and mobile GS scan dynamically adjust the orientation of the transmitter and receiver lenses to maintain beam alignment. However, the PAT system is insufficient to compensate for random position fluctuations caused by sudden changes in the speed of the AWACS and mobile ground station.

The change in height on the z-axis for AWACS, UAVs, and mobile GSs is not taken into account as this is negligible compared to their distance.

AWACS-to-UAV link:

For these links, the combined radial displacement vector from the

i th

UAV detector center to the center of the beam footprint at the receiver aperture on the UAV is expressed as

r_{S R_{i}} = r_{S} + r_{R} = [x_{S R_{i}}, y_{S R_{i}}]

, where

r_{S} = [x_{s}, y_{s}]

is the displacement vector of the AWACS and

r_{R} = [x_{R}, y_{R}]

is the displacement vector of the UAV, as shown in Figure 2a. This fluctuation, caused by a large number of random events, follows a Gaussian distribution; we have

x_{S R_{i}} \sim N (0, σ_{S R_{i} x}^{2})

and

y_{S R_{i}} \sim N (0, σ_{S R_{i} y}^{2})

. The position deviation of the AWACS is caused by sudden changes in its velocity. The velocity variation is denoted as

v_{S} = [v_{S x}, v_{S y}]

, where

v_{S x}

and

v_{S y}

follow the Gaussian distribution

N (0, σ_{S v}^{2})

with mean zero and the velocity variance of the AWACS

σ_{S v}^{2}

. Assuming that there is a slight change in the AWACS’s speed within a short time interval

Δ t

, the displacement distances can be expressed as

x_{S} = v_{S x} Δ t / 2

and

y_{S} = v_{S y} Δ t / 2

. The hovering UAV’s position fluctuation is denoted by

r_{R} = [x_{R}, y_{R}]

, where

x_{R} \sim N (0, σ_{R x}^{2})

and

y_{R} \sim N (0, σ_{R y}^{2})

. Mathematically speaking, the variance of

x_{S R_{i}}

and

y_{S R_{i}}

can be expressed as

σ_{S R_{i} x}^{2} = σ_{S x}^{2} + σ_{R x}^{2} = σ_{S v}^{2} {(Δ t)}^{2} / 4 + σ_{R x}^{2}

(16)

σ_{S R_{i} y}^{2} = σ_{S y}^{2} + σ_{R y}^{2} = σ_{S v}^{2} {(Δ t)}^{2} / 4 + σ_{R y}^{2}

(17)

2.: UAV-to-GS link:

For these links, the combined radial displacement vector from the mobile GS detector center to the center of the

i th

beam footprint at the receiver aperture on the GS is expressed as

r_{R_{i} D} = r_{R} + r_{θ} + r_{D} = [x_{R_{i} D}, y_{R_{i} D}]

, where

x_{R_{i} D} \sim N (0, σ_{R_{i} D x}^{2})

y_{R_{i} D} \sim N (0, σ_{R_{i} D y}^{2})

, and

r_{θ} = [x_{θ x}, x_{θ y}]

are the displacement vectors caused by the orientation fluctuation of hovering UAVs, and

r_{D} = [x_{D}, y_{D}]

is the displacement vector of the mobile GS, as shown in Figure 2b. Assuming that the UAV jitter angle in the

x - axis

θ_{x}

and

y - axis

θ_{y}

is sufficiently small, the values of

x_{θ x}

and

x_{θ y}

can be approximated as

x_{θ x} ≃ L_{R D} θ_{x}

and

x_{θ y} ≃ L_{R D} θ_{y}

, where

L_{R D}

is the transmitted distance, and

θ_{x}, θ_{y} \sim N (0, σ_{θ}^{2})

. The position deviation of the mobile GS with an unsteady velocity is caused by sudden changes in its velocity. The velocity variation is denoted as

v_{D} = [v_{D x}, v_{D y}]

, where

v_{D x}

and

v_{D y}

follow the zero mean Gaussian distribution

N (0, σ_{D v}^{2})

, and

σ_{D ν}^{2}

is the velocity variance of GS. The displacement distances within

Δ t

can be expressed as

x_{D} = v_{D x} Δ t / 2

and

y_{D} = v_{D y} Δ t / 2

. Therefore, the variance of

x_{R_{i} D}

and

y_{R_{i} D}

can be expressed as

σ_{R_{i} D x}^{2} = σ_{R x}^{2} + L_{R D}^{2} σ_{θ}^{2} + σ_{D v}^{2} {(Δ t)}^{2} / 4

(18)

σ_{R_{i} D y}^{2} = σ_{R y}^{2} + L_{R D}^{2} σ_{θ}^{2} + σ_{D v}^{2} {(Δ t)}^{2} / 4

(19)

The total radial displacement

r_{j} = \sqrt{x_{j}^{2} + y_{j}^{2}}, j \in \{S R_{i}, R_{i} D\}

follows the Beckmann distribution and can be approximated by the modified Rayleigh distribution as

f_{r_{j}} (r_{j}) = \frac{r_{j}}{σ_{j}^{2}} \exp (\frac{- r_{j}^{2}}{2 σ_{j}^{2}}), r_{j} > 0, j \in \{S R_{i}, R_{i} D\}

(20)

where

σ_{j}^{2}

is modified beam-jitter variance approximation, the modified jitter standard deviation of the AWACS-to-UAV link is

σ_{S R_{i}}^{2} = {(\frac{σ_{S R_{i} x}^{6} + σ_{S R_{i} y}^{6}}{2})}^{1 / 3}

, and the modified jitter standard deviation of the UAV-to-GS link is

σ_{R_{i} D}^{2} = {(\frac{σ_{R_{i} D x}^{6} + σ_{R_{i} D y}^{6}}{2})}^{1 / 3}

The PDF of

h_{j}^{p}

can be expressed as

f_{h_{j}^{p}} (h_{j}^{p}) = \frac{g_{j}^{2}}{A_{0, j}^{g_{j}^{2}}} {(h_{j}^{p})}^{g_{j}^{2} - 1}, j \in \{S R_{i}, R_{i} D\},

(21)

where

A_{0, j} = {[e r f (v_{j})]}^{2}

represents the fraction of the collected optical power when the difference between the optical spot center and the detector center is equal to zero, and

e r f (\cdot)

is the error function.

v_{j} = \sqrt{π} a / \sqrt{2} ω_{z, j}

is the ratio between aperture radius

a

and beamwidth

ω_{z, j}

at the distance of

L_{j}

. Moreover, the pointing error coefficient

g_{j} = ω_{Z_{e q}} / 2 σ_{j}

, where

ω_{Z_{e q, j}}^{2} = ω_{z, j}^{2} \sqrt{π} e r f (v_{j}) / 2 v_{j} e^{- v_{j}^{2}}

is the equivalent beamwidth.

