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2240 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 71, NO. 3, MARCH 2022
Infrastructure-to-Vehicle Visible Light
Communications: Channel Modelling and
Performance Analysis
Hossien B. Eldeeb , Member, IEEE, Mohammed Elamassie , Senior Member, IEEE,
Sadiq M. Sait , Senior Member, IEEE, and Murat Uysal , Fellow, IEEE
Abstract—Visible light communication (VLC) has emerged as
a potential wireless connectivity solution for infrastructure-to-
vehicle (I2V) communications. In this paper, we investigate the
performance of I2V VLC systems with access points in the form
of streetlights. Particularly, we consider a typical two-lane high-
way road where the light poles are located at both roadsides and
uniformly separated from each other. Based on non-sequential ray
tracing simulations, we first propose a closed-form path loss ex-
pression as a function of transceiver and infrastructure parameters.
Then, we statistically analyze the path loss and derive a closed-form
expression for its probability distribution function (PDF). Utilizing
the derived PDF, we derive an approximate closed-form bit error
rate (BER) expression. Weconfirm the accuracy of derived BER ex-
pression through comparison with Monte Carlo simulation results
and demonstrate the effect of transceiver and infrastructure pa-
rameters such as receiver aperture, pole height, car height, lateral
shift, and spacing between light poles on the BER performance.
Index Terms—Channel modeling, channel statistics, Internet of
Vehicle, ray tracing, street light communication, vehicular visible
light communications.
I. INTRODUCTION
INTELLIGENT transportation systems (ITSs) are a critical
component of future smart cities [1], [2]. ITSs aim to im-
prove road safety, traffic flow, and passenger comfort by en-
abling information sharing between vehicles and infrastructures
[3]. For wireless connectivity to empower vehicle-to-vehicle
(V2V), vehicle-to-infrastructure (V2I), and infrastructure-to-
vehicle (I2V) links, radio frequency (RF) technologies are typ-
ically used [4], [5]. For example, dedicated short-range com-
munication (DSRC) is already commercially available by some
Manuscript received July 28, 2021; revised November 9, 2021 and January 5,
2022; accepted January 6, 2022. Date of publication January 13, 2022; date of
(Corresponding author: Hossien B. Eldeeb.)
Hossien B. Eldeeb, Mohammed Elamassie, and Murat Uysal are with
the Department of Electrical and Electronics Engineering, Özyeˇgin Uni-
versity, 34794 Istanbul, Turkey (e-mail: hossien.eldeeb@ozyegin.edu.tr; mo-
hammed.elamassie@ozyegin.edu.tr; murat.uysal@ozyegin.edu.tr).
Sadiq M. Sait is with the Department of Computer Engineering, Center for
Communications & IT Research, Research Institute, King Fahd University of
Petroleum & Minerals, Dhahran 31261, Saudi Arabia (e-mail: sadiq@kfupm
.edu.sa).
Digital Object Identifier 10.1109/TVT.2022.3142991
auto manufacturers [6], while Cellular vehicle-to-everything
(C-V2X) fifth generation (5G) chipsets are being produced [7].
Another alternative wireless connectivity solution is visible light
communication (VLC) [8]–[10]. VLC is based on the principle
of modulating the intensity of the light-emitting-diode (LED)
and enables the dual use of LEDs for both illumination and
communication purposes. The ubiquitous availability of LED-
based streetlights, traffic lights, and automotive exterior lighting
positions VLC as a potential wireless connectivity solution for
vehicular networks.
As in any other communication system, channel modeling
is critical for the design, analysis, and optimization of VLC
systems. Earlier results in the literature have focused on indoor
channel modeling, see [11] and references therein. Those results
are obviously not applicable to vehicular VLC systems, which
exhibit inherently different characteristics in comparison to in-
door counterparts. In the current literature, there have been some
efforts to model vehicular VLC channels. Most of the existing
works address V2V and V2I channels [12]–[15] where the
vehicle headlights and taillights are used as wireless transmitters.
It can be noted that each outdoor light source has a different
illumination purpose. Consequently, they are designed with
different intensity distributions [16]. For example, the vehicle
headlights are designed to provide adequate road illumination
on the movement direction minimizing glare of oncoming traffic,
and backward reflections to the driver [16], [17]. On the other
side, the streetlights are designed to focus the light into the road
surfaces and increase the illuminated area in the two directions
of the road (i.e., around the light pole), which results in a sub-
stantially different distribution pattern [18], [19]. Considering
that in a vehicular VLC system, the outdoor lighting module is
the transmit antenna, any modification of the antenna pattern
naturally affects the communication performance [15], [16],
[20]. Therefore, the channel models derived based on a headlight
module (i.e., V2V and V2I links) cannot be generalized for I2V
links which deploy streetlight modules with different radiation
patterns.
