BER performance analysis of drone-assisted optical wireless systems with APD receiver

Journal Pre-proof BER performance analysis of drone-assisted optical wireless systems with APD receiver Saeed Khankalantary, Mohammad Taghi Dabiri, Hossein Safi

PII: DOI: Reference:

S0030-4018(20)30037-7 https://doi.org/10.1016/j.optcom.2020.125309 OPTICS 125309

To appear in:

Optics Communications

Received date : 30 December 2019 Revised date : 9 January 2020 Accepted date : 12 January 2020 Please cite this article as: S. Khankalantary, M.T. Dabiri and H. Safi, BER performance analysis of drone-assisted optical wireless systems with APD receiver, Optics Communications (2020), doi: https://doi.org/10.1016/j.optcom.2020.125309. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

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BER Performance Analysis of Drone-Assisted Optical Wireless Systems with APD Receiver Saeed Khankalantarya,∗, Mohammad Taghi Dabirib , and Hossein Safic a Department

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of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran (e-mail: [email protected]). b Department of Communication Technologies, Iran Telecommunication Research Center (ITRC), Tehran, Iran (e-mail: [email protected]). c Department of Electrical Engineering, Shahid Beheshti University G. C., Tehran, Iran (e-mail: h [email protected]).

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Abstract

The integration of unmanned aerial vehicles (UAVs) and free space optical (FSO) systems has been recently proposed as a promising solution to establish flexible and high data rate backhaul/fronthaul links. However, due to the random fluctuations of hovering UAVs which cause optical beam fluctuations at

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the receiver, establishing UAV-assisted FSO links is technically challenging. In this paper, an avalanche photo diode (APD) at the optical receiver is utilized to successfully combat the effect of UAV’s fluctuations. To this aim, we first model the end-to-end signal-to-noise ratio (SNR) of an APD-based UAV-assisted FSO link. Then, given the analytical SNR model that we developed, closed-form expressions for the bit error rate (BER) of the considered system under different turbulence conditions are derived. The accuracy of the analytical expressions is verified by performing Monte Carlo simulations. Moreover, we study the effect of different link parameters, i.e., received optical beamwidth, the receiver field-of-view, optical transmit power, and different levels of UAV instability on the performance of the system. The results of this paper reveal insights into the importance of utilizing APD for UAV-based FSO system to mitigate the

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degradation effects of UAV’s fluctuations. ∗ Corresponding

author Email address: [email protected] (Saeed Khankalantary)

Preprint submitted to Journal of LATEX Templates

January 13, 2020

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Keywords: Angle-of-arrival fluctuations, atmospheric turbulence, free-space

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optics, unmanned aerial vehicles.

1. Introduction

Free-space optical (FSO) communication systems have recently attracted a

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great deal of attention as a cost-effective and easy-to-deploy solution for the backhaul/fronthaul of next generation of wireless networks [1, 2]. Significant advantages such as very large bandwidth, high transmission security, immunity to jamming, and low implementation cost make FSO systems as an ideal solution for establishing communication links. However, vulnerability to signal blockage

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is one of the fundamental limitations of FSO links which essentially confine the receiver (Rx) to be placed within the line-of-sight (LoS) of the transmitter (Tx). As maintaining LoS propagation over long distance FSO links is not feasible due to physical obstacles, conventional terrestrial FSO links are inherently distance

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limited specially in dense urban areas with tall buildings. Here, to increase the link reliability and system performance, relay nodes can be insert between the Tx and Rx. However, optimal relay placement is not always possible and also particular attention should be devoted to the risk of exposure at rental relay locations.

Recently, unmanned aerial vehicles (UAVs), also known as drones, have attracted much attention by exploiting the potential of deploying as either aerial access points or mobile relay fronthaul links to satisfy provisional capacity requirements in a hotspot area such as a stadium [3]. Due to the increasing demand for high capacity and secure communications as well as the need for low power consumption, low size and light-weight transceiver, the FSO technology is an attractive alternative for incorporating in UAV-based communica-

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tions instead of using congested radio frequency bands [4]. However, deploying an UAV-based FSO communication system rises new challenges which are addressed in more recent works [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. For instance, an innovative approach is proposed in [5] where the flying platforms

2

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transport the backhaul/fronthaul traffic between the access and core networks by using FSO communications. The authors illustrate that the UAV-based FSO

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backhaul/fronthaul links can achieve throughput higher than the baseline alternatives, i.e., RF-based links, and can be considered as a practical solution for backhaul/fronthaul of the 5G+ wireless cellular networks. To study another

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aspects regarding the feasibility of UAV-assisted FSO links, the flight time of UAVs used in these types of communication links is optimized in [6]. Meanwhile, the works in [8, 9] propose new relaying protocols employing mixed RF/FSO communication links to maximize the end-to-end link throughput. In [10], two integration scenarios for a buffer-aided moving relay UAV-based FSO system are