3.1.4. AOA Fluctuations

The beam no longer maintains orthogonality with the receiver plane due to the vibration of the hovering UAV. When the incident laser reaches the receiving plane at an angle

θ_{a, j}

, the Airy pattern may exceed the detector range due to the significant deviation in direction. The AoAs are defined as

θ_{a, j} ≃ \{\begin{matrix} \sqrt{θ_{r x}^{2} + θ_{r y}^{2}}, j = S R_{i} \\ \sqrt{θ_{t x}^{2} + θ_{t y}^{2}}, j = R_{i} D \end{matrix},

(22)

where

θ_{t x}

and

θ_{r x}

represent directional deviations in the horizontal plane of Tx and Rx.

θ_{t y}

and

θ_{r y}

are directional deviations in the vertical plane of Tx and Rx.

θ_{a, j}

follows the Rayleigh distribution as

f_{θ_{a, j}} (θ_{a, j}) = \frac{θ_{a, j}}{σ_{θ}^{2}} \exp (- \frac{θ_{a, j}}{2 σ_{θ}^{2}}), θ_{a, j} \geq 0, j \in \{S R_{i}, R_{i} D\},

(23)

where

θ_{F o V, j}

is the field-of-view (FOV) angle of Rx. The link outage when

h_{j}^{a o a} = 0

occurs for

θ_{a, j} > θ_{F o V, j}

, and

h_{j}^{a o a} = 1

for

θ_{a, j} \leq θ_{F o V, j}

otherwise. Therefore, the PDF of

h_{j}^{a o a}

can be expressed as

f_{h_{j}^{a o a}} (h_{j}^{a o a}) = \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}}) δ (h_{j}^{a o a}) + [1 - \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}})] δ (h_{j}^{a o a} - 1), j \in \{S R_{i}, R_{i} D\},

(24)

where

δ (\cdot)

is the Dirac delta function [16].

3.1.5. Doppler Effect

We assume that in order to ensure the information transmission of the AWACS, the relay formation composed of UAVs and the AWACS remains relatively stationary at all times. Therefore, we do not take into account the Doppler effect in the AWACS-to-UAV link.

The Doppler frequency shift between UAV-to-GS links is induced by the relative motion between the mobile GS and the UAVs, which is expressed as

Δ f = v f_{F S O} \cos (ξ_{G S}) / c

, where

v

is the relative velocity between the

i th

UAV and GS,

f_{F S O}

is the optical carrier frequency, and

c

is the speed of light. The current designs of FSO receivers can correct for frequency shifts up to ±15 GHz [17]. In other words, for an optical signal with

λ = 1550 nm

, if

v < 6458 km / h

, the resulting Doppler shift can be corrected. It is evident that the current UAV and mobile GS (i.e., vehicle) cannot exceed this value in terms of their relative speed. Therefore, the Doppler effect of the UAV-to-GS links can be ignored.

3.1.6. Overall Channel Statistical Characteristics

The combined FSO channel fading due to atmospheric attenuation, turbulence, PE, and AOA, respectively, and can be expressed as

h_{j} = h_{j}^{a} h_{j}^{t} h_{j}^{p} h_{j}^{a o a}, j \in \{S R_{i}, R_{i} D\}

(25)

The PDF of

h_{j}

can be expressed as

f_{h_{j}} (h_{j}) = \int_{0}^{\infty} \frac{1}{h_{j}^{*}} h_{j}^{a o a} (\frac{h_{j}}{h_{j}^{*}}) f_{h_{j}^{*}} (h_{j}^{*}) d h_{j}^{*}, j \in \{S R_{i}, R_{i} D\},

(26)

where

h_{j}^{*} ≜ h_{j}^{a} h_{j}^{t} h_{j}^{p}

. By using Equations (11), (13) and (21), and substituting Equation (24) into Equation (26), we obtain the PDF of

h_{j}

as (27):

f_{h_{j}} (h_{j}) = \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}}) δ (h_{j}) + [1 - \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}})] \frac{α_{j} β_{j} g_{j}^{2}}{A_{0, j} h_{j}^{a} Γ (α_{j}) Γ (β_{j})} \times G_{1, 3}^{3, 0} [\frac{α_{j} β_{j}}{A_{0, j} h_{j}^{a}} h_{j} |\begin{array}{l} g_{j}^{2} \\ g_{j}^{2} - 1, α_{j} - 1, β_{j} - 1 \end{array}], j \in \{S R_{i}, R_{i} D\}

(27)

Using Equations 07.34.21.0001.01 and 07.34.16.0001.01 in [18], the cumulative distribution function (CDF) of the AWACS-to-UAV and UAV-to-GS

F_{γ_{j}^{F S O}} (γ_{t h_{F S O}})

is given by

\begin{array}{l} F_{γ_{j}^{F S O}} (γ_{t h_{F S O}}) = \int_{0}^{γ_{t h_{F S O}}} f_{γ_{j}^{F S O}} (γ_{j}^{F S O}) d γ_{j}^{F S O} \\ = \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}}) + [1 - \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}})] \frac{g_{j}^{2}}{Γ (α_{j}) Γ (β_{j})} G_{2, 4}^{3, 1} [\frac{α_{j} β_{j}}{A_{0, j} h_{j}^{a}} \sqrt{γ_{t h_{F S O}} σ_{f}^{2} / 2 η^{2} P_{f, j}^{2}} |\begin{array}{l} 1, g_{j}^{2} + 1 \\ g_{j}^{2}, α_{j}, β_{j}, 0 \end{array}], j = S R_{i}, R_{i} D \end{array}

(28)

3.2. RF Channel

The RF channel coefficient

I_{j}, j \in \{S R_{i}, R_{i} D\}

can be modeled by Nakagami-m distribution, which is closer to the actual fading of the AWACS-to-UAV and UAVs-to-GS channel. The PDF is presented as [19]

f_{I_{j}} (I_{j}) = \frac{I_{j}^{m - 1}}{Γ (m)} {(\frac{m}{{\bar{γ}}_{j}^{R F}})}^{m} \exp (- \frac{m I_{j}}{{\bar{γ}}_{j}^{R F}}), I_{j} \geq 0, j \in \{S R_{i}, R_{i} D\},

(29)

where

{\bar{γ}}_{j}^{R F} = P_{r, j} G_{j} / σ_{r f}^{2}

is the average SNR, and

m

is the Nakagami-m parameter known as the RF fading factor.

