Modeling and Performance Study of Vehicle-to-Infrastructure Visible Light Communication System for Mountain Roads

There are many research directions in outdoor VLC. In [7,8,9], Vieira et al. verified the feasibility of VLC in vehicular networks and ITS and also did some hardware experiments and prototype system simulations. In [10], Vieira et al. improved their previous work and presented a cooperative vehicular traffic scenario. Similarly, Cailean et al. also investigated cooperative communication between vehicles and road infrastructure and demonstrated that the proposed device is suitable for transmitting data using VLC technology [11]. In [12], Liu et al. investigated a hybrid communication system based on VLC and radio frequency (RF). The system can provide location-based services as well as improve the broadcasting downlink efficiency of the traffic broadcast system. In [13,14], Irfan et al. studied the effect of realistic optical interference on vehicular VLC and proposed different models for analyzing the performance of VLC systems. In [15,16], Sharda et al. investigated reflecting intelligent surfaces (RISs)-assisted vehicular VLC. The application of optical RIS can overcome the practical limitation of LOS blockage in V2V–VLC and enhance the reliability of transmission. In [17,18], Yahia et al. introduced the application and development of V2V–VLC, utilizing Multiple-Input Multiple-Output (MIMO). In addition, they analyzed the effect of lateral movement of the vehicle and refracted light on the system. In [19], Aly et al. studied the effect of using different lens combinations on vehicular VLC systems in outdoor environments. In addition, there are many other research directions in vehicular VLC, such as system architecture [20,21,22], signal modulation and demodulation methods [23,24,25], multi-user networks [26,27], MAC layer protocols [28], angle diversity reception [29], etc.

Among the numerous research directions of VLC, one of the important research issues is to develop realistic outdoor VLC channel models for analyzing various performance metrics of vehicular VLC networks. To this end, some efforts have been made in [30,31,32,33,34,35,36,37,38,39,40]. From the perspective of VLC scenarios, in [30], Eldeeb et al. performed channel modeling and performance analysis of I2V–VLC, and also focused on the performance of I2V–VLC systems with access points in the form of streetlights, and derived an approximate closed-form bit error rate (BER) expression. In [31], to study ITS suitable for road safety applications, Kumar et al. used the Lambertian radiation model to model the VLC channel and implemented hardware system simulation using two development kits in field programmable gate array (FPGA). In [32], unlike the general studies using PDs as Rx, Yamazato et al. employed an image sensor-based Rx for vehicle VLC and simultaneously performed optical flow measurements for vehicles in three VLC scenarios: I2V, V2I, and V2V. Moreover, most of the existing studies are based on V2V–VLC scenarios. In [33,34], Viriyasitavat et al. derived a system model for V2V–VLC and conducted a performance evaluation study using empirical data obtained from real-world or measured headlight beam models. The results show that the existing optical channel models cannot accurately estimate the system channel behavior. In [35,36,37], Kim et al. focused on the effect of fog and rain on V2V–VLC performance. In [35], experimental demonstrations on V2V–VLC under fog conditions were conducted and a solution to effectively alleviate the effects of fog by using Fresnel lenses and multiple PDs was proposed. However, the authors only simulated and analyzed the hardware system without giving the channel modeling. In [36], Elamassie et al. quantified the performance of the V2V–VLC link using the ray tracing optical design software Zemax^®. The proposed link used car high beams as Txs under clear weather, rain, and fog conditions. However, the final expression for path loss is obtained through data fitting, so the expression cannot reflect the functional relationship between the parameters of the proposed system and path loss. Similarly, in [37], a study by Eldeeb et al. also used Zemax^®’s non-sequential ray tracing tool for channel modeling, and Mie scattering was considered to simulate the weather conditions of clear weather, rain, and fog. Furthermore, the study derived the path loss exponent as a function of distance and different weather conditions. In [38], Mishra et al. used an NS3.25 simulator for realistic channel modeling of VLC-based V2V connection, simulated the system for two modulation methods, open-keyed and variable pulse code modulation, and investigated the proposed system. Most of the above studies consider only LOS links, while, in [39], a model of a V2V–VLC system that considers the effect of atmospheric turbulence (AT) and shadowing was proposed. Under this model, Sharda et al. considered both LOS and NLOS links and proposed a novel Rx architecture using the diversity-multiplexing tradeoff (DMT). In [40], Xie et al. took the Internet of Vehicles as the starting point and used the Lambertian radiation model for channel modeling to analyze the reliability performance of ultrareliable and low-latency communications (URLLC) in outdoor V2V–VLC systems. A comparison of the proposed V2I–VLC model in this paper with the existing research results is shown in Table 1.