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proposed for which the outage probability is adopted as a performance evaluation criterion. A novel discovery method is proposed in [11] to compensate the problem of automatic discovery and establishment of LoS alignment between UAVs with directional FSO transceivers. To mitigate the effects of angle-ofarrival (AoA) fluctuations due to orientation deviations of hovering UAVs, a

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fast and power-efficient adaptive beam control technique is proposed in [12]. A novel joint spatial tracking and data detection method is proposed in [13]. In [14], the authors study the impact of heights and positions of different obstacles on the optimal location of an UAV-based FSO relay system under the assumption that the Rx is thermal noise limited. Accordingly, in this work, the optimal UAV location as well as the optimal optical beam pattern are obtained while the outage probability is minimized.

In [15, 16], the authors develop a novel channel model for UAV-based FSO systems and analyze the system performance in terms of outage probability and ergodic capacity. The results of [15, 16] are obtained by assuming a background noise limited scenario at the receiver. Also, novel closed-form statistical channel models for hovering UAV-based FSO communications are derived in [17, 18] by

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taking into account the effects of UAV’s fluctuations. The authors then evaluate the system performance by calculating the outage probability assuming signal independent background noise. All of these prior works are developed based on the assumption that the Rx 3

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is limited by signal independent background and/or thermal noise. Although this assumption is valid for an FSO receiver with PIN photodetector, it is not

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accurate when an avalanche photo diode (APD) is employed at the receiver. In fact, APDs are highly sensitive photodetectors that exploit the photoelectric effect to convert light into phtocurrents, and thus, the output noise of an APD

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depends on the received optical signal level. For a UAV-based FSO system, due to the UAV’s fluctuations, the received optical signal varies over a wide range which induces changes in the statistical model of the APD output noise. Accordingly, performance analysis of such UAV-based FSO systems is more challenging than those with PIN photodiodes. Therefore, a dedicated study

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should be carried out to investigate the performance of UAV-based FSO systems when an APD is employed at the RX.

In this paper, assuming that an APD is employed at the Rx, we study the performance of a UAV-based FSO system. In particular, we first model the endto-end signal to noise ratio (SNR) of the system. Then, given the analytical SNR

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model that we developed, we derive closed-form expressions for the bit error rate (BER) of the considered UAV-based system under weak turbulence conditions (statistically modeled by log-normal distribution), and moderate to strong turbulence conditions (statistically modeled by gamma-gamma distribution). As we will discuss in the paper, our derived analytical expressions can be also used for PIN photodiodes (as a special case of APDs). Moreover, we study the effect of different link parameters, i.e., received optical beamwidth, Rx field-of-view (FoV), optical transmit power, and different levels of UAV instability on the performance of the system. The analytical expressions provided in this paper are also corroborated by performing Monte Carlo simulations. The results of this paper reveal insights into the importance of utilizing APD for UAV-based FSO system to mitigate the degradation effects of UAV’s fluctuations.

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The rest of the paper is organized as follows. Section II presents the system

model and main assumptions. Next, in Section III, we provide the BER analysis of the considered system under different atmospheric turbulence conditions. Section III presents the numerical results to verify the derived analytical expres4

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sions and to study the link performance and parameter optimization. Section

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IV concludes this paper. 2. System Model and Main Assumptions

We consider an intensity modulation with direct detection (IM/DD) UAV-

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based FSO link where ON–OFF keying (OOK) modulation is performed at the Tx. Optical beam, through its way from the Tx to the Rx, will be affected by the atmospheric turbulence as well as UAVs’ position and orientation fluctuations. The Rx lens collects a fraction of the received optical beam. However, in addition to the desired optical signal, undesired background radiations due to

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the scattered sunlight is also collected by the Rx lens. Accordingly, optical filters are employed to filter out the background light and reduce the background noise level at the Rx. The converging lens guides the collected optical beam towards the surface of the APD.

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Depending on whether the transmitted bit is “0” or “1”, the APD output noise is different. As a result, the received signal at the Rx can be expressed as r = ηhPt s + n,

(1)

where s ∈ {0, 1} denotes the transmitted OOK symbols, Pt denotes the average transmitted optical power, h denotes the instantaneous channel coefficient of the UAV-based system. Moreover, in (1), η =

eGµ hplanck ν

where hplanck is the Planck

constant, ν = c/λ is the optical frequency, c = 3 × 108 is the speed of light, λ is the optical wavelength, µ is the APD quantum efficiency, and G is the average APD gain. Also, n is the APD output noise which can be well modeled as zero-mean Gaussian distribution with variance [19]

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2 σn2 = σs2 hs + σth + σb2 .