The path loss

G_{j}

in Equations (5) and (6) can be expressed as

G_{j} (d B) = G_{t} + G_{r} - 20 \log_{10} (\frac{4 π L_{j}}{f_{R F}}) - (κ_{o x y} + κ_{w}) L_{j}, j \in \{S R_{i}, R_{i} D\},

(30)

where

G_{t}

and

G_{r}

are the gains of the transmitting and receiving antennas,

f_{R F}

is the RF,

κ_{o x y}

and

κ_{w}

are the attenuation coefficients due to the oxygen and weather condition, respectively.

κ_{w} = K M_{C L W C}

, where

K

is specific attenuation coefficient. The CDF of the RF link is given by

F_{γ_{j}^{R F}} (γ_{{th}_{R F}}) = \frac{1}{Γ (m)} Γ (m, \frac{m γ_{{th}_{R F}}}{{\bar{γ}}_{j}^{R F}}) = \frac{1}{Γ (m)} Γ (m, \frac{m σ_{r f}^{2} γ_{{th}_{R F}}}{P_{r, j} G_{j}}), j = S R_{i}, R_{i} D,

(31)

where

Γ (α, x)

is the incomplete gamma function.

4. Performance Evaluation

In this section, the overall statistical characteristic of the proposed system is analyzed. Then, the outage probability and average BER expressions are derived.

4.1. Outage Probability

The outage probability is a crucial metric that reflects the performance of wireless communication systems, defined as the probability that the end-to-end SNR falls below a specified threshold

γ_{t h}

, and resulting in data transmission failure. The outage probability can be expressed as [20]

P_{o u t} = \Pr (γ_{S D} < γ_{t h}) = F_{γ_{S D}} (γ_{t h}),

(32)

where

F_{γ_{S D}} (γ_{t h})

is the CDF of

γ_{S D}

4.1.1. Outage Analysis of Max-Select Relaying

In case 1, the instantaneous SNR of the

i th

end-to-end link is as follows:

γ_{S D_{i}} = \min_{i = 1, 2 \dots, N} \{γ_{S R_{i}}, γ_{R_{i} D}\},

(33)

where

γ_{S R_{i}} = \max \{γ_{S R_{i}}^{F S O}, γ_{S R_{i}}^{R F}\}

and

γ_{R_{i} D} = \max \{γ_{R_{i} D}^{F S O}, γ_{R_{i} D}^{R F}\}

. The UAV node

i = I_{1}

is selected according to the best channel quality, and the maximum end-to-end instantaneous SNR of case 1 can be expressed as

γ_{S D 1} = \max_{i = 1, 2 \dots, N} \{γ_{S D_{i}}\},

(34)

Therefore, the outage probability of case 1 can be given as

P_{o u t 1} = \Pr [γ_{S D 1} < γ_{t h}] = \prod_{i = 1}^{N} [1 - (1 - F_{γ_{S R_{i}}^{F S O}} (γ) F_{γ_{S R_{i}}^{R F}} (γ)) (1 - F_{γ_{R_{i} D}^{F S O}} (γ) F_{γ_{R_{i} D}^{R F}} (γ))],

(35)

After substituting (28) and (31) in (35), the outage probability can be obtained.

4.1.2. Outage Analysis of Source-Relay-Select Relaying

In case 2, the relay

i = I_{2}

is selected according to the SNR of the first hop, as given in Equation (8); the maximum instantaneous SNR between AWACS-to-UAV links is

γ_{S R_{I_{2}}} = \max_{i = 1, 2 \dots, N} \{γ_{S R_{i}}^{F S O}, γ_{S R_{i}}^{R F}\}

(36)

In the second hop, the SNR in the selected UAV-to-GS link is

γ_{R_{I_{2}} D} = \max \{γ_{R_{I_{2}} D}^{F S O}, γ_{R_{I_{2}} D}^{R F}\}

(37)

The maximum end-to-end instantaneous SNR of case 2 obtained is

γ_{S D 2} = \min \{γ_{S R_{I_{2}}}, γ_{R_{I_{2}} D}\}

(38)

As a result, the outage probability of case 2 can be given as

P_{o u t 2} = 1 - \Pr (γ_{S R_{I_{2}}} \geq γ_{t h}) \Pr (γ_{R_{I_{2}} D} \geq γ_{t h}) = 1 - (1 - \prod_{i = 1}^{N} (F_{γ_{S R_{i}}^{F S O}} (γ) F_{γ_{S R_{i}}^{R F}} (γ))) (1 - F_{γ_{R_{I_{2}} D}^{F S O}} (γ) F_{γ_{R_{I_{2}} D}^{R F}} (γ))

(39)

After substituting (28) and (31) in (39), the outage probability can be obtained.

4.1.3. Outage Analysis of Relay-Destination-Select Relaying

In case 3, the relay

i = I_{3}

is selected according to the SNR of the second hop, as given in Equation (9); the maximum instantaneous SNR between AWACS-to-UAV links is

γ_{S R_{I_{3}}} = \max \{γ_{S R_{I_{3}}}^{F S O}, γ_{S R_{I_{3}}}^{R F}\}

(40)

The SNR in the UAV-to-GS link is

γ_{R_{I_{3}} D} = \max_{i = 1, 2, \dots N} \{γ_{R_{i} D}^{F S O}, γ_{R_{i} D}^{R F}\}

(41)

The maximum end-to-end instantaneous SNR of case 3 obtained is

γ_{S D 3} = \min \{γ_{S R_{I_{3}}}, γ_{R_{I_{3}} D}\}

(42)

As a result, the outage probability of case 3 can be given as

P_{o u t 3} = 1 - \Pr (γ_{S R_{I_{3}}} \geq γ_{t h}) \Pr (γ_{R_{I_{3}} D} \geq γ_{t h}) = 1 - (1 - F_{γ_{S R_{I_{3}}}^{F S O}} (γ) F_{γ_{S R_{I_{3}}}^{R F}} (γ)) (1 - \prod_{i = 1}^{N} (F_{γ_{R_{i} D}^{F S O}} (γ) F_{γ_{R_{i} D}^{R F}} (γ)))

(43)

After substituting (28) and (31) in (44), the outage probability can be obtained.