A. Literature Review
The topic of I2V VLC communications was widely adopted in
the open literature where traffic lights [21]–[31] or streetlights
[32]–[40] are used as VLC transmitters. Considering the I2V
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The work of Hossien B. Eldeeb was supported by the Horizon 2020 MSC ITN
VISION under Grant 764461. The work of Murat Uysal was supported by the
the Turkish Scientific and Research Council (TUBITAK) under Grant 121N004
(sub-grant of 120N573). The work of Sadiq M. Sait was supported by KFUPM
Deanship of Scientific Research under Grant SB191038.
ELDEEB et al.: INFRASTRUCTURE-TO-VEHICLE VISIBLE LIGHT COMMUNICATIONS: CHANNEL MODELLING AND PERFORMANCE ANALYSIS 2241
systems with access points in the form of streetlights, which
is the focus of this paper, the contributions of the existing
works can be summarized as follows. In [32]–[34], the authors
assumed line-of-sight (LoS) reception from streetlights located
only at one side of the road to calculate the signal-to-noise-ratio
(SNR) [32], [33] or to develop a handover technique [34]. The
reception from the streetlights, located on both roadsides, was
then considered in [35] again under the LoS assumption. The
focus of [35] is introducing a channel estimation method based
on a decision feedback. In addition to LoS reception, the impact
of road reflections was considered in [36], [37], but a fixed
reflectance value was assumed for road surfaces which is not
realistic for visible wavelengths [13], [41]. The focus of [36] is
implementing a light fidelity (LiFi) system prototype, while the
focus of [37] is introducing an architecture of a hybrid VLC and
RF system.
It should be further emphasized that the aforementioned
works in [32]–[37] build upon the assumption that the streetlight
LED source follows a Lambertian model. While this model can
be well suited for many indoor LED luminaries, it fails to match
with the illumination characteristics of streetlights with their
asymmetrical intensity distributions [18], [19]. In particular, the
streetlights have narrow beam angles in the vertical plane to
focus the light into the road surfaces and have wide beam angles
in the horizontal plane to increase the illuminated distances
along the road. In an attempt to consider such an asymmetrical
pattern, the authors in [38], [39] used ray tracing to obtain the
channel impulse response (CIR) for an I2V VLC system where
the radiation pattern of the LED street lamp was imported from
the Dialux library. This work considered only a single streetlight
located at a specific distance from the car in static conditions and
again assumed a fixed reflectance value for the road surface. The
focus of [38] is calculating the SNR at different optical bands
(i.e., UV, IR, VL), while the focus of [39] is comparing the
delay time for V2I and V2V cases. The wavelength-dependent
reflectance of the road surface together with the asymmetrical
pattern of a commercial streetlight was more recently considered
in [40] where a specific I2V scenario with a fixed pole height, a
fixed spacing between poles, and a fixed aperture photodetector
(PD) was considered.
B. Contributions
In this paper, we present a comprehensive study on channel
modeling and performance analysis of I2V VLC systems. As
discussed in the previous section, most of the works [32]–[37]
assumed the ideal Lambertian model for streetlight LEDs. While
the Lambertian model is a good model for indoor luminaries,
such a model fails to match with the illumination characteristics
of streetlights with their asymmetrical intensity distribution
[18], [19]. The works in [38]–[40] considered the effect of the
asymmetrical pattern of the streetlights in channel modeling.
However, they present only numerical results and do not pro-
vide any I2V channel path loss models. A closed-form path
loss expression provides critical insight into system design and
performance analysis. In an effort to fill this research gap, we
introduce a channel model for the I2V VLC system with access
points in the form of streetlights. Specifically, we consider a
typical two-lane highway road where the light poles are located
at both roadsides and uniformly separated from each other (see
Fig. 1). In our study, we first obtain the CIRs for the I2V link
between the streetlight and the vehicle using non-sequential ray
tracing. In our simulations, we take into account the asym-
metrical intensity pattern of commercial streetlights and the
wavelength-dependent reflectance of surface materials for accu-
rate modeling. Based on data fitting to CIRs obtained during the
travel distance, we propose a closed-form path loss expression
as a function of transceiver and infrastructure parameters. These
include the following:
rThe spacing distance between the streetlight poles.
rThe height of the streetlight poles.
rThe height of the vehicle.
rThe longitudinal distance between the vehicle and the
streetlight pole.
rThe lateral shift between the vehicle and streetlight pole.
rThe aperture size of the PD.
In addition to channel modeling, we investigate the perfor-
mance of I2V VLC systems through the derivation of bit error
rate (BER). Due to the mobility of the vehicular communication
system, the path loss is no longer deterministic. Considering
the variation of the channel coefficient, we derive statistical
distributions to model the channel coefficient as well as the re-
sulting SNR. Utilizing the derived probability density functions
(PDFs), we derive an approximate closed-form BER expression.
We confirm the accuracy of derived BER expression through
comparison with Monte Carlo simulation results. Finally, we
demonstrate the effect of transceiver and infrastructure param-
eters on the BER performance of the I2V system.