(2)

In (2), σs2 is the noise variance due to the desired received signal and can be obtained as

σs2 = 2eGF Be ηPt , 5

(3)

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where F is the excess noise factor and Be is the electrical bandwidth. Moreover, 2 in (2), σth is the variance of thermal noise and can be obtained as

4kboltz Tr Be , RL

(4)

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2 σth =

where kboltz is the Boltzmann constant, Tr is the Rx’s equivalent temperature,

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and RL is the Rx’s resistance. Finally, σb2 is the noise variance due to the undesired background radiation and can be obtained as σb2 = 2eGF Be ηPb , where Pb =

2 2 π 2 ra Bo Nb (λ)θFOV 4

(5)

is the background power, ra is the Rx lens radius,

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Bo is the bandwidth of the optical filter, Nb (λ) is the is the spectral radiance of 2

the background radiations at wavelength λ (in Watts/cm -µm-srad), and θFOV is the Rx’s FoV angle [17].

As we observe from (2), the term σs2 hs in (2), is a signal dependent term. As a results, by varying instantaneous coefficient of h, in addition to the instan-

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taneous received optical power, the instantaneous variance of noise changes and by increasing the values of G, the dependency of noise variance to the instantaneous channel coefficient h increases. However, for the case of PIN photo diode, we have G = 1, and thus the dependency of the output noise to the channel coefficient is much less than APD case. Accordingly, it is a conventional assumption in the literature of FSO systems to approximate the output noise of a PIN photo-detector as [20, 21]

2 σn2 ' σth + σb2 .

(a3)

2.1. Channel modeling

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For modeling of the channel, we consider the joint effects of deterministic

propagation loss, denoted by hl , the random intensity fluctuation due to atmo-

spheric turbulence, denoted by ha , the geometrical loss due to the deviation between the Rx lens center and the received beam center, denoted by hpg , and 6

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the link interruption due to the AoA fluctuations, denoted by hpa . Thus, the channel coefficient h can be written as [17] (6)

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h = hl ha hpg hpa .

For the considered UAV-based FSO communication links, under weak to moder-

is given as [18]

  +C1 1−exp −

θF2 OV 2 + σ2 ) 2 (σto ro θF2 OV 2 + σ2 ) 2 (σto ro

where     

δ (h)





hC2 Q 

T (A0 hl )T

ln



h A0 hl



σR

C2 = T − 1,

+ C3

(7)



,

  2 exp 0.5 × σR T (1 + T ) ,

2 (1 + 2T ), C3 = 0.5 × σR

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   

C1 =



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 fh (h) = exp −

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ate turbulence conditions, the probability density function (PDF) of the channel

2 is the Rytov variance, and Q(·) is the Q-function, δ(·) is Dirac delta function, σR 2 2 σtp and σto are the variances of position and orientation deviations of the Tx 2 2 are the variances of position and orientaand σro UAV node, respectively, σrp

tion deviations of the Rx UAV node, respectively, and T =

Moreover, A0 = (erf(ν))2 , ν = wz2eq tion.

=

√ πerf(ν) wz2 2ν exp(−ν 2)

1 Throughout

√ √ πra , 2wz

wz2eq

2 +σ 2 +σ 2 ) 4(Z 2 σto rp tp

.1

wz is the beamwidth at the receiver,

is the equivalent beamwidth, and erf(·) is the error func-

this paper, we assume an UAV-to-UAV link as we consider the effects of

orientation fluctuations on both Tx and Rx nodes. The typical values of standard deviation of orientation fluctuations in a ground FSO system is on the order of 100 µrad [22], which is much less than its aerial counterpart. Accordingly, we can reasonably neglect the effect of

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orientation fluctuation of ground node compared to the UAV node on the system performance. Thereby, our derived model in this paper can be readily adopted to either a ground-to-UAV FSO link or an UAV-to-ground FSO link, respectively, by setting the parameters related to ground node fluctuations to zero.

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Also, the channel PDF under moderate to strong turbulence conditions is given as [18] 

            

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c2 , and c3 are obtained as

n+β−T − c4 c6 hn+α−T c1 = c4 c5 hm m

c2 = c3 = c4 = c5 = c6 =

c4 c6 (hl A0 )n+α−T c4 c5 (hl A0 )n+β−T πT (hl A0 )T Γ(α)Γ(β) sin(π(α−β)) (αβ)n+β (n+β−T )Γ(n−α+β+1)n! (αβ)n+α (n+α−T )Γ(n+α−β+1)n!




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where the constants c1 ,              

(8)

of

 θF2 OV fh (h) = exp − 2 + σ 2 ) δ (h) 2 (σto ro    X N  2 θF OV c1 hT −1 + C1 1 − exp − 2 + σ2 ) 2 (σto ro n=0  n+α−1 n+β−1  + c2 h − c3 h , 0 ≤ h ≤ hl A0 hm ,

.