4.1.4. Outage Analysis of Dual-Distributed-Select Relaying

In case 4, the signal transmitted through the relay

i = I_{a}

is referred to as path 1, and its SNR is

γ_{S R_{I a} D}

γ_{S R_{I a} D} = \min \{γ_{S R_{I a}}, γ_{R_{I a} D}\},

(44)

where

γ_{S R_{I a}} = \max_{i = 1, 2 \dots, N_{a}} \{γ_{S R_{i}}^{F S O}, γ_{S R_{i}}^{R F}\}

is the instantaneous SNR of the first hop, and

γ_{R_{I a} D} = \max \{γ_{R_{I a} D}^{F S O}, γ_{R_{I a} D}^{R F}\}

is the instantaneous SNR of the second hop.

Similarly, the signal transmitted through the relay

i = I_{b}

is referred to as path 2, and its SNR is

γ_{S R_{I b} D}

γ_{S R_{I b} D} = \min \{γ_{S R_{I b}}, γ_{R_{I b} D}\},

(45)

where

γ_{S R_{I b}} = \max \{γ_{S R_{I b}}^{F S O}, γ_{S R_{I b}}^{R F}\}

and

γ_{R_{I b} D} = \max_{i = 1, 2 \dots, N_{b}} \{γ_{R_{i} D}^{F S O}, γ_{R_{i} D}^{R F}\}

, respectively.

The two path signals arrive at the GS, and the SC technique is adopted. The end-to-end instantaneous SNR of case 4 is

γ_{S D 4} = \max \{γ_{S R_{I a} D}, γ_{S R_{I b} D}\}

(46)

The outage probability of case 4 can be given as (47):

\begin{array}{l} P_{o u t 4} = \Pr (γ_{S R_{I a} D} < γ_{t h}) \Pr (γ_{S R_{I b} D} < γ_{t h}) = F_{γ_{S R_{I a} D}} (γ) F_{γ_{S R_{I b} D}} (γ) \\ = [1 - (1 - F_{γ_{S R_{I a}}} (γ)) (1 - F_{γ_{R_{I a} D}} (γ))] [1 - (1 - F_{γ_{S R_{I b}}} (γ)) (1 - F_{γ_{R_{I b} D}} (γ))] \\ = [\prod_{i = 1}^{N_{a}} (F_{γ_{S R_{i}}^{F S O}} (γ) F_{γ_{S R_{i}}^{R F}} (γ)) + F_{γ_{R_{I a} D}^{F S O}} (γ) F_{γ_{R_{I a} D}^{R F}} (γ) - \prod_{i = 1}^{N_{a}} (F_{γ_{S R_{i}}^{F S O}} (γ) F_{γ_{S R_{i}}^{R F}} (γ)) F_{γ_{R_{I a} D}^{F S O}} (γ) F_{γ_{R_{I a} D}^{R F}} (γ)] \\ \times [F_{γ_{S R_{I b}}^{F S O}} (γ) F_{γ_{S R_{I b}}^{R F}} (γ) + \prod_{i = 1}^{N_{b}} (F_{γ_{R_{i} D}^{F S O}} (γ) F_{γ_{R_{i} D}^{R F}} (γ)) - \prod_{i = 1}^{N_{b}} (F_{γ_{R_{i} D}^{F S O}} (γ) F_{γ_{R_{i} D}^{R F}} (γ)) F_{γ_{S R_{I b}}^{F S O}} (γ) F_{γ_{S R_{I b}}^{R F}} (γ)] \end{array}

(47)

4.2. Average BER

The average BER

B

is calculated by averaging the conditional BER:

B = \int_{0}^{\infty} P_{e} f_{h} (h) d h,

(48)

where the

P_{e}

is the conditional probability, and

f_{h} (h)

is the PDF of the channel coefficient.

For the FSO link with OOK modulation and IM/DD detection, the conditional probability is given by [21]

P_{e}^{f s o, j} = Q (\sqrt{\frac{γ_{j}^{F S O}}{2}}) = \frac{1}{2} erfc (\frac{P_{f, j} η h_{j}}{\sqrt{2} σ_{f}}), j = S R_{i}, R_{i} D,

(49)

where

Q (\cdot)

is the Gaussian Q function and related to the error function by

erfc (x) = 2 Q (\sqrt{2} x)

Using Equation 07.34.03.0619.01 in [18], the

erfc (\cdot)

can be expressed as

erfc (\sqrt{z}) = 1 / \sqrt{π} G_{1, 2}^{2, 0} [z |\begin{array}{l} 1 \\ 0, 1 / 2 \end{array}]

(50)

After substituting Equations (49), (50), and (27) in Equation (48), the average BER of the FSO link can be derived by

\begin{array}{l} B_{j}^{F S O} = & \frac{1}{2} \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}}) + \frac{2^{α_{j} + β_{j} - 4} g_{j}^{2}}{π^{3 / 2} Γ (α_{j}) Γ (β_{j})} [1 - \exp (- \frac{θ_{F o V, j}^{2}}{2 σ_{θ}^{2}})] \\ \times G_{6, 3}^{2, 5} [\frac{8 {(A_{0, j} h_{j}^{a} P_{f, j} η)}^{2}}{{(α_{j} β_{j} σ_{f})}^{2}} |\begin{matrix} \frac{2 - g_{j}^{2}}{2}, \frac{1 - α_{j}}{2}, \frac{2 - α_{j}}{2}, \frac{1 - β_{j}}{2}, \frac{2 - β_{j}}{2}, 1 \\ 0, \frac{1}{2}, \frac{, - g_{j}^{2}}{2} \end{matrix}], j = S R_{i}, R_{i} D \end{array}

(51)

For the RF link, the signal uses the MPSK modulation, and the conditional probability is given by

P_{e}^{r f, j} = \frac{A}{2} e r f c (\sqrt{γ_{j}^{R F}} B)

, where

A = 1

and

B = 1

when

M = 2

(BPSK) and where

A = 2 / \log_{2} M

and

B = \sin (π / M)

when

M > 2

. We substitute (29) and

P_{e}^{r f, j}

into (48). Using Equation 07.34.21.0088.01 in [18] after some simple algebraic manipulations, the closed form of the BER can be expressed as

\begin{array}{l} B_{j}^{R F} & = \int_{0}^{\infty} \frac{A}{2 \sqrt{π}} G_{1, 2}^{2, 0} [γ_{j}^{R F} B^{2} |\begin{array}{l} 1 \\ 0, 1 / 2 \end{array}] \frac{γ_{j}^{R F m - 1}}{Γ (m)} {(\frac{m}{{\bar{γ}}_{j}^{R F}})}^{m} \exp (- \frac{m γ_{j}^{R F}}{{\bar{γ}}_{j}^{R F}}) d γ_{j}^{R F} \\ = \frac{A}{2 \sqrt{π} Γ (m)} G_{2, 2}^{2, 1} [\frac{B^{2} {\bar{γ}}_{j}^{R F}}{m} |\begin{array}{l} 1 - m, 1 \\ 0, 1 / 2 \end{array}], j = S R_{i}, R_{i} D \end{array}