The rest of the paper is organized as follows: In Section II,
we first explain the I2V system and channel modeling approach,
then present the proposed channel path loss model. In Section III,
we derive a closed-form expression for the average BER. In
Section IV, we present numerical results and discussion. Finally,
we conclude in Section V.
II. SYSTEM AND CHANNEL MODEL
A. System Model
As illustrated in Fig. 1, we consider an I2V VLC system with
access points in the form of street lights. We assume a two-lane
highway road with a total width of WTand a lane width of WL.
The light poles have a height of HPand are located at both sides
of the road. On each side, they are uniformly separated from each
other with a spacing of dT. Each street light LED has an optical
power of PTand an electrical-to-optical conversion of η.The
vehicle has a height of HVand travels at a longitudinal distance
of dwith respect to the street light pole and has a possible lateral
shift of dhwith respect to the road center. The vehicle is equipped
with a PD located at its top. The PD has an aperture size of Dr,
a responsivity of R, and a half field-of-view angle of FoV.
B. Methodology for Channel Modelling
For channel modeling, we use ray tracing approach[42],
which was first proposed for indoor VLC channels [11] and
later applied for vehicular VLC channels [13], [14], [40]. This
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2242 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 71, NO. 3, MARCH 2022
Fig. 1. I2V VLC system under consideration.
approach builds upon advanced non-sequential ray tracing fea-
tures of OpticStudio software and allows the integration of any
realistic light source radiation pattern. It can handle a large num-
ber of reflections for better accuracy. Wavelength-dependent re-
flectance of surface coating for each material in the environment,
which is particularly important at visible light wavelengths,
as well as different types of reflections (specular, diffuse, or
mixed), can be considered for a precise characterization. VLC
channel models developed through this ray tracing approach
were adopted as reference channel models in IEEE 802.15.13
and IEEE 802.11bb [43]. Experimental validations of the data
generated by this channel modeling approach were demonstrated
for different VLC scenarios. For example, the broadband chan-
nel measurements with a frequency sweeping technique were
conducted in [44] considering different indoor VLC scenarios,
including both the LoS and non-LoS cases. Then, the typical
scenarios were modeled in the 3D ray tracing platform. The
obtained CIRs and the channel frequency responses (CFRs) of
the two methods indicated a very good agreement validating
the ray tracing approach. In [13], the path loss for a V2V VLC
system was obtained using the ray tracing approach and then
compared with the experimental measurements in [15]. It was
demonstrated that the ray tracing results provide a very good
match with the measurement ones.
In this work, we adopt this well-established realistic channel
modeling approach. First, we construct the 3D propagation envi-
ronment (including vehicles, streetlights, roads, etc.) in the Op-
ticStudio 18.9 software. To precisely capture the interaction of
the rays with the environment, we specify the optical character-
istics of the road surface, streetlight poles, and vehicle coating by
defining their wavelength-dependent reflectance values utilizing
the built-in function “Table Coating” provided by OpticStudio
tools. For transmitter modeling in the simulation platform, we
create the photometric data (i.e., IES file) of the streetlight
under consideration which contains the luminous intensity in all
different planes. The photometric file is imported to the software
along with the spectral power distribution of the LED (see
Fig. 2). For receiver modeling, we specify the PD properties, i.e.,
FoV, aperture size. To model the atmospheric weather condition
in the visible light band where the size of water droplets in the
atmosphere is comparable to the wavelength of the incident light,
Mie scattering model is utilized [46]. In OpticStudio simulator,
the built-in function “Volume Physics” allows providing the
required input parameters of Mie model such as “particle index”,
“particle radius”, and “density of particles”. The values of these
parameters for clear weather under consideration are given in
[13], [46].
After the simulation platform is constructed, we run non-
sequential ray tracing. The output includes the received power
and the path length information for each ray which is emitted
from the light source and reaches the detector. Let Pij and τij
respectively denote the power and the propagation delay of the
ith ray, i=1,2,...,N
rj, which is emitted from the jth street
light, j=1,2,...,N
p, and reached to the detector. The CIR at
the PD is therefore expressed as [46]
h(t)=
Np
j=1
Nrj
i=1
Pij δ(t−τij ),(1)
where δ(t)is the Dirac delta function. We consider only the
received signals from the four closest poles, therefore set NP=
4, because the contribution from the other poles is too small and
negligible. Based on (1), the path loss in dB is written as
hdB =10 log10 ∞
0
h(t)dt.(2)
C. Channel Model
Based on the channel modeling approach described in the
previous section, we obtain CIRs between the streetlights and the
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ELDEEB et al.: INFRASTRUCTURE-TO-VEHICLE VISIBLE LIGHT COMMUNICATIONS: CHANNEL MODELLING AND PERFORMANCE ANALYSIS 2243
Fig. 2. Optical characteristic of street light under consideration [45] (a) Rela-
tive intensity distributions at both vertical and horizontal planes (the quantities
on the circular axis represent the emission angle and the quantities on the vertical
axis denote the normalized magnitude of the intensity) and (b) Relative spectral
power distribution.