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We note that in (8), the values of both parameters N and hm depend on the Rytov variance σr2 . In this regard, the best choices for N and hm as a function 2 of σR are provided in [18, Table I]. Also, α and β are the effective number of

large-scale and small-scale eddies, respectively, and can be represented as [23] 







  α = exp     β = exp  

2 0.49σR

1+

12/5 1.11σR 2 0.51σR

1+

12/5 0.69σR



−1

,



−1

.

  7/6  − 1   5/6  − 1

(9)

3. BER Analysis

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Im this section, we study the performance of the considered UAV-based

system in terms of BER. To do so, BER analysis is derived under weak to moderate, and also moderate to strong atmospheric turbulence conditions. In the sequel, the developed analytical approaches are provided in details. 8

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3.1. BER under Weak to Moderate Turbulence Conditions Let ps (s = 1) and ps (s = 0) denote the a priori probability of transmitting bit

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“1” and “0”, respectively, and ~thr denote the receiver threshold for detecting bits “0” and “1”. Thus, for OOK signaling, BER conditioned on h can be

Pe = ps (s = 1)

Z

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obtained as

Pe|h,s=1 fh (h)dh Z + ps (s = 0) Pe|h,s=0 fh (h)dh,

where

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  Pe|h,s=1 = Probr < ~0thr s = 1, h,   Pe|h,s=0 = Probr > ~0thr s = 0, h.

(10)

(11) (12)

From (1) and (2), the probability of received signal conditioned on s and h can be written as

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  1 |r|2 exp − 2 + σ2 ) , 2 + σ2 ) 2(σth 2π(σth b b 1 =p 2 + σ2 ) 2π(σs2 h + σth  b  |r − ηhPt |2 × exp − 2 + σ2 ) . 2(σs2 h + σth b

pr|s=0,h = p pr|s=1,h

Using [24, eq. (15)], (1), and (2), we obtain    Pe|h,s=1 = Prob  ηhPt + n

 2 + σ2  σth  pb

p s = 0, h  2 2 2 2 σs2 h + σth + σb + σth + σb p

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ηhPt

9

(13)

(14)

(15)

(16)

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From (2), (15), (16), and since ps (s = 1) + ps (s = 0) = 1, Eq. (10) can be obtained as

!

fh (h)dh.

(17)

(18)

Substituting (7) in (17), we have   1 θF2 OV Pe = exp − 2 + σ2 ) 2 2 (σto ro    θF2 OV + C1 1 − exp − 2 + σ2 ) 2 (σto ro   Z ∞ ln (h/A h ) + C3 0 l × hC2 Q σR 0

ηhPt p p 2 + σ2 + 2 + σ2 σs2 h + σth σth b b

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×Q

of

Q

ηhPt p p 2 + σ2 + 2 + σ2 σs2 h + σth σth b b

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Pe =

Z

!

dh.

In the following derivations, we utilize the identity [25] 3 X

ai exp(−a0i x2 ),

(19)

i=1

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Q(x) '

where a1 = 5/24, a2 = 4/24, a3 = 1/24, a01 = 2, a02 = 11/20, and a03 = 1/2 [25].

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Given the fact that Q(x) = 1 − Q(−x), Eq. (18) can be rewritten as      1 θF2 OV θF2 OV Pe = exp − + C 1 − exp − 1 2 + σ2 ) 2 + σ2 ) 2 2 (σto 2 (σto ro ro   2 ! Z ∞ 3 X  ln (h/A h ) + C  0 l 3 ai  hC2 exp −a0i ×   σ R h 1 i=1 ! ηhPt p dh. ×Q p 2 + σ2 + 2 + σ2 σs2 h + σth σth b b "  2 !# Z h1 ln (h/A0 hl ) + C3 C2 0 + h 1 − exp −ai σR 0 !   ηhPt  p ×Q p dh  , 2 2 2 2 2 σs h + σth + σb + σth + σb

(20)

where h1 = A0 hl e−C3 . Using [26, eq. (06.25.02.0001.01)] and [27], and after some manipulations, Eq. (20) is approximated as      θF2 OV θF2 OV 1 Pe = exp − + C 1 − exp − 1 2 + σ2 ) 2 + σ2 ) 2 2 (σto 2 (σto ro ro 10

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 Z 3 X ai  hC1 2 +1   × −  2  C2 + 1

C2

h

exp

0

i=1

Z

h1

∞



−a0i



ln (h/A0 hl ) + C3 σR  !

2 !