(52)

The average BER of a parallel FSO/RF link is

B_{j} = P_{j}^{F S O} B_{j}^{F S O} + P_{j}^{R F} B_{j}^{R F}, j = S R_{i}, R_{i} D,

(53)

where

P_{j}^{F S O}

is the probability that the FSO link is selected, and

P_{j}^{R F}

is the probability of using the RF link. The link selection probability can be formulated as

P_{j} = \{\begin{matrix} P_{j}^{F S O} = \frac{1 - F_{γ_{j}^{F S O}} (γ_{t h_{F S O}})}{1 - F_{γ_{j}^{F S O}} (γ_{t h_{F S O}}) F_{γ_{j}^{R F}} (γ_{t h_{R F}})} \\ P_{j}^{R F} = \frac{F_{γ_{j}^{F S O}} (γ_{t h_{F S O}}) (1 - F_{γ_{j}^{R F}} (γ_{t h_{R F}}))}{1 - F_{γ_{j}^{F S O}} (γ_{t h_{F S O}}) F_{γ_{j}^{R F}} (γ_{t h_{R F}})} \end{matrix}, j = S R_{i}, R_{i} D

(54)

It is worth noting that in a parallel UAV relay system, when each path state is distributed independently, the average BER of the system is equal to the average BER of a single path, which can be expressed as

B_{S R} = B_{S R_{i}}

and

B_{R D} = B_{R_{i} D}

. In this case, the four relay selection modes have the same average BER. This system can be considered as a serial double-hop system with DF relay, and its end-to-end average BER can be expressed as [22,23]

B_{S D} = B_{S R} + B_{R D} - B_{S R} B_{R D}

(55)

After substituting Equations (51), (52), (53), and (54) in (55), the end-to-end average BER of the system can be obtained.

5. Numerical Results and Discussion

In this section, the impact of key system parameters on link performance is analyzed. It is worth noting that we make the assumption that all UAV relays experience the same atmospheric conditions and

P_{f, j} = P_{r, j} = P_{t}

. The parameters are shown in Table 1.

Figure 3a–d show the outage probability versus average transmitted power for different numbers of relays of case 1, case 2, case 3, and case 4, respectively. As these figures indicate, the transmit power increases significantly improve the overall outage probability performance. In addition, the simulation results of Figure 3a,c,d reveal that the outage probability generally decreases as the number of relays

N

increases. However, it is observed that the outage probability remains unaffected by the number of relays in case 2. It is noteworthy that the outage probability performance of

N = 5

did not show any significant improvement compared to

N = 4

across all four cases. Consequently, considering prudent cost management, the number of UAV relay deployments will not exceed four.

In Figure 4, we observe the outage performance of the proposed modes, when the transmit power is equal to 25 dBm. As expected, increasing the velocity variance

σ_{S v}^{2}

amplifies the pointing error as the jitter standard deviation of the AWACS-to-UAV link

σ_{S R_{i}}^{2}

increases, resulting in the deterioration of the overall outage performance. In Figure 4a, when the velocity variance of the GS

σ_{D v}^{2} = 2

and

σ_{S v}^{2}

is below 8, case 1 exhibits optimal end-to-end outage performance ranges from about

10^{- 20}

10^{- 10}

. It is worth noting that when

σ_{S v}^{2}

exceeds 8, the outage probability curves of case 1 and case 4 coincide. Furthermore, when

σ_{S v}^{2}

exceeds 15, the curve of case 2 aligns with those of cases 1 and 4. In other words, when

σ_{S v}^{2}

exceeds 8, case 4 can replace case 1 to reduce the system’s CSI requirements, and when

σ_{S v}^{2}

surpasses 15, the simpler case 2 can substitute both cases 4 and 1. Therefore, in practical applications, there are some tradeoffs between the complexity and performance of these cases.

The increase in

σ_{D v}^{2}

to 10, as shown in Figure 4b, leads to a rise in the overall end-to-end outage probability and causes variability in the outage performance of different cases. As we can see from the figure, when

σ_{S v}^{2}

is below 2, cases 1 and 3 exhibit optimal end-to-end outage performance ranges from about

10^{- 8}

, but with the increase in

σ_{S v}^{2}

, the outage performance of case 3 deteriorates rapidly. In contrast to Figure 4a, the outage performance of case 2 is consistently poor, remaining at approximately

10^{- 3}

. In addition, the outage probability of case 4 is approximately

10^{- 5}

when

σ_{S v}^{2}

is small and slightly increases with an increase in

σ_{S v}^{2}

. Moreover, with the increase in

σ_{S v}^{2}

, the outage probability curve of case 4 closely aligns with that of case 1. However, the outage performance remains unsatisfactory at a level of

10^{- 4}

due to significant velocity variances of the AWACS and mobile GS.

Compared with Figure 4b, a UAV relay is added in Figure 4c. It is evident that the additional relay significantly enhances the system’s overall outage performance. The outage probability of cases 1 and 3 decreases to approximately

10^{- 11}

when

σ_{S v}^{2}

is below 2, and the outage probability of case 4 reduces to around

10^{- 8}

. However, there is no significant change in case 2. The outage probability of case 1 remains stable at about

10^{- 5}

σ_{S v}^{2}

increases, whereas case 4 maintains stability at around

10^{- 4}

, which is similar to

N = 3

Figure 5 shows the outage probability versus the

σ_{D v}^{2}

. It can be observed that the outage performance becomes worse the larger the

σ_{D v}^{2}

. Similarly, a large

σ_{D v}^{2}

will result in a large pointing error. The performance of different cases when

σ_{S v}^{2} = 2

is analyzed in Figure 5a. When

σ_{D v}^{2}

exceeds 3, the outage probability curve of case 4 coincides with that of case 1, indicating that case 4 can serve as a viable replacement for the complex case 1. Furthermore, when

σ_{D v}^{2}

surpasses 6, the curves of case 3 align with those of cases 1 and 4, suggesting that case 3 can be adopted as a simpler alternative relay mode.

As depicted in Figure 5b, the value of

σ_{S v}^{2}

increases to 10, and the simultaneous increase in the AWACS and mobile GS results in a significant deterioration of outage performance. It is observed from the figure that the outage probability of case 1 and case 2 exhibits the lowest values compared to other cases, about

10^{- 9}

. However, case 2 experiences a rapid deterioration in performance as

σ_{D v}^{2}

increases, which differs from case 4 which exhibits a minimum outage probability of about

10^{- 6}

but changes relatively slowly with increasing

σ_{D v}^{2}

. In addition, the outage probability of case 3 consistently remains at approximately

10^{- 3}

without significant variation as

σ_{D v}^{2}

increases.

