1 Introduction

Vehicular communication is one of the main techniques of ITSs (Pribyl et al. 2019; Eldeeb et al. 2021). It offers exchanging data between the infrastructure and the vehicle. Additionally, the information is sent between the vehicles themselves. Infrastructure-to-Vehicle (I2V) communication provides the linked vehicles with a different data (e.g., traffic congestion, changing routes, road services, etc.), while a Vehicle-to-Vehicle (V2V) communication is essential for safety likewise sensing before crashing and collision warning (Chen et al. 2017; Mishra et al. 2023). RF became one of the significant technologies for establishing vehicle communication (MacHardy et al. 2018; Cai et al. 2017; Ghafoor et al. 2019). Due to the drawbacks of the RF technologies such as bandwidth restriction and licenses charge, an Optical Wireless Communication (OWC) technology called VLC became an excellent alternative solution (Chamani et al. 2022).

Owing to the extensive utilization of the light-emitting diode (LED) in headlight, taillight of the vehicle, low cost, streetlight, and flexibility, leads to using LED as a transmitter in VLC systems (Shaaban et al. 2021; Fon et al. 2023). A photodiode (PD) is served as a receiver (Rx) of the VLC system. However, a camera is an optimum solution to be used as the receiver in VLC systems as an alternative for PD which would demand a modification of hardware, additional filters and amplification circuitry (El-Garhy et al. 2022). This would provide a flexible, reliable, and low-cost wireless communications.

On the other hand, another OWC technology called FSO uses the Near Infra-Red (NIR) spectrum as the channel medium which has a lower-level attenuation, FSO can be applied using visible light (VL) and ultraviolet (UV) spectrum as illumination is not essential. Narrow beam Laser Diode (LD) light sources are utilized to allow fast communication systems as an alternative to LEDs, with PDs as optical receivers (Mohsan et al. 2023). Due to the coherent nature of laser technology and the high data rate, it offers a larger coverage distance (Rahaim et al.2017; Tonini et al. 2019; Esmail et al. 2019; Yang et al. 2014; Sharma 2014). Video surveillance, campus connectivity, cellular network backhauls, Local Area Network (LAN)-to-LAN connectivity, inter-chip connectivity, underwater communication, space communication, fiber backup, etc. are all applications for FSO systems. Although, the significant benefits of FSO systems have significant benefits across a wide range of applications, one drawback associated with FSO is the vulnerability of the communication link to some factors that limit its reliability, such as external weather conditions (e.g., fog, storms, and rain), air turbulences, and physical infrastructure.

Researchers have recently focused on an optical/optical hybrid wireless technology like FSO/VLC to overcome the limitation of both systems. A hybrid FSO/VLC system connectivity is introduced in (Pesek et al. 2018; Zhitong et al. 2017). It extensively discussed how to develop and deploy an FSO/VLC hybrid network coordination system, as well as how to support user mobility, localization, routing algorithm, intelligent transportation, and handover difficulties.

In this work, a VLC standalone vehicular system structure is presented for outdoor applications. By calculating the SNR, coverage distance needed, and BER, the efficiency of the standalone VLC system is examined. In addition, a hybrid FSO/VLC system is proposed and investigated. This system uses both FSO and VLC communications. The SNR and BER are calculated. This is followed by a comparative study that is applied between standalone VLC system and hybrid FSO/VLC system in term of coverage distance, SNR, and BER. This paper can be considered a review paper including a comparative study between the standalone VLC system and a hybrid FSO/VLC system to provide ITS, without implantation of the RF system due to its limitations. This hybrid system is capable to maintain acceptable coverage distance. Furthermore, the efficiency of both standalone VLC and FSO/VLC system is examined by estimating BER and SNR of both systems.

The reminder of this paper is organized as follows. Section 2 explains the system structure and the mathematical model. The obtained results are presented and discussed in Sec. 3. Section 4 is devoted to the main conclusions.

2 System structures and mathematical models

In this section, a structure and mathematical model for VLC standalone system and FSO/VLC system are explained.

2.1 Standalone VLC system

In this section the VLC structure and system model are explained.