moving vehicle at every 1 m over the traveling distance between
two poles. The intensity pattern and relative spectral power
distribution of streetlights used in simulations (Vestel Ephesus
M4S [45]) are illustrated in Fig. 2. All simulation parameters
are provided in Table I. In our simulations, we assume that the
optical power of each street light is unity. We can then scale
the CIR for any given value of transmit power PTto calculate
the received power (Pr)asPr=PT(∞
0h(t)dt)[47]. The
corresponding path loss is obtained based on (2) and presented
in Fig. 3 for different combinations of HP,Dr,HV,dT, and dh
values (See Table II). It can be noted that the considered channel
modeling approach has been recently validated via broadband
measurements [48] and is considered as a primary modeling
step used to obtain the CIRs for any VLC system, i.e., indoor,
underwater, and vehicular channels. Therefore, further analysis
for deriving path loss models for any specific VLC system is
required, which is performed out of this software and yields
to different models according to the transceiver and system
parameters. Since the streetlights are uniformly distributed along
the road and with specific spacing distances, the vehicle on its
way approaches a lighting pole and moves away from it. As
a result, the received power exhibits a periodic pattern. In the
following, we propose a closed-form expression for the I2V
channel model to describe this sinusoidal behavior.
Let 2CPand CSA respectively denote the peak-to-peak
change of received power and the sinusoidal axis. The path loss
is written as
hdB =CPz+CSA,(3)
where z=cos((2π/dT)d)with ddenotes the moving distance
of the vehicle from one streetlight pole to the next one. CP
and CSA in (3) are constants that can be calculated for a given
scenario. Their values are influenced by the height of the lighting
pole (HP), the height of the vehicle (HV), the distance between
two lighting poles (dT), lateral shift (dh), and the diameter of
the PD (Dr) in cm. Based on non-linear curve fitting [49], we
obtain CPand CSA as (4) and (5), respectively.
CP=0.5f(Dr,H
P,H
V,d
T,d
h,b1)
−0.5f(Dr,H
P,H
V,d
T,d
h,b2),(4)
CSA =0.5f(Dr,H
P,H
V,d
T,d
h,b1)
+0.5f(Dr,H
P,H
V,d
T,d
h,b2),(5)
Here, f(Dr,H
P,H
V,d
T,d
h,bi),i=1,2 are defined as
(6) where HD=HP−HV+1.371 and bi,j denotes the jth
element of bi. It can be readily checked from (6) that each of
transceiver and infrastructure parameters has a different impact
on the CPand CSA values. The values of CP,CSA, and biare
determined through data fitting and provided, respectively, in
Table II and Table III. It can be noted that the coefficients of bi
vector given in Table III are fixed for all system configurations.
f(Dr,H
P,H
V,d
T,d
h,bi)=Dr(bi,1+bi,2dh
+bi,3HD+bi,4dT+bi,5Dr)
+dT(bi,6+bi,7dh+bi,8HD+bi,9dT)
+HD(bi,10 +bi,11dh+bi,12 HD)
+dh(bi,13 +bi,14 dh)+bi,15,(6)
To validate the proposed model in (3), we consider the pole
height range as 6 m ≤HP≤10 m which is the typical pole
height for streets in residential, commercial, and historical con-
texts [50]. Based on the pole height, the spacing range between
the poles (dT) is calculated which should be between 2.5-3 times
the height [50]. Therefore, the spacing range of 15 m ≤dT≤
30 m is considered. Also, different receiver apertures, i.e., Dr
=1cm,Dr=2.5 cm, and Dr=4 cm are considered which
are commercially available [51]. For the vehicle height (HV),
without loss of generality, we choose three values representing
the lowest, average, and tallest height of current production
cars which are given respectively as HV=0.8 m, HV=1.37
m, and HV=1.9 m. For the lateral shift (dh), we consider
four possible values within the minimum and maximum limits
according to the width of the car and the road-lane which are
given as dh=1m,dh=1.5 m, dh=2 m, and dh=2.5 m. In our
simulation, we consider the received signals from the four closest
poles (i.e., NP=4), because the contribution from the other
poles is too small and negligible. Also, the coating materials
for roads, vehicles, and poles are considered as asphalt, black
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2244 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 71, NO. 3, MARCH 2022
TAB L E I
SIMULATION PARAMETERS
gloss paint, and galvanized steel metal, respectively, which have
reflectance values given in [52], [53]. We consider PDs with
various values for FoV angles from 65◦up to 90◦. Relatively
large FoV values are selected since a narrow FoV angle might
be a significant impediment in vehicular VLC systems as it limits
the mobility [18], [26]. In contrast, a large FoV angle results in
a higher tolerance to horizontal and vertical movements in real
driving scenarios [16] and allows the reception from different
directions1.