Furthermore, the outage probability performance of cases 1, 2, and 4 is improved by the increase in the number of relay nodes, as depicted in Figure 5c. However, the outage probability of case 3 remains relatively unchanged compared to Figure 5b.

In Figure 6, we compare the outage performance of the proposed cases with respect to the

H_{U A V}

. As can be observed, with the increase in

H_{U A V}

, the outage probabilities of cases 1, 2 and 4 increase sharply and then reach a stable state. In case 3, the outage probability does not change significantly when

H_{U A V}

is less than 0.5 km. This is because the utilization of diversity technology in the UAV-to-GS links enhances the outage performance of the second hop significantly; thereby, the overall end-to-end outage performance of the system is limited by the first hop from the AWACS to the UAV. In other words, when the system imposes a requirement on outage probability (such as not exceeding

10^{- 10}

), the altitude of UAVs in cases 1 and 3 should be limited to a maximum of 700 m. In case 4, the altitude of UAVs should not exceed 500 m, and for case 2 it should not exceed 300 m.

Figure 7 shows the impact of

σ_{S v}^{2}

on the average BER performance of the system for

σ_{D v}^{2} = 2

σ_{D v}^{2} = 10

, and

σ_{D v}^{2} = 20

considering

H_{U A V} = 0.5 km

and

P_{t} = 25 dBm

. As expected, increasing the velocity variance deteriorates the overall BER performance as the pointing error increases. Also, we can see that increasing the

σ_{D v}^{2}

results in a significant rise in the average BER when the value of

σ_{S v}^{2}

is small. Conversely, the BER of the three curves tend to converge when

σ_{S v}^{2}

is large. Similarly, an increase in

σ_{S v}^{2}

leads to a rapid escalation in the BER from

10^{- 5}

10^{- 1}

when

σ_{D v}^{2} = 2

; however, when

σ_{D v}^{2} = 20

, although there is still an increment with

σ_{S v}^{2}

, it only exhibits a slight rise.

Figure 8 shows the average BER results for different weather conditions, according to the attenuation values corresponding to weather conditions in [24]. The attenuation coefficient

ω = [0.43, 4.2, 20, 42.2, 125] \times 10^{- 3} m^{- 1}

corresponds to clear air, haze, light fog, moderate fog, and heavy fog. It is found that the increase in

ω

results in a slight increase in the average BER. The parallel FSO/RF hybrid link and the utilization of UAV relays enhance the system’s capability to adapt to weather variations.

Design Guidelines:

In summary, we provide important design guidelines that can help design the UAV-based hybrid FSO/RF aeronautical communication system:

The use of UAV relays improves the system’s performance. The increase in the number of relays improves outage performance to some extent when $N \leq 4$ . However, when N > 4, increasing the number of relays does not have a positive impact on outage probability. Considering cost-saving, it is recommended that the total number of relays in this system should not exceed four.
In mobile scenarios, the velocity variance of the AWACS and GS directly impact the outage and average BER performance of the hybrid FSO/RF aeronautical communication system. Excessive velocity variance in either AWACS or GS can lead to degradation in system performance.
In the multi-UAV relay system, the outage performance varies among different relay selection modes. Generally, the Max-Select mode demonstrates the best performance; however, it requires the most feedback channels. In fact, for lower $σ_{S v}^{2}$ values and higher $σ_{D v}^{2}$ , the simpler Relay-Destination-Select mode can replace Max-Select mode. In addition, for higher $σ_{S v}^{2}$ values and lower $σ_{D v}^{2}$ , the Source-Relay-Select mode can replace Max-Select mode. When both $σ_{S v}^{2}$ and $σ_{D v}^{2}$ exhibit large values, the Dual-Distributed-Select mode can also serve as a viable alternative for approximating performance. The tradeoffs between complexity and performance vary depending on the actual usage.
The end-to-end outage probability of the system is influenced by the deployment altitude of UAV relays. Within the acceptable range of UAV flight characteristics, lower flight altitudes result in enhanced outage performance. When $P_{t} = 25 dBm$ , to ensure that the outage probability is controlled within $10^{- 5}$ , the flight altitude should not exceed 1 km for cases 1 and 3, 800 m for case 4, and 500 m for case 2.

6. Conclusions

In this paper, an aeronautical communication system based on multi-UAV relays is proposed, considering the hybrid FSO/RF link transmission and the mobility of platforms. Furthermore, we propose four relay selection modes and derive the exact closed-form expressions for the end-to-end outage probabilities. Moreover, the influence of the velocity variance of the AWACS and the mobile GS on the outage probability and BER of the system is simulated, followed by an analysis of the applicability of the relay selection modes under different mobile characteristics. The numerical results analyzed include the optimal number of UAVs and the deployment altitude. Finally, guidelines were provided for the design of a multiple UAV-based hybrid FSO/RF aeronautical communication system.

Author Contributions

X.Z.: methodology, software and writing; S.Z.: conceptualization and supervision; Y.W.: software and validation; H.H.: funding acquisition.; G.Y.: investigation; X.S.: visualization; X.L. and J.L.: data curation. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Shaanxi Province Natural Science Basic Research Program (2024JC-YBMS-514).

Data Availability Statement

The data are only available upon request to the corresponding author.

Conflicts of Interest

Author Guangmingzi Yang was employed by the company China Mobile System Integration Co. Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