2.1.1 System structure of VLC standalone system

A Line of Sight (LoS) connection is considered between the transmitter and the receiver as in Fig. 1. The transmitter is the LED in traffic light, while the receiver is an image sensor placed above the engine hood of the vehicle at height Hr = 1 m from the ground. The LED traffic light's half-power semi-angle ∅½ = 15\(^\circ\). The angle of vertical inclination is θ and the angle of field of view (FOV) referred as ψc16 (Momen et al. 2019). The location of the vehicle can be determined by \(x\mathrm{^{\prime}}\) which is the distance in the lane direction and the width direction is denoted by the letter y. It is assumed that the width of the lane is 3.5 m and the traffic light’s height is H1 = 6.21 m17 (Zaki et al. 2019).

Fig. 1
figure 1

Multilane traffic link mode (Momen et al. 2019)

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2.1.2 Mathematical model of standalone VLC system

The procedure of conducting and evaluating the standalone VLC system is illustrated in Fig. 2.

Fig. 2
figure 2

Flow chart of VLC standalone system

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The LED transmitted power is (Momen et al. 2019)

$${P}_{tr}\left(\varphi \right)=\frac{m+1}{2\pi }{P}_{t}{cos}^{m+1}\left(\varphi \right) ,$$
(1)

where \({P}_{t}\) is the average power transmitted, \(\varphi\) refers to the irradiance angle while m is the Lambertian emission order given by

$$m = \left[ {\frac{ln\left( 2 \right)}{{ln\left( {\cos \left( {\phi_{1/2} } \right)} \right)}}} \right] ,$$
(2)

where \(\phi_{1/2}\) denotes the half power semi angle.

The channel gain is calculated by (Momen et al. 2019; Akanegawa et al. 2001)

$$h\left( 0 \right) = \left\{ {\begin{array}{*{20}l} {\left[ {\frac{{\left( {m + 1} \right)A^{\prime } }}{{2\pi d^{2} }}} \right]cos^{m} \left( \varphi \right)T_{f} \left( \psi \right)T_{{c,i}} \left( \psi \right)cos\left( \psi \right)0 \le \psi \le \psi _{c} } \hfill \\ {0\psi \ge \psi _{c} } \hfill \\ \end{array} } \right.,$$
(3)

where the detector’s area is \({A}^{\mathrm{^{\prime}}}\), \({T}_{f}\left(\psi \right)\) denotes the constant of filter transmission, and \({T}_{c, i}\left(\psi \right)\) indicates the image size fraction on ith pixel given by (Kahn and Barry 1997)

$${T}_{c, i}\left(\psi \right)=-0.1982{\psi }^{2}+0.0425\psi +0.8778 ,$$
(4)

at which \(\psi\) represents the angle of incident.

The LoS distance between the traffic light and the veichle is given by

$$d = \sqrt {x^{{\prime 2}} + y^{2} + z^{2} } .$$
(5)

The irradiance angle is denoted by

$$\varphi = cos^{{ - 1}} \left( {\frac{{x^{\prime } }}{d}} \right).$$
(6)

While the angle of incidence is expressed by

$$\psi = cos^{{ - 1}} \left( {\frac{{sin\left( \theta \right) + tan^{{ - 1}} \left( {\frac{z}{{x^{\prime } }}} \right)\sqrt {x^{2} + z^{2} } }}{d}} \right),$$
(7)

where \(\theta\) is the vertical inclination angle of the receiver.

The power of the desired pixel obtained at the receiver is (Momen et al. 2019)

$${P}_{rx, i}={P}_{tr}\left(\varphi \right)h\left(0\right) .$$
(8)

Therefore, the total power of received signal is calculated by (Momen et al. 2019)

$${P}_{t}\left(t\right)={P}_{rx, i}+n\left(t\right) ,$$
(9)
$${P}_{t}\left(t\right)={P}_{tr}\left(\varphi \right)h\left(0\right)+n\left(t\right) .$$
(10)

where n(t) is noise.