In Fig. 3, along with the simulation results, we present the
proposed path loss expression in (3). It is observed that the pro-
posed model is in a good agreement with the simulation results
for all HP,HV,dT,Dr, and dhvalues under consideration with
a maximum difference of 0.45 dB. In Fig. 3(a), we assume fixed
values of HP=7m,HV=1.37 m, dT=20 m, dh=2 m, and Dr
=1 cm and present the channel path loss results for different
large FoV angles (i.e., 65◦,75
◦,85
◦, and 90◦). A negligible
change (i.e., less than 0.2 dB) in the path loss is observed when
the FoV angle changes from 90◦to 65◦.
In Fig. 3(b), we assume fixed values of HP=7m,HV=
1.37 m, dT=20 m, and dh=2 m and investigate the effect
1Commercial PDs with wide FoV angles are already available from different
suppliers [54]–[57].
of different receiver apertures, i.e., Dr=1cm,Dr=2.5 cm,
and Dr=4 cm. It is observed that the path loss is significantly
affected by the receiver aperture with a nonlinear relationship,
which indicates that even a small decrease in the diameter can
significantly increase the path loss. For example, consider the
car moves at the middle between two lighting poles (i.e., d=10
m). The path loss for Dr=4cmis−59.3 dB. This increases
to −63 dB and −71.7 dB for Dr=2.5 cm and Dr=1cm,
respectively.
In Fig. 3(c), we assume fixed values of HP=7, HV=1.37 m,
dT=20 m, and Dr=1 cm and investigate the effect of lateral
shift, i.e., dh=1m,dh=1.5 m, dh=2 m, and dh=2.5 m. It
is observed that the impact of the lateral shift ( dh)isverysmall
which is only visible when the vehicle is very close to either
the light pole or to the middle between two poles. It is also seen
that when dhincreases, the path loss reduces at shorter distances
(i.e., smaller d) and increases at larger distances (i.e., larger d).
This is because at shorter distances, increasing dhmeans that
the vehicle becomes closer to the light pole where the maximum
power can be received and hence a lower path loss occurs. At
a larger distance and with a larger dh, the car becomes in the
middle between two light poles located on one roadside (where
minimum power is received) and far away from the light poles
located on the other roadside.
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ELDEEB et al.: INFRASTRUCTURE-TO-VEHICLE VISIBLE LIGHT COMMUNICATIONS: CHANNEL MODELLING AND PERFORMANCE ANALYSIS 2245
Fig. 3. Path loss results for (a) Different FoV angles assuming Dr=1cm,HP=7m,dh=2m,HV=1.37 m, and dT=20 m, (b) Different sizes of receiver
apertures (Dr) assuming HP=7m,dh=2m,HV=1.37 m, and dT=20 m, (c) Different lateral shifts (dh) assuming HP=7m,Dr=1cm,HV=1.37
m, and dT=20 m, and (d) Different vehicle heights (HV) assuming HP=7m,dh=2m,Dr=1cm,anddT=20 m, (e) Different pole heights (HP)and
spacing distances (dT) assuming Dr=1cm,dh=2m,andHV=1.37 m.
In Fig. 3(d), we assume fixed values of HP=7m,dh=2
m, dT=20 m, and Dr=1 cm and investigate the effect of car
height, i.e., HV=0.8 m, HV=1.37, and HV=1.9 m. It is
observed that the taller height of the car the lower the path loss
at shorter distances (i.e., ≤3 m) and higher path loss at larger
distances. Closer to the lighting pole, the higher the car the more
the collected power. This is due to the relatively small height
difference between the PD and the streetlight pole and hence less
propagation distance. At a larger distance, however, a taller car
reduces the amount of collected power from the streetlight poles
around the car. For example, consider the car is located under
the light pole. The path loss is given for the lowest car height of
HV=0.8 m as −61.6 dB. This reduces to −61.15 dB and −60.8
dB for HV=1.37 m and HV=1.9 m, respectively. When the
car reaches the middle distance between two neighboring poles
(i.e., d=10 m), the path loss is given for HV=0.8 m, HV=
1.37 m, and HV=1.9 m as −71 dB, −71.6 dB, and −72.1 dB,
respectively.
In Fig. 3(e), we assume fixed values of Dr=1cm,HV=
1.37 m, and dh=2 m and investigate the effect of pole heights,
i.e., HP=6m,HP=7m,HP=8m,HP=9 m, and HP=10
m with their corresponding spacing distance of dT=15 m, dT
=20 m, dT=22 m, dT=24 m, and dT=30 m, respectively.
It is observed the reverse effect comparing with the effect of
the car height (HV) where the smaller height of streetlights the
lower path loss, particularly when the car moves closer to the
lighting pole. This is due to the relatively shorter propagation
distance and hence less attenuation. For example, consider the
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2246 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 71, NO. 3, MARCH 2022
TAB L E II
SYSTEM PARAMETERS UNDER CONSIDERATION
TABLE III
VALUES OF biCOEFFICIENTS IN (6)
car location is under the lighting pole. The path loss for HP=
10 m is −63.6 dB. This reduces for HP=9m,HP=8m,HP
=7 m, and HP=6mto−62.6 dB, −62 dB, −61.15 dB, and
−60.2 dB, respectively.