Dabiri, M.T.; Khankalantary, S.; Piran, M.J.; Ansari, I.S.; Uysal, M.; Saad, W.; Hong, C.S. UAV-assisted free space optical communication system with amplify-and-forward relaying. IEEE Trans. Veh. Technol. 2021, 70, 8926–8936. [Google Scholar] [CrossRef]
Erdogan, E.; Altunbas, I.; Kabaoglu, N.; Yanikomeroglu, H. A cognitive radio enabled RF/FSO communication model for aerial relay networks: Possible configurations and opportunities. IEEE Open J. Veh. Technol. 2020, 2, 45–53. [Google Scholar] [CrossRef]
Fawaz, W.; Abou-Rjeily, C.; Assi, C. UAV-aided cooperation for FSO communication systems. IEEE Commun. Mag. 2018, 56, 70–75. [Google Scholar] [CrossRef]
Dabiri, M.T.; Rezaee, M.; Ansari, I.S.; Yazdanian, V. Channel modeling for UAV-based optical wireless links with nonzero boresight pointing errors. IEEE Trans. Veh. Technol. 2020, 69, 14238–14246. [Google Scholar] [CrossRef]
Dabiri, M.T.; Sadough SM, S.; Ansari, I.S. Tractable optical channel modeling between UAVs. IEEE Trans. Veh. Technol. 2019, 68, 11543–11550. [Google Scholar] [CrossRef]
Dabiri, M.T.; Sadough SM, S.; Khalighi, M.A. Channel modeling and parameter optimization for hovering UAV-based free-space optical links. IEEE J. Sel. Areas Commun. 2018, 36, 2104–2113. [Google Scholar] [CrossRef]
Choi, M.; Song, S.; Ko, D.E.; Chung, J.M. Trajectory optimization for fso based u-iot backhaul networks. IEEE Trans. Netw. Sci. Eng. 2023, 10, 2030–2044. [Google Scholar] [CrossRef]
Nguyen, T.V.; Le, H.D.; Pham, A.T. On the design of RIS–UAV relay-assisted hybrid FSO/RF satellite–aerial–ground integrated network. IEEE Trans. Aerosp. Electron. Syst. 2022, 59, 757–771. [Google Scholar] [CrossRef]
Zhang, X.; Zhao, S.; Wang, Y.; Wang, X.; Song, X.; Li, X.; Li, J. 3D Trajectory Optimization for UAV-Assisted Hybrid FSO/RF Network with Moving Obstacles. IEEE Trans. Aerosp. Electron. Syst. 2024, 32, 45–53. [Google Scholar] [CrossRef]
Wang, P.; Cao, T.; Guo, L.; Wang, R.; Yang, Y. Performance analysis of multihop parallel free-space optical systems over exponentiated Weibull fading channels. IEEE Photonics J. 2015, 7, 7900715. [Google Scholar] [CrossRef]
Cao, T.; Wang, P.; Guo, L.; Yang, B.; Li, J.; Yang, Y. Average bit error rate of multi-hop parallel decode-and-forward-based FSO cooperative system with the max–min criterion under the gamma–gamma distribution. Chin. Opt. Lett. 2015, 13, 080101. [Google Scholar]
Miglani, R.; Malhotra, J.S. An innovative approach for performance enhancement of 320 Gbps free space optical communication system over turbulent channel. Opt. Quantum Electron. 2019, 51, 289. [Google Scholar] [CrossRef]
Fadhil, H.A.; Amphawan, A.; Shamsuddin, H.A.; Abd, T.H.; Al-Khafaji, H.M.; Aljunid, S.; Ahmed, N. Optimization of free space optics parameters: An optimum solution for bad weather conditions. Optik 2013, 124, 3969–3973. [Google Scholar] [CrossRef]
Zhang, X.; Zhao, S.; Wang, Y.; Wang, X.; Tian, Q.; Song, X.; Li, X. A weather-dependent UAV relay-assisted hybrid FSO/RF airborne communication system. Opt. Commun. 2024, 554, 130196. [Google Scholar] [CrossRef]
Touati, A.; Abdaoui, A.; Touati, F.; Uysal, M.; Bouallegue, A. On the effects of combined atmospheric fading and misalignment on the hybrid FSO/RF transmission. J. Opt. Commun. Netw. 2016, 8, 715–725. [Google Scholar] [CrossRef]
Wang, J.Y.; Ma, Y.; Lu, R.R.; Wanga, J.-B.; Lin, M.; Cheng, J. Hovering UAV-based FSO communications: Channel modelling, performance analysis, and parameter optimization. IEEE J. Sel. Areas Commun. 2021, 39, 2946–2959. [Google Scholar] [CrossRef]
Fernandes, M.A.; Loureiro, P.A.; Fernandes, G.M.; Monteiro, P.P.; Guiomar, F.P. Digitally mitigating Doppler shift in high-capacity coherent FSO LEO-to-earth links. J. Light. Technol. 2023, 41, 3993–4001. [Google Scholar] [CrossRef]
“MeijerG function,” Wolfram Research. 2020. Available online: https://functions.wolfram.com/PDF/MeijerG.pdf (accessed on 1 January 2022).
Usman, M.; Yang, H.C.; Alouini, M.S. Practical switching-based hybrid FSO/RF transmission and its performance analysis. IEEE Photonics J. 2014, 6, 7902713. [Google Scholar] [CrossRef]
Michailidis, E.; Nomikos, N.; Bithas, P.; Vouyioukas, D.; Kanatas, A.G. Outage probability of triple-hop mixed RF/FSO/RF stratospheric communication systems. In Proceedings of the SPACOMM 2018: The Tenth International Conference on Advances in Satellite and Space Communications, Athens, Greece, 22–26 April 2018. [Google Scholar]
Sandalidis, H.G.; Tsiftsis, T.A.; Karagiannidis, G.K.; Uysal, M. BER performance of FSO links over strong atmospheric turbulence channels with pointing errors. IEEE Commun. Lett. 2008, 12, 44–46. [Google Scholar] [CrossRef]
Swaminathan, R.; Sharma, S.; Vishwakarma, N.; Madhukumar, A.S. HAPS-based relaying for integrated space–air–ground networks with hybrid FSO/RF communication: A performance analysis. IEEE Trans. Aerosp. Electron. Syst. 2021, 57, 1581–1599. [Google Scholar]
Morgado, E.; Mora-Jimenez, I.; Vinagre, J.J.; Ramos, J.; Caamano, A.J. End-to-end average BER in multi-hop wireless networks over fading channels. IEEE Trans. Wirel. Commun. 2010, 9, 2478–2487. [Google Scholar] [CrossRef]
Le, H.D.; Nguyen, T.V.; Pham, A.T. Cloud attenuation statistical model for satellite-based FSO communications. IEEE Antennas Wirel. Propag. Lett. 2021, 20, 643–647. [Google Scholar] [CrossRef]

Figure 1. The multiple UAV-based aeronautical communication system with hybrid FSO/RF links.

Figure 2. The Gaussian beam footprint at receiver aperture: (a) the receiver is on the

i th

UAV; (b) the receiver is on the GS.

Figure 2. The Gaussian beam footprint at receiver aperture: (a) the receiver is on the

i th

UAV; (b) the receiver is on the GS.

Figure 3. Outage probability of the proposed four different relay selection modes for different numbers of UAV relays when

σ_{S v}^{2} = σ_{D v}^{2} = 1

and

H_{U A V} = 0.5

km: (a) case 1; (b) case 2; (c) case 3; (d) case 4.

