Performance of BPSK-FSO Communication
Author Proof
Over Turbulence and Fog Attenuation
Abdeslam Fakchich1 , Mohamed Bouhadda2(B) , Rachid El Alami1 ,
Fouad Mohammed Abbou3 , Abdelouahed Essahlaoui2 , Mohammed El Ghzaoui1 ,
Hassan Qjidaa1 , and Mohammed Ouazzani Jamil4
1 Sidi Mohammed Ben Abdellah University, Fez, Morocco
2 Engineering Sciences Laboratory (LSI), Multidisciplinary Faculty, Sidi Mohammed Ben
Abdellah University, Taza, Morocco
mohamed.bouhadda@usmba.ac.ma
3 School of Sciences and Engineering, Al Akhawyen University, Ifrane, Morocco
4 LSEED Laboratory, UPF, Fez, Morocco
Abstract. Free space optical communication is a technology that uses optical
signals to transmit data between transmitters and receivers. In this paper, we ana-
lyze the performance of optical wireless transmission using heterodyne binary
phase-shift keying (BPSK) modulation. The system is operating under various
atmospheric channel effects. More precisely, the combined effects of atmospheric
turbulence and fog. Atmospheric turbulence induces intensity fluctuations, and
fog causes losses in signal power. To evaluate the optical wireless performances,
we derived a mathematical expression of the bit error rate (BER) that combines
fog attenuation and turbulence fading. We used a gamma-gamma distribution for
modeling atmospheric turbulence fading and Meijer’s G-function for approximat-
ing complex calculus. We carried out numerical simulations of the bit error rate
for different link distances, Rytov variances, and transmitted powers. The results
show that the effects of turbulence and fog are very important for strong turbulence,
and these effects limit link transmission. According to the simulation results, it
is clear that we can decrease the BER and increase the link communication by
raising transmitted power.
Keywords: Optical wireless · Atmospheric turbulence · Fog attenuation · BPSK
modulation
1 Introduction
Recently, the evolution of communication networks, namely, 5th generation cellular
networks and the Internet of Things, has caused an exponential increase in the demand
for a high data transmission rate [1]. Most existing wireless communication systems use
the propagation of radio waves in the atmosphere to transmit data. However, with this
demand for a high data rate in wireless communications, the radio frequency spectrum
will not be able to support broadband transmission. Optical wireless communication is a
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
S. Motahhir and B. Bossoufi (Eds.): ICDTA 2023, LNNS 668, pp. 1–9, 2023.
https://doi.org/10.1007/978-3-031-29857-8_33
2 A. Fakchich et al.
technology that uses light propagating through the atmosphere to transmit data between
Author Proof
transmitters and receivers.
The laser signal provides tremendous data rates in the optical fiber link. However,
optical fiber deployment and maintenance after installation are very expensive. Conse-
quently, it is very important to also consider the optical spectrum for wireless communi-
cation networks. Seen in this light, the use of optical wireless communication technology
has been the subject of much research because it offers a high transmission capacity sim-
ilar to that of optical fiber [2]. The remarkable advantages of this wireless technology are
unlicensed transmission, absence of interference, simple deployment, and high security
[3]. Low power consumption and sufficient spectral resources [2] distinguish communi-
cation systems based on free space optics. In recent years, the capacity of wireless optical
data transmission has greatly increased. The combination of 16 QAM dual-polarization
modulation and reception with soft-decision forward error correction allowed a laser
communication link with 53 WDM channels to transmit data at a rate of 200 gigabits
per second in each channel [4]. The FSO is an emerging communication technology
that uses a light-emitting-diode to generate infrared and visible light waves in the band
(390–750 nm) for data transmission in indoor optical wireless. In addition, the FSO
uses the laser in the near-infrared band (750–1600 nm) for a terrestrial optical network,
intersatellite, ground-to-air, and satellite-to-ground.
Free space laser communication has tremendous benefits over optical fiber and radio
frequency transmissions; however, atmospheric channel effects degrade the FSO system
performance. In particular, air turbulence is due to irregular changes in atmospheric tem-
perature and pressure. This turbulence causes a random fluctuation of the atmospheric
refractive index, which induces phase fluctuation and intensity fading. The phase fluctu-
ation is modeled as temporal pulse broadening, which causes intersymbol interference
that increases the BER of the FSO system [5, 6]. Pulse broadening limits the link and
the capacity communication of the FSO system [7]. The intensity fading is modeled sta-
tistically by different probability density functions. The log-normal distribution is used
in the case of weak turbulence. For weak, moderate, and strong atmospheric turbulence,
the FSO link can be modeled by distributions such as Gamma-Gamma, Malaga, and
Weibull.