For the ith pixel, the noise variance is approximately calculated by (Momen et al. 2019)

(11)

where \({{\text{P}}}_{{\text{b}},\mathrm{ i}}\) refers to the power of ambient light find out by the ith pixel, the responsivity detector is indicated by R, the electronic charge is expressed by e, \({I}_{2}\) and \({I}_{3}\) are constants denoting the noise band-width, B representing the bandwidth, Boltzmann constant is \({{\text{k}}}_{{\text{B}}}\), \(\upeta\) denotes the capacitance per unit area, \(T\) represents the absolute temperature, the voltage gain of open-loop is given by \({\text{G}}\), Г is the channel noise factor of the FET, \({{\text{G}}}_{{\text{m}}}\) refers to the FET transconductance and the effective area of the detector is expressed by where

(12)

The ambient light detected by the FOV of the pixel can be formulated as (Momen et al. 2019).

$$P_{b, i} = 4\pi AB_{sky} \Delta \lambda T_{f} T_{c, i} \cos \left( {\psi_{i} } \right)\sin^{2} \left( {\frac{{\psi_{a,i} }}{2}} \right) ,$$
(13)

where the skylight power spectral density is represented by \({B}_{sky}\), \(\Delta \lambda\) denotes the filter’s bandwidth and \({\psi }_{a,i}\) refers to FOV of the detector pixels.

The maximum angle of FOV (\({\psi }_{c, max}\)) is given by (Momen et al. 2019)

$${\psi }_{c, max}={\mathit{tan}}^{-1}\frac{u}{f} ,$$
(14)

where

$$\theta +{\psi }_{c, max}\le {90}^{^\circ } ,$$
(15)

where \(u\) represents the distance that links the center of the image sensor and its edge, while \(f\) is the focal length.

The output signal can be calculated by (Cailean et al. 2014)

$$y\left( t \right) = x\left( t \right) \otimes rh\left( t \right) + N\left( t \right),$$
(16)

where the channel impulse response is denoted by h(t), and \({\text{N}}\left({\text{t}}\right)\) represents additive noise, and ⨂ signifies convolution. Hence, the SNR can be estimated from.16 (Momen et al. 2019)

$$SNR=\frac{{R}^{2}{P}_{rx,i}^{2}(t)}{{\sigma }^{2}} .$$
(17)

2.2 The hybrid FSO/VLC system

In this section the VLC structure and system model are explained.

2.2.1 System structure of FSO/VLC system

A hybrid FSO/VLC system model is shown in Fig. 3. The traffic data is transmitted via an FSO link from traffic light signal [i.e., source (S)] to street light [i.e. relay 1 (R)], where the relay is mounted on it to retransmit data for a distance > 500 m to the vehicle [i.e. destination (D)] through VLC link.

Fig. 3
figure 3

System architecture for FSO/VLC hybrid system

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The procedure of conducting and evaluating a hybrid FSO/VLC system is illustrated in Fig. 4.

Fig. 4
figure 4

Flow chart of hybrid FSO/VLC system

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2.2.2 Mathematical model of FSO system

The FSO system normalized channel coefficient is defined as (Abaza et al. 2016)

$$h={h}_{a}{h}_{\beta }{h}_{p} ,$$
(18)

where the coefficient of channel fading air turbulence is denoted by \({h}_{a}\), \({h}_{p}\) is the misalignment error channel coefficient and, \({h}_{\beta }\) refers to the path loss that can be formulated by (Abaza et al. 2016)

$$h_{\beta } = 10^{{ - \alpha d^{\prime } /10}} \times \frac{{D_{R}^{2} }}{{\left( {D_{T} + \theta_{T} d^{\prime } } \right)^{2} }} ,$$
(19)

where the \(d\mathrm{^{\prime}}\) refers to linked distance between source and relay, \(\alpha\) represents the coefficient of the weather attenuation, \({D}_{T}\) and \({D}_{R}\) are the transmitter and receiver aperture diameters, respectively, and \({\theta }_{T}\) indicates the optical beam angle of divergent.