2

exp

ηPt . 2 +σ 2 ) 8(σth b

pro

where b1 = √

h

−a0i

of

ln (h/A0 hl ) + C3 dh σR h1  M  2 X (−1)m b2m+1 hC2 +2m+2  1  +√ − 1   C2 + 2m + 2 π m=0 m!(2m + 1)  2 ! Z ∞ ln (h/A h ) + C 0 l 3 − hC2 +2m+1 exp −a0i dh σR h1   2 !  Z h1  ln (h/A0 hl ) + C3   C2 +2m+1 0  h exp −ai + dh    , σ R 0 +

C2

dh

(21)

Using [28] and [29, eq. (2.33.1)], by applying the change

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re-

of variable y = ln(h/h1), and after some mathematical manipulations we obtain   θF2 OV 1 Pe = exp − 2 + σ2 ) 2 2 (σto ro     X 3 θF2 OV ai hC1 2 +1   1  + C1 1 − exp −  2  C2 + 1 2 2 (σto + σro ) 2 i=1 !   2 √ σR (C2 + 1) σR π σR (C2 + 1)2 p erf + p 0 exp 4a0i ai 2 a0i  M 1 2 X (−1)m (b1 h1 )2m+1    +√ − m!(2m + 1)  C2 + 2m + 2 π m=0  2  √ σR π σR (C2 + 2m + 2)2 + p 0 exp 4a0i ai !   σR (C2 + 2m + 2)   .  p 0 (22) × erf     2 ai Next, we obtain BER under moderate to strong turbulence conditions. Sub-

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stituting (8) in (17), we have      1 θF2 OV θF2 OV Pe = exp − + C 1 − exp − 1 2 + σ2 ) 2 + σ2 ) 2 2 (σto 2 (σto ro ! ro Z hl A0 hm ηhPt p × Q p 2 + σ2 2 + σ2 + σs2 h + σth σth 0 b b ×

N   X c1 hT −1 + c2 hn+α−1 − c3 hn+β−1 dh.

n=0

11

(23)

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Numerical Numerical Analytical Analytical

σto = σro = 6 mrad

10 -6

-10

-5

0

re-

σto = σro = 3 mrad

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BER

10 -2

10 -4

APD PIN APD PIN

of

10 0

results, results, results, results,

5

10

15

20

Pt (dBm)

Figure 1: BER under weak turbulence conditions versus Pt for wz = 4 m and two different

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UAV’s instability conditions, σto = σro = 3 and 6 mrad.

Using [28] and after some mathematical manipulation, the closed-form expression for BER under moderate to strong turbulence conditions is derived as   θF2 OV 1 (24) Pe = exp − 2 + σ2 ) 4 2 (σto ro     X N  c1 (hl A0 hm )T θF2 OV   + C1 1 − exp −  2 + σ2 )  2 (σto T ro n=0 c2 (hl A0 hm )n+α c3 (hl A0 hm )n+β − n+α n+β  M 2m+1 2 X (−1)m b1  c1 (hl A0 hm )T +2m+1  −√  T + 2m + 1 π m=0 m!(2m + 1) +

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  c2 (hl A0 hm )n+α+2m+1 c3 (hl A0 hm )n+β+2m+1    + −   . n + α + 2m + 1 n + β + 2m + 1

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Table 1: System Parameters for Simulations

Parameter G F F µ

30 2.75 1 0.8

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APD Gain Excess noise factor of APD Excess noise factor of PIN APD and PIN Quantum Efficiency Plank's Constant Wavelength Receiver Load Receiver Temperature Boltzmann constant

Setting

of

Description

Bo Z hl ra

6.6 × 10−34 m2 Kg/s 1550 nm 1 kΩ 300° K 1.38064852 × 10−23 m2 kg s−2 K−1 1 Gbps 109 10−3 2 Watts/cm -µm-srad 1 nm 500 m 10 dB 4 cm

θFOV wz

5-50 mrad 1-30 m

Weak turbulence modeled by log-normal

2 σR

0.2

Moderate to strong turbulence modeled by gamma-gamma

2 σR α β

0.6-2 4-5.4 1.7-3.8

σto

1-10 mrad

σro

1-10 mrad

σtp

30 cm

σrp

30 cm

reRb Be Nb (λ)

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Data rate Electrical bandwidth Spectral radiance of background radiation Optical filter bandwidth Link length Channel Loss Lens radius

hplank λ Rl Tr kboltz

Rx’s FoV Beamwidth at Rx

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UAV parameters ————————— ————————— Standard deviation of orientation fluctuations of Tx Standard deviation of orientation fluctuations of Rx Standard deviation of position fluctuations of Tx Standard deviation of position fluctuations of Rx

13

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results, results, results, results,

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Weak: σR2 = 0.6

10 -6

-10

Strong: σR2 = 2

0

re-

BER

10 -2

10 -4

APD PIN APD PIN

of

10

Numerical Numerical Analytical Analytical

0

10

20

Pt (dBm)

2 = 0.6 Figure 2: BER versus Pt under moderate atmospheric turbulence conditions when σR

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2 = 2. and strong atmospheric turbulence conditions when σR