The performance of FSO link communication is also degraded by optical signal
attenuation due to propagation in the atmosphere. This attenuation is the result of the
absorption of electromagnetic energy by gases and particles constituting the atmosphere
[8]. Among the meteorological atmospheric conditions, fog affects the performance of
optical free-space link transmission by causing different scatterings. Physically, fog is
formed by condensation of water vapor near the ground, and this vapor is in the shape
of very small diameter dimensions. The concentration of particles in fog is lower than
that in clouds. The particles of fog are numerous enough to give an opaque appearance
to the atmosphere, which drastically reduces visibility.
In optical wireless communication, the transmitted data can be modulated by sev-
eral formats such as OOK (On-Off Keying), BPSK (Binary Phase-Shift Keying), QPSK
(Quadrature PSK), DPSK (Differential PSK), and 8-PSK. These modulation techniques
are used for a FSO channel, which is assumed to be memoryless and stationary with
Performance of BPSK-FSO Communication Over Turbulence 3
additive white Gaussian noise (AWGN). In this paper, we focus our work on BPSK mod-
Author Proof
ulation because the FSO system presents the best BER performance compared with other
FSO systems using OOK, QPSK, DPSK, and 8-PSK. BPSK has the lowest power penalty
for a reference BER of 10–9 compared to these latter modulation techniques [9]. The
BPSK modulation technique is more suitable for use in wireless optical communication
with a turbulent channel.
The rest of the document is organized as follows. In section two, we present the system
and atmospheric channel model. In section three, we derive a mathematical model of
fog attenuation. In the fourth section, we model the optical wireless bit error rate due to
the combined effects of atmospheric turbulence and fog attenuation. We devote the fifth
section to discuss and analyze the simulation results. Finally, we conclude the work.
2 System and Channel Model
We consider a terrestrial optical wireless system with BPSK modulation and heterodyne
detection. We assume that the communication channel is memoryless and stationary
with additive white Gaussian noise (AWGN). The received signal is given as:
y = hx + n (1)
where x is the transmitted power, h is the channel fading, and n is the additive Gaussian
noise.
The channel state is considered as the product of two factors h = hl ha , where hl
is the deterministic path loss and ha is the random optical signal attenuation due to
atmospheric turbulence.
The probability density of the Gamma-Gamma turbulence model is expressed as
[10]:
(2)
where is the Gamma function [11], Kυ (.) is the υth-order modified Bessel function
of the second kind [11]. A and β are the parameters of scintillation and are expressed as
[10]:
⎡ ⎛ ⎞ ⎤−1
⎢ ⎜ ⎟ ⎥
⎢ ⎜ 0.49σR2 ⎟ ⎥
α=⎢ exp
⎢ ⎜
⎜ ⎟ − 1⎥
7 ⎟ ⎥ (3)
⎣ ⎝ 12 6 ⎠ ⎦
1 + 1.11σR5
⎡ ⎛ ⎞ ⎤−1
⎢ ⎜ ⎟ ⎥
⎢ ⎜ 0.49σR2 ⎟ ⎥
α=⎢ exp
⎢ ⎜
⎜ ⎟ − 1⎥
7 ⎟ ⎥ (4)
⎣ ⎝ 12 6 ⎠ ⎦
1 + 1.11σR5
4 A. Fakchich et al.
The parameter σR2 is the Raytov variance, which is a measure of the strength of
Author Proof
turbulence fluctuations [12]. It is expressed by [10]:
σR2 = 1.23Cn2 K 7/6 z 11/6 (5)
where k = 2π/λ is the optical wavenumber, Cn2 is the refractive index structure, which
is constant for a horizontal link, λ is the wavelength, and z is the link distance [12].
3 Fog Attenuation
The atmospheric attenuation loss is mathematically modeled by the exponential Beers-
Lambert low as [13]:
hl = exp(−Az) (6)
where A is the attenuation coefficient and z is the link distance. The loss depends on atmo-
spheric visibility, which is defined as the distance where the optical signal of wavelength
550 nm is attenuated to a fraction of 5% or 2% of its initial power [14].
The mathematical model that expresses the relationship between attenuation and
visibility was developed by Kruse as [15]:
3.912 λ −q
A= (7)
V 0.55
where V is the atmospheric visibility and q is the parameter related to the particle size
distribution in the atmosphere. The parameter q was determined based on the Kruse
model, which was modified by Kim as follows [16]:
⎧
⎪
⎪ 1.6 if V > 50 km
⎪
⎪
⎪
⎨ 1.3 if 6 km < V < 50 km
q = 0.16 V + 0.34 if 1 km < V < 6 km (8)
⎪
⎪
⎪
⎪ V − 0.5 if 0.5 km < V < 1 km
⎪
⎩ 0 if V < 0.5 km
4 Average BER in the Presence of Atmospheric Turbulence
and Fog.
The bit error rate of BPSK modulation is modeled as [9]:
1
P(e|h) = erfc SNR(h) (9)
2
where SNR(h) is the electrical signal-to-noise ratio, which is expressed by SNR(h) =
2RPr ha 2
qB , with Pr being the received power, q being the electron charge, R being the
receiver responsivity and B being the bandwidth.