III. BER ANALYSIS
We assume that unipolar M-ary pulse amplitude modulation
(M-PAM) is employed. Furthermore, let h=10 hdB/10 denotes
the channel coefficient in normal scale. The conditional BER
(conditioned on h), Pe,c takes the form of [58, Ch 3]
Pe,c =(M−1)
Mlog2(M)erfc 3
2(M−1)(2M−1)γ,(7)
where Mdenotes the modulation order and erfc(·)is the
complementary error function. In (7), γdenotes for the in-
stantaneous received SNR. It is given by γ=γ0h2where
γ0=R2η2PE/N0BWis the transmit SNR (i.e., SNR without
including the effect of channel propagation) with N0denotes the
noise power spectral density, Bwis bandwidth, and PEis the
average electrical AC power of the LED.
The path loss exhibits a sinusoidal pattern which can be con-
sidered as large-scale fading [59]. Specifically, zin (3) produces
a distribution given by [60, Eq. (73)]
fz(z)= 1
π√1−z2,−1≤z≤1·(8)
Utilizing (3) and (8) within density transforma-
tion in [61, Eq. (3.11)], we obtain the PDF of hdB,
CSA −CP≤hdB ≤CSA +CPas
fhdB (hdB)= 1
πC2
P−(hdB −CSA)2(9)
Noting the relationship between hand hdB, we obtain the
PDF of h,10
(CSA−CP)/10 ≤h≤10(CSA +CP)/10,as
fh(h)= 10
ln(10)hπC2
P−(10log10(h)−CSA)2,(10)
Let λmin =γ0102(CSA−CP)/10 and λmax =γ0102(CSA +CP)/10,
the PDF of the instantaneous SNR (i.e., γ=γ0h2),
λmin ≤γ≤λmax, is then obtained as
fγI2V (γ)= 10
ln(10)2γπC2
P−10 log10γ
γ0−CSA
2·(11)
Taking an expectation of (11) with respect to γ, we write the
average BER as
Pe=5F
πln(10)
×
γmax
γmin
erfc √Cγ
γC2
P−10log10 γ
γ0−CSA2dγ. (12)
where F=(M−1)/(Mlog2(M)) and C=
3/(2(M−1)(2M−1)). By applying a variable change
as ξ=[(10/CP)log10(γ/γ0)−(CSA/CP)], we rewrite (12)
as
Pe=F
π
1
−1
1
1−ξ2erfcCγ0100.2(ξCP+CSA)dξ. (13)
By using Gauss-Chebyshev quadrature method of integration in
[62, Eq. (25.4.38)], we approximate (13) as
Pe≈F
k
k
j=1
erfc Cγ010(0.1CPcos((2j−1)π
2k)+0.1CSA),
(14)
where kis the order of approximation.
IV. PERFORMANCE RESULTS AND DISCUSSIONS
In this section, we present numerical results for the average
BER performance of I2V VLC system under consideration.
Unless otherwise stated, we assume pole height of HP=7m,
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ELDEEB et al.: INFRASTRUCTURE-TO-VEHICLE VISIBLE LIGHT COMMUNICATIONS: CHANNEL MODELLING AND PERFORMANCE ANALYSIS 2247
Fig. 4. Proposed average BER expression and comparison with simulation
results (Dr=2.5 cm, HP=7m,dh=2m,HV=1.37 m, and dT=20 m
are assumed).
pole spacing of dT=20 m, car height of HV=1.37 m, and
lateral shift of dh=2 m. We consider a receiver with aperture
of Dr=2.5 cm and a FoV of 90◦. We also consider PAM with
M=4, N0=1×10−21 A2/Hz [63, Chapter 19], and Bw=5
MHz [64]. The values of ηand Rare considered respectively
as 0.8 W/A and 0.4 A/W [65]. In our simulation, we consider
the received signals from the four closest poles (i.e., NP=4),
because the contribution from the other poles is too small and
negligible. Also, the coating materials for road, vehicles, and
poles are considered as asphalt, black gloss paint, and galvanized
steel metal which have reflectance values given in [52], [53].
In Fig. 4, we present the closed-form BER expression derived
in (14) and confirm its accuracy with comparison to simulation
results. The accuracy of the approximation in (14) depends on
the value of k. It can be observed that the derived expression
provides an excellent match to the simulation results for k≥5.
In the following, we present the effect of receiver aperture,
pole height, car height, lateral shift, and spacing between poles
on the average BER performance considering k=5.
Fig. 5 illustrates the average BER for different values of
receiver apertures (Dr) considering HP=7m,HV=1.37 m,
dT=20 m, and dh=2 m. It is observed that increasing the value
of Drhas a significant improvement on the BER performance.