The coefficient of channel fading as a result of misalignment error is calculated by (Farid and Hranilovic 2007)

$${h}_{p}\approx {A}_{o}{\text{exp}}\left(\frac{-2{r}^{2}}{{w}_{zeq}^{2}}\right) ,$$
(20)

where r represents the radial displacement, that is modeled by Rayleigh distribution and the width of the beam denoted as \({w}_{zeq}^{2}\) calculated by (Farid and Hranilovic 2007)

$${w}_{zeq}^{2}=\frac{{w}_{z}^{2} \sqrt{\pi }{\text{erf}}(\upsilon )}{2\upsilon {\text{exp}}(-{\upsilon }^{2})} ,$$
(21)

where

$$\upsilon =\frac{\sqrt{\pi }{D}_{R}}{2\sqrt{2}{w}_{z}} .$$
(22)

\({w}_{z}\) represents the beam waist, \({A}_{\rm O}\) denotes the fraction of collected power at R = 0 and is calculated in terms of erf (·), the error function, as (Gradshteyn and Ryzhik 2007)

$${A}_{o}={\left[{\text{erf}}(\upsilon )\right]}^{2} .$$
(23)

The radial displacement, \({f}_{r}\left(r\right)\) can formulated as

$$f_{r} \left( r \right) = \frac{r}{{\sigma_{s}^{2} }}\exp \left( { - \frac{r}{{2\sigma_{s}^{2} }}} \right),\quad r > 0,$$
(24)

where \({{\sigma }_{s}}^{2}\) refers to the receiver jitter variance.

The probability density function (PDF) of Log Normal (L-N) channel can be calculated by (Farid and Hranilovic 2007)

$${f}_{h}=\frac{{\xi }^{2}{h}^{\left({\xi }^{2}-1\right)}}{2{\left({A}_{\rm O}\beta \right)}^{{\xi }^{2}}}{\text{erfc}}\left(\frac{\mathit{ln}\left(\frac{h}{{A}_{\rm O}\beta }\right)+q}{\sqrt{8}{\sigma }_{x}}\right){\text{exp}}\left(2{\sigma }_{x}^{2}{\xi }^{2}\left(1+{\xi }^{2}\right)\right) ,$$
(25)

where the complementary error function in (Elgala et al. 2011) is erfc(·) and the coefficient of normalized path loss is \(\beta\), knowing that

$$\beta = {{h_{\beta } } \mathord{\left/ {\vphantom {{h_{\beta } } {\beta_{h} }}} \right. \kern-0pt} {\beta_{h} }},$$
(26)

where \({\beta }_{h}\) represents the path loss.

The variance of an independent and identically distributed Gaussian random variables is

$${\sigma }_{x}^{2}=0.30545 {k}^{7/6}{C}_{n}^{2}{\mathrm{d{\prime}}}^{11/6} ,$$
(27)

where \({C}_{n}^{2}\) indicates the structure parameter refractive index, the wave number is \(k\) and can be calculated by \(k\) = (2π/λ), λ is the wavelength of the signal transmitted.

where

$$q=2{\sigma }_{x}^{2}\left(1+2{\xi }^{2}\right) ,$$
(28)

where \(\xi\) is the ratio between the width of beam and the receiver’s pointing error displacement standard deviation, like in (Gradshteyn and Ryzhik 2007).

$$\xi =\frac{{w}_{zeq}^{2}}{2{\sigma }_{s}^{2}} ,$$
(29)

The channel fading coefficient \({h}_{a}\) is calculated as

$${h}_{a}={\text{exp}}\left(2x\right) ,$$
(30)

\(x\) is an independent and identically distributed (i.i.d.) Gaussian random variable with a variance \({\sigma }_{x}^{2}\) and mean \({\mu }_{x}\) (Taher et al. 2019; Abaza et al. 2015).

3 Results and discussion

In this section, SNR for both systems is investigated, and the evaluation of system performance is conducted through the utilization of BER. Table 1 presents the simulation parameters corresponding to the standalone VLC system and the hybrid FSO/VLC system.