4. Numerical Results

In this section, we provide numerical results in terms of BER to evaluate the performance of UAV-based FSO systems for two cases: (a) APD photodetector with G = 30, F = 2.75 and µ = 0.8; and (b) PIN photodetector with G = 1, F = 1, and µ = 0.8. We consider an uncoded OOK modulation scheme and set the system parameters as specified in Table 1. Most of the parameter values in Table 1 are available in the related recent literature (see for instance [17, 18, 2]). Due to the size and weight limitations of UAV’s payload, we consider Rx’s lens radius ra = 4 cm that causes higher geometrical loss values than the conventional ground FSO systems with lens radius in the order of 10-25 cm. Moreover, due

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to the higher orientation fluctuations of the mounted FSO systems on UAVs compared to their ground counterparts, we analyze our considered UAV-based FSO system over a wide range of beamwidth, i.e., we assume wz ∈ [1, 30] m. The beamwidth of ground FSO systems is mainly in the order of one meter 14

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Numerical Numerical Analytical Analytical

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BER

10 -2

10 -4

APD PIN APD PIN

of

10 0

results, results, results, results,

θF OV = 12 mrad

10 -6

-10

0

re-

θF OV = 50 mrad 10

20

Pt (dBm)

Figure 3: BER versus Pt for two different scenarios, i.e., when θFOV = 12 mrad, and when

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θFOV = 50 mrad.

10 0

θF OV = 40 mrad θF OV = 20 mrad

PIN

BER

10 -2

10 -4

APD

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10 -6

5

10

15

20

25

wz (m)

Figure 4: BER versus wz for two different values of FoV, σFOV = 20 and 40 mrad.

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10 0 APD PIN

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σto = 7 mrad

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BER

10 -2

10 -4

σto = 3 mrad 10 -6

10

15

20

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5

wz (m)

Figure 5: BER versus wz for two different levels of UAV stability, σto = 3 and 7 mrad.

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[1, 2, 30]. Moreover, we study the BER performance of the UAV-based FSO system under different levels of UAV’s instability characterized by σto , σro , σtp , and σrp .

Figure 1 depicts the BER of considered system versus Pt for wz = 4 m, θFOV = 40 mrad, and two levels of UAV’s stability, i.e., low level of stability when σto = σro = 6 mrad, and high level of stability when σto = σro = 3 mrad. The results of Fig. 1 are provided for weak turbulence conditions. The results show that by increasing the stability of UAV from σto = 6 mrad to σto = σro = 3 mrad, the BER of both APD-based and PIN-based receivers decreases significantly. Moreover, the APD-based receiver when σto = 6 mrad outperforms the PIN-based receiver when σto = 3 mrad. The closed-form BER expression for the BER of considered system is derived in (22). Also, numerical

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results confirm the accuracy of analytical results of BER derived in (22). In Fig. 2, we investigate the performance of the UAV-based FSO system

2 2 under moderate (σR = 0.6) and strong (σR = 2) turbulence conditions. The

results of Fig. 2 are obtained for wz = 12 m, θFOV = 40 mrad, and σto = 2 mrad. 16

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As expected, for both APD- and PIN-based receivers, the BER increases by increasing turbulence strength. For instance, for the APD-based receiver, Pe =

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10−4 can be achieved for Pt = 13 dBm under moderate turbulence conditions, while, under strong turbulence conditions, to achieve BER values less than 10−4 , Pt must be higher than 22 dBm. Under moderate to strong turbulence

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conditions, we have derived the closed-form analytical expressions of the BER of UAV-based FSO systems in (24). In addition, the perfect match between the analytical and simulation-based results in Fig. 2 confirms the accuracy of our analytical expressions.

To mitigate the effect of AoA fluctuations on the system performance, the

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values of the Rx FoV should be chosen larger than those of conventional ground FSO links. However, undesired background radiation increases by increasing Rx FoV which degrades the system performance. Here, in Fig. 3, we study the effect of Rx FoV on the BER performance of the UAV-based FSO system. The 2 = 0.6, and two different results of Fig. 3 are obtained for σto = 2 mrad, σR

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values of Rx FoV, θFOV = 12 and 50 mrad. From this figure, for both APD- and PIN-based systems, an error floor can be noticed in case of insufficient values of θFOV , i.e., when θFOV = 12 mrad. This error floor can also be realized from the derived analytical expressions. In particular, from (22) and (24), we have   1 θF2 OV Pe > exp − (25) 2 + σ2 ) . 4 2 (σto ro As we can observe from (25), for the low values of FoV, BER is lower bounded   θ 2 OV to 14 exp − 2(σ2F +σ 2 ) . Under this circumstance, the RX FoV should be into

ro

creased to improve the system performance. However, as we observe from Fig. 3, unlike PIN-based systems, increasing the receiver FoV does not necessarily improve the performance of APD-based systems. From Fig. 3, for the APDbased system under low transmit power regime, i.e., when Pt < 14 dBm, the

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receiver with θFOV = 12 mrad achieves better performance than the receiver with θFOV = 50 mrad. This is not surprising since the inherent gain of the APD receiver increases the level of both desired signal and undesired background radiation. Consequently, for APD-based systems, the optimal value of θFOV can 17

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be obtained by balancing a tradeoff between desired performance and the link power budget.