This is due to the fact that the larger receiving area the larger
number of photons that can be captured by the PD. For example,
assume that an average BER of 10−3is targeted. The required
SNR value assuming Dr=1 cm is 159 dB. This decreases
to 141.9 dB and 135 dB for Dr=2.5 cm, and Dr=4cm,
respectively. One can notice that a PD with Dr≤1 cm might
not be practical for I2V VLC with the system parameters under
consideration. This is due to that I2V systems suffer a large SNR
reduction when the vehicle becomes near the center between two
streetlight poles, with a significant impact on the average BER
performance.
Fig. 5. Effect of receiver aperture (Dr) on the average BER assuming HP=
7m,dh=2m,HV=1.37 m, and dT=20 m.
Fig. 6. Effect of pole height (HP) with corresponding spacing distance (dT)
on the average BER assuming Dr=2.5 cm, HV=1.37 m, and dh=2m.
Fig. 6 illustrates the effect of pole height (HP) with the
corresponding spacing distance (dT) on the average BER for
fixed values of Dr=2.5 cm, HV=1.37 m, and dh=2m.
It is observed that decrease in HPimproves the average BER
performance since the corresponding spacing distance reduces
with decreasing HP. For example, the required SNR value to
achieve targeted BER of 10−3for HP=10 m with dT=30 m
is 147 dB. This decreases to 143.9 dB, 142.5 dB, 141.9 dB, and
137 dB for HP=9 m with dT=24 m, HP=8 m with dT=
22 m, HP=7 m with dT=20 m, and HP=6mwithdT=
15 m, respectively. A small change in the BER performance is
observed between HP=7m,HP=8 m, and HP=9 m while
a large change is observed between either HP=7 m and HP=
6morHP=9 m and HP=10 m. This is due to the relatively
larger difference between the spacing distances in these cases
where the path loss further increases, particularly at the middle
area between the poles (see Fig. 3(e)). Note, the lowest value of
the spacing distance is considered for HP=6 m (i.e., dT=15
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2248 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 71, NO. 3, MARCH 2022
Fig. 7. Effect of lateral shift (dh) on the average BER assuming HP=7m,
Dr=2.5 cm, HV=1.37 m, and dT=20 m.
Fig. 8. Effect of spacing distance between poles (dT) on the average BER
assuming HP=7m,Dr=2.5 cm, HV=1.37 m, and dh=2m.
m) while the highest one is considered for HP=10 m (i.e., dT
=30 m) to illustrate the best and the worst cases, respectively.
Fig. 7 illustrates the effect of lateral shift (dh) on the average
BER performance for fixed values of HP=7m,HV=1.37 m,
Dr=2.5 cm, and dT=20 m. It is observed that the effect
of dhis almost negligible, where smaller dhvalues lead to
only slightly lower average BER. This is due to that when the
vehicle becomes between two streetlight poles at one roadside,
the smaller value allows the vehicle to collect slightly more
power from the streetlights located at the other roadside.
Fig. 8 illustrates the effect of the spacing distance between
the poles (dT) on the average BER for fixed values of Dr=
2.5, HP=7m,HV=1.37 m, and dh=2 m. It is observed
that the longer spacing for the same pole height worsens the
average BER performance. This is due to that the attenuation
of the light signal as it travels through the air increases as long
as the propagation distance increases. For example, the required
SNR value to achieve a targeted BER of 10−3for dT=21 m is
Fig. 9. Effect of car height (HV) on the average BER assuming HP=7m,
Dr=2.5 cm, dT=20 m, and dh=2m.
143 dB. This decreases to 141.9 dB, 140.5 dB, and 139.1 dB for
dT=20 m, dT=19 m, and dT=18 m, respectively.
Finally, Fig. 9 illustrates the effect of car height (HV)onthe
average BER performance for fixed values of HP=7m,Dr=
2.5 cm, dh=2 m, and dT=20 m. It is observed that the increase
in HVworsens the average BER performance. This is due to that
when the taller car moves close to the middle distance between
two light poles, the collected power from the streetlight poles
around the car is less. For example, the required SNR value to
achieve targeted BER of 10−3for HV=0.8 m is 140.8 dB. This
increases to 141.9 dB and 143.2 dB for HV=1.37 m and HV
=1.9 m, respectively.
V. CONCLUSION
In this paper, we have investigated the performance of I2V
VLC links with access points in the form of street lights.
Based on the non-sequential ray tracing simulations, we have
introduced for the first time a path loss channel model of the
I2V link taking into account the intensity pattern of commercial
street lights and the wavelength-dependent reflectance of the
surface materials. Our results demonstrate that the received
power exhibits a sinusoidal pattern. We have derived the PDF
for this large-scale fading coefficient and obtained a closed-form
average BER expression under the assumption of PAM. We have
investigated the effect of several transceiver and infrastructure
parameters on the BER. Our results have demonstrated that the
receiver aperture and the spacing between the street light poles
have a significant impact on the system performance while the
effect of the lateral shift is negligible.