Performance of BPSK-FSO Communication Over Turbulence 5
In the presence of attenuation due to fog, the received power is expressed by Pr =
Author Proof
Pt e−Az , with Pt being the transmitted power. Then, the signal-to-noise ratio is given by:
2RPt e−Az ha 2
SNR(h) = (10)
qB
The BER of an optical wireless link in the presence of atmospheric turbulence is
expressed as:
∞
P(e) = P(e|ha )fha (ha )dha (11)
0
By substituting (9) and (2) in (11), the average BER can be expressed as:
α+β ∞
(αβ) 2 α+β
−1
P(e) = ha 2 erfc 2μTh2a Kα−β 2 αβha dha (12)
(α)(β)
0
2RP h2
where μ is the average signal-to-noise ratio, which is given as μ = E qBs a =
2RPt 2
qB E ha .
To simplify the calculation, we express Kα−β in terms of the hypergeometric Meijer’s
m,n
G-function Gp,q [11]. Then (12) can be expressed as:
α+β ∞ α+β −
√(αβ) 2 −1 2,0
αβha | α−β β−α
2
P(e) = ∫ ha G0,2
2 π (α)(β)
0 2 , 2
! (13)
2,0 1
G1,2 2μTh2a d ha
0, 21
By using the equality (21) in [17], we can calculate the integral in (13). Then the
average BER can be expressed as:
1−α 2−α 1−β 2−β
2α+β−3 2,4 16μ 2 , 2 , 2 , 2 ,1
P(e) = 3 G5,2 (14)
π 2 (α)(β) αβ(α + 1)(β + 1) 0, 21
5 Numerical Results and Discussion
We carried out the simulation results using MATLAB software. We considered a turbu-
lent channel with AWGN noise in the presence of fog attenuation. The system parameters
used in this section are listed in Table 1.
6 A. Fakchich et al.
Table 1. System parameters.
Author Proof
Parameter Value
Wavelength (λ) 1550 nm
Receiver optical efficiency 0.75
Transmitter optical efficiency 0.75
Responsivity 0.85 A/W
Transmitting divergence angle θ 2.10–3
The photodiode bandwidth 2.5 GHz
The photodiode load resistor 1k
The average BER versus link distance for various values of the turbulence strength,
is depicted in Fig. 1. In addition to the turbulence, we consider the signal attenuation due
to fog, and we set the visibility value to 8 km. We use different values of Rytov variance
(0.4, 1, 2), which represent weak, moderate, and strong turbulence, respectively. The
curves in this figure show that the average BER increases with link distance, and the
increase in BER is very important for strong turbulence (σR2 = 2). For weak turbulence
(σR2 = 0.4), it is possible to achieve a longer link distance with a bit error rate lower
than the reference 10−9 .
Fig. 1. Average BER versus link distance for V = 8 km
Next, we assume a visibility of 4 km to investigate the effect of fog on optical
wireless communication. Figure 2 presents the variation in the average BER versus the
link distance for various values of the Raytov variance. This figure shows that the effect
of fog on FSO communication is very significant, and the BER increases significantly
compared to its increase in Fig. 1.
Performance of BPSK-FSO Communication Over Turbulence 7
Author Proof
Fig. 2. Average BER versus link distance for V = 4 km
Figure 3 presents the average BER versus transmitted power for different link dis-
tances. The Rytov variance is assumed to be constant and equal to σR2 = 0.6, which repre-
sents moderate turbulence. It is clear that by increasing the transmitted power, the average
BER decreases. The curves in this figure show that as the link distance increases, more
power is needed to achieve a reference bit error rate of 10–9 . The use of a laser produc-
ing pulses with a power greater than 50.5 mW is required for transmitting data over an
optical wireless link distance of 9 km. However, it is important to consider the effects of
high laser power on human eyes and to design short-link wireless optical networks when
transceivers are close to homes and public places. The increase in optical power can be
Fig. 3. Average BER versus transmitted power
8 A. Fakchich et al.
achieved using a laser with an optical wavelength of 1550 nm because the absorption for
Author Proof
this wavelength by the eye is made by the cornea and not by the retina [18].
6 Conclusion
We investigated the BER performance of an optical wireless communication system with
BPSK modulation and heterodyne detection. We derived an expression of the bit error rate
of an optical link operating over atmospheric turbulence in the presence of the fog effect.
A fading distribution including the combined effects of fog and atmospheric turbulence
is analytically derived by exploiting Meijer’s G-function. The simulation results show
that the combined effects of fog and turbulence limit the link distance, increase the BER
and degrade the system performance. It is possible to decrease the BER and achieve a
longer link by increasing the transmitted power. The 1550 nm wavelength laser pulses
are used to increase power while maintaining user safety.
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