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To have a deeper understanding about the effect of the beamwidth wz on the performance of the system, in Figs. 4 and 5, we have depicted the BER performance versus wz under moderate atmospheric turbulence conditions with

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2 σR = 0.7. In particular, in Fig. 4, BER performance is plotted versus wz for

σto = σro = 4 mrad, and two different values of FoV, θFOV = 20 and 40 mrad. As we can observe from Fig. 4, increasing wz can help compensate for the effects of UAV’s orientation fluctuations on the system performance. Meanwhile, there exists an optimal point for determining the value of wz , and, thus, increasing

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wz does not necessarily improve the system performance. For instance, in our setup, when σto = 4 mrad, the optimal value of wz is approximately equal to 8 m for both APD- and PIN-based receivers. Moreover, we notice that the change in the values of FoV from 20 to 40 mrad, improves the performance of APDbased systems. Indeed, this improvement is significant when the bandwidth wz

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is set optimally. Also, from Fig. 4, we can realize that the BER is floored at low values of θFOV . In Fig. 5, BER is plotted versus wz for θFOV = 40 mrad, and two different levels of UAV stability, σto = 3, and 7 mrad. The results of this figure clearly show that the optimal values of wz increases by decreasing UAV stability. For instance, in our setup, by increasing σto = 3 to σto = 7 mrad, the optimal wz increases from 6 to 13 m. This is reasonable because for high levels of instability we can make the beam more wider to reduce the effect of AoA fluctuations on the receiver.

5. Conclusion

In this paper, we analyzed the performance of UAV-assisted FSO systems

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using an APD at the receiver. Subsequently, we modeled end-to-end SNR of the considered FSO link and derived closed form expressions for the BER of the system under different turbulence conditions. Then, we studied the performance of considered system for both APD and PIN cases over different channel

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parameters such as received optical beamwidth, receiver’s FoV, optical transmit power, different levels of UAV instability, and different level of atmospheric

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turbulence conditions. From the result of this study, when both effects of position and AOA fluctuations are taken into account, APD-based UAV-assisted FSO systems outperform their PIN-based counterparts in terms of BER. Thus,

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employing APDs at the receiver can help compensate for the effects of UAV’s orientation fluctuations on the system performance.

References

[1] M. A. Khalighi, M. Uysal, Survey on free space optical communication:

re-

A communication theory perspective, IEEE Communications Surveys and Tutorials 16 (4) (2014) 2231–2258.

[2] Z. Ghassemlooy, W. Popoola, S. Rajbhandari, Optical wireless communi-

urn al P

cations: system and channel modelling with Matlab®, CRC press, 2019. [3] M. T. Dabiri, H. Safi, S. Parsaeefard, W. Saad, Analytical channel models for millimeter wave UAV networks under hovering fluctuations, arXiv preprint arXiv:1905.01477.

[4] H. Kaushal, G. Kaddoum, Optical communication in space: Challenges and mitigation techniques, IEEE Communications Surveys and Tutorials 19 (1) (2017) 57–96.

[5] M. Alzenad, M. Z. Shakir, H. Yanikomeroglu, M.-S. Alouini, FSO-based vertical backhaul/fronthaul framework for 5G+ wireless networks, IEEE Communications Magazine 56 (1) (2018) 218–224. [6] J.-H. Lee, K.-H. Park, Y.-C. Ko, M.-S. Alouini, A UAV-mounted free

Jo

space optical communication: Trajectory optimization for flight time, IEEE Transactions on Wireless Communications.

[7] J.-H. Lee, K.-H. Park, Y.-C. Ko, M.-S. Alouini, Free space optical communication on UAV-assisted backhaul networks: Optimization for service 19

Journal Pre-proof

time, in: IEEE Global Communications Conference (GLOBECOM 2019), IEEE, 2019.

of

[8] J.-H. Lee, K.-H. Park, Y.-C. Ko, M.-S. Alouini, Throughput maximization of mixed FSO/RF UAV-aided mobile relaying with a buffer, arXiv preprint

pro

arXiv:2001.01193.