The availability of such a realistic and comprehensive I2V
channel model has the perspective to open unexploited research
paths in the field of vehicular communication systems. In the
physical layer counterpart, this model can help in estimating
the overall system performance prior to optimizing the system
design. Also, it can be utilized in vehicular network develop-
ment (handover, resource allocation, etc.). Furthermore, a well
understanding of vehicular VLC channel behavior gives insights
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ELDEEB et al.: INFRASTRUCTURE-TO-VEHICLE VISIBLE LIGHT COMMUNICATIONS: CHANNEL MODELLING AND PERFORMANCE ANALYSIS 2249
on how vehicular VLC systems can be combined with the
other vehicular communication disciplines such as DSRC and/or
C-V2X in a way to maximize the overall system performance.
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Hossien Eldeeb (Member, IEEE) received the B.Sc.
and M.Sc. degrees in electronics and electrical com-
munication engineering from Menoufia University
and Cairo University, Al Minufiyah, Egypt, in 2008
and 2018, respectively, and the Ph.D. degree in elec-
trical and electronics engineering from Özye˘gin Uni-
versity,Istanbul, Turkey,in 2021. His current research
interests include optical and wireless communica-
tions, 6G/mmwave communications, and vehicular
communications. He has authored some 27 publica-
tions and received more than 200 citations with an
h-index of eight. He was the recipient of Best Student Paper Award in IEEE/IET
CSNDSP, in 2020.
Mohammed Elamassie (Senior Member, IEEE) re-
ceived the B.Sc. and M.Sc. degrees in electrical en-
gineering from the Islamic University of Gaza, Gaza,
Palestine, in 2006 and 2011, respectively, and the
Ph.D. degree in electrical and electronics engineering
from Özye˘gin University, Istanbul, Turkey, in June
2020. His current research interests include optical
communications, performance analysis, and experi-
mental verifications. He has authored more than 30
publications and received more than 400 citations,
with an h-index of eleven. Dr. Elamassie’s major
achievements include Best Paper Award in IEEE International Black Sea Con-
ference on Communications and Networking, Sochi, Russia, in 2019. He also
was the recipient of the 2020 IEEE Turkey Ph.D. Thesis Award.
Sadiq M. Sait (Senior Member, IEEE) was born
in Bengaluru. He received the bachelor’s degree in
electronics engineering from Bangalore University,
Bengaluru, India, in 1981, and the master’s and
Ph.D. degrees in electrical engineering from the King
Fahd University of Petroleum & Minerals (KFUPM),
Dhahran, Saudi Arabia, in 1983 and 1987, respec-
tively. He is currently a Professor of computer engi-
neering, and the Director of the Center for Communi-
cations and IT Research, Research Institute, KFUPM.
He has authored more than 200 research articles,
contributed chapters to technical books, granted several U.S. patents. He has
lectured more than 30 countries. He is also the Principle Author of two books
published by the McGraw Hill Book Co., IEEE, IEEE Computer Society Press,
and World Scientific. He was the recipient of Best Electronic Engineer Award
from the Indian Institute of Electrical Engineers, Bengaluru, in 1981, and several
other awards during the course of his career.
Murat Uysal (Fellow, IEEE) received the B.Sc. and
M.Sc. degrees in electronics and communication en-
gineering from Istanbul Technical University, Istan-
bul, Turkey, in 1995 and 1998, respectively, and the
Ph.D. degree in electrical engineering from Texas
A&M University, College Station, TX, USA, in 2001.
He is currently a Full Professor and the Chair of
the Department of Electrical and Electronics Engi-
neering, Özye˘gin University, Istanbul, Turkey. He is
also the Founding Director of Center of Excellence
in Optical Wireless Communication Technologies
(OKATEM). Prior to joining Özye˘gin University, he was a tenured Associate
Professor with the University of Waterloo, Waterloo, ON, Canada. His research
interests include communication theory with a particular emphasis on the
physical layer aspects of wireless communication systems in radio and optical
frequency bands. On these topics, he has authored some 400 journal and confer-
ence papers and received more than 16000 citations with an h-index of 59. He
is the former Chair of IEEE Turkey Section. He currently serves on the Editorial
Board of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS.In the past,
he was the Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS, IEEE
TRANSACTIONS ON VEHICULAR TECHNOLOGY, and IEEE COMMUNICATIONS
LETTERS. He was involved in the organization of several IEEE conferences
at various levels. In particular, he was the Technical Program Committee Chair
of major IEEE conferences including WCNC 2014, PIMRC 2019 and VTC-Fall
2019.
Prof. Uysal’s major distinctions include NSERC Discovery Accelerator
Award in 2008, University of Waterloo Engineering Research Excellence Award
in 2010, Turkish Academy of Sciences Distinguished Young Scientist Award in
2011, Özye˘gin University Best Researcher Award in 2014, National Instruments
Engineering Impact Award in 2017, Elginkan Foundation Technology Award in
2018 and IEEE Communications Society Best Survey Paper Award in 2019
among others.
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