Figure 3. Outage probability of the proposed four different relay selection modes for different numbers of UAV relays when

σ_{S v}^{2} = σ_{D v}^{2} = 1

and

H_{U A V} = 0.5

km: (a) case 1; (b) case 2; (c) case 3; (d) case 4.

Figure 4. Outage probability for different relay selection modes versus the velocity variance of the AWACS

σ_{S v}^{2}

when

H_{U A V} = 0.3 km

and

P_{t} = 25 dBm

: (a)

N = 3 (N_{a} = 2, N_{b} = 1)

and

σ_{D v}^{2} = 2

; (b)

N = 3 (N_{a} = 2, N_{b} = 1)

and

σ_{D v}^{2} = 10

; (c)

N = 4 (N_{a} = 2, N_{b} = 2)

and

σ_{D v}^{2} = 10

Figure 4. Outage probability for different relay selection modes versus the velocity variance of the AWACS

σ_{S v}^{2}

when

H_{U A V} = 0.3 km

and

P_{t} = 25 dBm

: (a)

N = 3 (N_{a} = 2, N_{b} = 1)

and

σ_{D v}^{2} = 2

; (b)

N = 3 (N_{a} = 2, N_{b} = 1)

and

σ_{D v}^{2} = 10

; (c)

N = 4 (N_{a} = 2, N_{b} = 2)

and

σ_{D v}^{2} = 10

Figure 5. Outage probability for different relay selection modes versus the velocity variance of the GS

σ_{D v}^{2}

when

H_{U A V} = 0.3 km

and

P_{t} = 25 dbm

: (a)

N = 3 (N_{a} = 1, N_{b} = 2)

and

σ_{S v}^{2} = 2

; (b)

N = 3 (N_{a} = 1, N_{b} = 2)

and

σ_{S v}^{2} = 10

; (c)

N = 4 (N_{a} = 2, N_{b} = 2)

and

σ_{D v}^{2} = 10

Figure 5. Outage probability for different relay selection modes versus the velocity variance of the GS

σ_{D v}^{2}

when

H_{U A V} = 0.3 km

and

P_{t} = 25 dbm

: (a)

N = 3 (N_{a} = 1, N_{b} = 2)

and

σ_{S v}^{2} = 2

; (b)

N = 3 (N_{a} = 1, N_{b} = 2)

and

σ_{S v}^{2} = 10

; (c)

N = 4 (N_{a} = 2, N_{b} = 2)

and

σ_{D v}^{2} = 10

Figure 6. The impact of

H_{U A V}

on the proposed cases in terms of outage probability when

σ_{S v}^{2} = σ_{D v}^{2} = 1

and

P_{t} = 25 dBm

Figure 6. The impact of

H_{U A V}

on the proposed cases in terms of outage probability when

σ_{S v}^{2} = σ_{D v}^{2} = 1

and

P_{t} = 25 dBm

Figure 7. Impact of the velocity variance of the AWACS and GS in terms of the average BER.

Figure 8. Impact of the weather conditions in terms of the average BER.

Table 1. Simulation parameters and their values.

Parameters	Values
The altitude of AWACS $H_{A W A C S}$	10 km
The zenith angle $ξ_{U A V} = ξ_{G S}$	$π / 3$
Wavelength $λ$	1550 nm
Responsivity $η$	0.9
Noise variance $σ_{f}^{2} = σ_{r f}^{2}$	$2.5 \times 10^{- 14}$
Turbulent factors of SR link $α_{1}$ - $β_{1}$	7.2–6.2
Turbulent factors of RD link $α_{2}$ - $β_{2}$	5.6–4.1
Cloud liquid water content $M_{C L W C}$	$0.3128 {mg / m}^{3}$
Cloud droplet concentration $N_{C}$	$0.5 {cm}^{- 3}$
Field-of-view angle $θ_{F o V, S R_{i}} = θ_{F o V, R_{i} D}$	8 mrad
Detector radius $a$	0.1 m
SD of UAV position $σ_{R x} = σ_{R y}$	0.1 m
SD of UAV orientation $σ_{θ}$	1.2 mrad
RF $f_{R F}$	20 GHz
Antenna gain $G_{t}$ = $G_{r}$	45 dB
Threshold $γ_{t h}$	5 dB
Oxygen attenuation coefficient $κ_{o x y}$	0.1 dB/km
Specific attenuation coefficient $K$	0.5 (dB/km)/(g/m³)
Time interval $Δ t$	1 s

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Zhang, X.; Zhao, S.; Wang, Y.; Hu, H.; Yang, G.; Song, X.; Li, X.; Li, J. Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios. Drones 2024, 8, 729. https://doi.org/10.3390/drones8120729

AMA Style

Zhang X, Zhao S, Wang Y, Hu H, Yang G, Song X, Li X, Li J. Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios. Drones. 2024; 8(12):729. https://doi.org/10.3390/drones8120729

Chicago/Turabian Style

Zhang, Xiwen, Shanghong Zhao, Yuan Wang, Hang Hu, Guangmingzi Yang, Xinkang Song, Xin Li, and Jianjia Li. 2024. "Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios" Drones 8, no. 12: 729. https://doi.org/10.3390/drones8120729

APA Style

Zhang, X., Zhao, S., Wang, Y., Hu, H., Yang, G., Song, X., Li, X., & Li, J. (2024). Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios. Drones, 8(12), 729. https://doi.org/10.3390/drones8120729

Article Menu

Performance Analysis of Multiple UAV-Based Hybrid Free-Space Optical/Radio Frequency Aeronautical Communication System in Mobile Scenarios

Abstract

1. Introduction

2. System and Signal Model

2.1. Space Environment

2.2. FSO Link

2.3. RF Link

2.4. Mode of Relay Selection

2.4.1. Case 1 (Max-Select)

2.4.2. Case 2 (Source-Relay-Select)

2.4.3. Case 3 (Relay-Destination-Select)

2.4.4. Case 4 (Dual-Distributed-Select)

3. Channel Model

3.1. FSO Channel

3.1.1. Atmospheric Attenuation

3.1.2. Turbulence-Induced Fading

3.1.3. Pointing Error

3.1.4. AOA Fluctuations

3.1.5. Doppler Effect

3.1.6. Overall Channel Statistical Characteristics

3.2. RF Channel

4. Performance Evaluation

4.1. Outage Probability

4.1.1. Outage Analysis of Max-Select Relaying

4.1.2. Outage Analysis of Source-Relay-Select Relaying

4.1.3. Outage Analysis of Relay-Destination-Select Relaying

4.1.4. Outage Analysis of Dual-Distributed-Select Relaying

4.2. Average BER

5. Numerical Results and Discussion

6. Conclusions

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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