[9] J.-H. Lee, K.-H. Park, M.-S. Alouini, Y.-C. Ko, On the throughput of mixed FSO/RF UAV-enabled mobile relaying systems with a buffer constraint, in: ICC 2019 IEEE International Conference on Communications (ICC), IEEE, 2019, pp. 1–6.

re-

[10] W. Fawaz, C. Abou-Rjeily, C. Assi, UAV-aided cooperation for FSO communication systems, IEEE Communication Magazine 56 (1) (2018) 70–75. [11] M. R. Khan, S. Bhunia, M. Yuksel, L. Kane, Line-of-sight discovery in 3D using highly directional transceivers, IEEE Transactions on Mobile Com-

urn al P

puting.

[12] V. V. Mai, H. Kim, Beam size optimization and adaptation for high-altitude airborne free-space optical communication systems, IEEE Photonics Journal 11 (2) (2019) 1–13.

[13] H. Safi, A. Dargahi, J. Cheng, Spatial beam tracking and data detection for an FSO link to a UAV in the presence of hovering fluctuations, arXiv preprint arXiv:1904.03774.

[14] M. T. Dabiri, S. M. S. Sadough, Optimal Placement of UAV-Assisted FreeSpace Optical Communication Systems with DF Relaying, IEEE Communications Letters (2019) 1–1doi:10.1109/LCOMM.2019.2949274.

Jo

[15] M. Najafi, H. Ajam, V. Jamali, P. D. Diamantoulakis, G. K. Karagiannidis, R. Schober, Statistical modeling of FSO fronthaul channel for dronebased networks, in: 2018 IEEE International Conference on Communications (ICC), IEEE, 2018, pp. 1–7.

20

Journal Pre-proof

[16] M. Najafi, H. Ajam, V. Jamali, P. D. Diamantoulakis, G. K. Karagiannidis, R. Schober, Statistical modeling of the FSO fronthaul channel for UAV-

of

based networks, arXiv preprint arXiv:1905.12424. [17] M. T. Dabiri, S. M. S. Sadough, M. A. Khalighi, Channel modeling and parameter optimization for hovering UAV-based free-space optical links,

pro

IEEE Journal on Selected Areas in Communications 36 (9) (2018) 2104– 2113.

[18] M. T. Dabiri, S. M. S. Sadough, I. S. Ansari, Tractable optical channel modeling between UAVs, IEEE Transactions on Vehicular Technology 68 (12)

re-

(2019) 11543–11550.

[19] M. T. Dabiri, S. M. S. Sadough, M. A. Khalighi, FSO channel estimation for OOK modulation with APD receiver over atmospheric turbulence and pointing errors, Optics Communications 402 (2017) 577–584.

urn al P

[20] F. Xu, M.-A. Khalighi, S. Bourennane, Impact of different noise sources on the performance of PIN-and APD-based FSO receivers, in: Proceedings of the 11th International Conference on Telecommunications, IEEE, 2011, pp. 211–218.

[21] M. T. Dabiri, S. M. S. Sadough, M. A. Khalighi, Blind signal detection under synchronization errors for FSO links with high mobility, IEEE Transactions on Communications 67 (10) (2019) 7006–7015. [22] F. Yang, J. Cheng, T. A. Tsiftsis, Free-space optical communication with nonzero boresight pointing errors, IEEE Transactions on Communications 62 (2) (2014) 713–725.

[23] L. C. Andrews, R. L. Phillips, Laser beam propagation through random

Jo

media, Vol. 52, SPIE press Bellingham, WA, 2005.

[24] H. Safi, A. A. Sharifi, M. T. Dabiri, I. S. Ansari, J. Cheng, Adaptive channel coding and power control for practical FSO communication systems

21

Journal Pre-proof

under channel estimation error, IEEE Transactions on Vehicular Technology 68 (8) (2019) 7566–7577.

of

[25] Q. Zhang, J. Cheng, G. K. Karagiannidis, Block error rate of optical wireless communication systems over atmospheric turbulence channels, IET

pro

Communications 8 (5) (2014) 616–625.

[26] Wolfram, The wolfram functions site: http://functions.wolfram.com/. [27] E.

W.

tion.,

From

Weisstein,

Normal

MathWorld–A

Distribution

Wolfram

Web

FuncResource.

http://mathworld.wolfram.com/NormalDistributionFunction.html.

re-

[28] E. W. Weisstein, Erf., From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Erf.html.

[29] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, 7th

urn al P

ed. Academic press, 2007.

[30] H. Savojbolaghchi, S. Sadough, M. Dabiri, I. Ansari, Generalized channel estimation and data detection for MIMO multiplexing FSO parallel chan-

Jo

nels over limited space, Optics Communications 452 (2019) 158–168.

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Declaration of competing interest

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author Contribution Statement

Saeed Khan Kalantari: Conceptualization, Methodology, Writing - Review & Editing

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M. T. Dabiri: Conceptualization, Methodology, Writing - Review & Editing

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H. Safi: Conceptualization, Methodology, Writing - Review & Editing