Table 1 Simulation parameters for both VLC standalone system and a hybrid FSO/VLC system
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3.1 SNR calculations

Based on Eq. (17) and using MATLAB, Fig. 5 represents a relation between SNR and distance for both a standalone VLC system and a hybrid FSO/VLC system using image sensor with a number of pixels 1024 × 1024 at the receiver. Figure 5a represents the SNR performance for standalone VLC system, while Fig. 5b presents the SNR of FSO/VLC system. According to Fig. 5a, it is clear that increasing the spatial separation between the origin and the target location leads to decrementing the SNR. To achieve a coverage distance of 500 m, it indicated that the SNR is \(\sim\) 18 dB. On the other side, Fig. 5b indicates that incrementing the coverage distance results in incrementing the SNR at a fixed BER \(\sim\) 10−6. It shows that at distance 100–500 m (= 600 m) and 500–400 m (= 900 m), the SNR increases from \(\sim\) 16.55 dB to ~ 27.27 dB which is equivalent to incrementing SNR by 10.72 dB to enlarge the coverage distance from 600 to 900 m.

Fig. 5
figure 5

Relation between coverage Distance and SNR of a standalone VLC system, b a hybrid FSO/VLC system

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Comparing both systems in terms of coverage distance, it is found that the maximum distance that can be covered in standalone VLC system with BER 10−6 is 500 m, while regarding to hybrid FSO/VLC system the corresponding coverage distance is 900 m.

3.2 Error performance

Figure 6 displays the relation between BER and SNR for both standalone VLC system and the hybrid FSO/VLC systems. In general, to enhance the error performance, the transmitted power is increased in each system i.e., increasing power improves the system performance. In Fig. 6a, by fixing the coverage distance to 500 m, it is clear that to achieve the desired BER (i.e., 10−6) the SNR must be ~ 15 dB. Figure 6b indicates that the hybrid system can achieve a BER of 10−6 with a larger coverage distance up to 900 m but with larger SNR \(\sim\) 25 dB. Increasing SNR by ~ 10 dB leads to enlarging the coverage distance by 600 m.

Fig. 6
figure 6

BER evaluation of a standalone VLC system, b a hybrid FSO/VLC system

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Generally, the VLC standalone system can achieve the desired BER with acceptable SNR ~ 15 dB, but, at the expense of the coverage distance (i.e., maximum distance 500 m). On the other hand, the hybrid system can achieve the desired BER with a larger SNR(~25) dB and a larger coverage distance.

A relation between BER and coverage distance at a fixed SNR of \(\sim\) 20 dB is shown in Fig. 7. In general, increasing the distance leads to degrading the BER performance. Regarding the VLC standalone system, it is evident that at a very small coverage distance, the curve is broken due to smaller pathloss with large incident angle, so, the receiver cannot detect the transmitted signal. Increasing the coverage distance from 157 to 300 m leads to degrading the BER performance from 10−11 to 10−2, respectively. While, according to the hybrid system in Fig. 7b increasing the distance from 600 m to 900 leads only to degrade the BER from 10−7 to 10−5 with an acceptable SNR for both systems.

Fig. 7
figure 7

Relation between BER and distance at a fixed SNR = 20 dB, a standalone VLC system, b a hybrid FSO/VLC system

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According to the references (Taher et al. 2019; Momen et al. 2019; El-Garhy et al. 2022), the acceptable value for SNR is ranging from 15 to 40 while the acceptable value of BER is ranging from 10−5 to 10−6, so, our results are within these acceptable values.

To clarify the significance and advantage of our work, the following table is added as a comparison between this work and that found in literature. Supplement references on intelligent transportation systems (ITSs) based on VLC and VLC/FSO technologies are used for comparison (Table 2).

Table 2 Comparison between our work and supplement references on ITS based on VLC FSO/VLC technologies
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4 Conclusion

In this paper, the implementation of a standalone VLC system model is discussed, using an image receiver used as an alternative to a photodiode receiver. As a result, both the transmitter power and BER were decreased, and the SNR is improved with an acceptable coverage distance of ~ 500 m. Moreover, a hybrid FSO/VLC approach is then suggested to offer the advantages of both systems when merged. The results demonstrated that compared to standalone VLC systems, the FSO/VLC systems gives a higher coverage area (up to 900 m at 1 Mbps) with BER = 10−6 and SNR ~ 25 dB. On the other hand, at the same SNR (~25 dB), the VLC standalone can cover only a distance up to ~ 272.5 m.