Based on the literature review above, it can be found that most of the existing studies are based on some idealized assumptions or ignore the impact of natural conditions on outdoor VLC systems and so their conclusions cannot fully reflect all the characteristics of vehicle-mounted VLC systems in specific scenarios. In addition, most studies focus on describing channel characteristics rather than quantifying the factors that affect the VLC channel model. The main contributions in this paper can be listed as follows:

By modeling the channel of the proposed V2V–VLC system and deriving closed-form expressions for performance indicators, it can be concluded that the considered propagation characteristics have a significant impact on the average path loss, received optical power, channel capacity, and outage probability of the V2I–VLC system. The research content and conclusions will provide strong support for subsequent work and the deployment of the infrastructure for the V2I–VLC system.

The rest of this paper is organized as follows. In Section 2, the system model and channel model of V2I–VLC are discussed. In Section 3, the performance analysis methods are discussed and closed-form expressions for the performance metrics, such as average path loss, received optical power, channel capacity, and outage probability, are derived. In Section 4, numerical results are presented. In Section 5, some discussions are provided. Finally, summary and conclusions are given in Section 6.

Currently, there are two main approaches to model VLC channels for V2I or V2V. One is to apply the Beer–Lambert formula [31,41] based on the Lambert source assumption. In this method, the radiation of Tx is required to obey the Lambertian radiation model, and then the angular distribution of the radiation intensity is modeled using the generalized Lambertian radiation intensity [42]. Then, the channel DC gain (optical power gain) and system impulse response (CIR) expressions are further obtained. The other method of VLC channel modeling pursues more realistic results. Researchers create a simulation environment in software such as OpticStudio^® or Zemax^®. Then, a type of non-sequential ray tracing is applied to the asymmetric light source to obtain data for calculating the CIR. Finally, these data are imported into Matlab^® software to construct the CIR [43,44].

However, the above two channel modeling approaches are mainly applied in indoor VLC systems and extended to outdoor VLC studies. The main difference between outdoor and indoor VLC is the propagation characteristics of light. Outdoor VLC is subject to sunlight, rain, fog, and AT [37,45,46]. Therefore, in [47,48], the authors proposed an outdoor vehicular VLC channel modeling under the influence of AT. This channel model considers the effect of AT in the outdoor environment, which is more realistic than the two methods mentioned above and is used in this paper. Considering the short transmission distance of the proposed V2I–VLC, the effects of AT are modeled using a weak turbulence mechanism, i.e., the received signal at Rx is as follows: where $\eta$ (in A/W) is the photoelectric conversion efficiency of the PD; $h_j$ is the real-valued channel coefficient of the link between the $j^{th}$ Tx and Rx, which can be modeled as follows: where $h^{PL\_av}$ denotes the average path loss. $h_a$ is the channel coefficient due to AT, which is generally modeled as a lognormal distribution with variance ${{\sigma }_l}^{ 2}$, and its probability density function (PDF) is as follows: where ${{\sigma }_l}^{ 2}=4{{\sigma }_y}^{ 2}$. In addition, $n$ in (1) denotes zero-mean additive Gaussian white noise (AWGN) with variance ${{\sigma }_o}^{ 2}$. The shot noise (with variance ${\sigma }_{\mathrm{shot}}^2$) and the thermal noise (with variance ${\sigma }_{\mathrm{thermal}}^2$) caused by sunlight and ambient light are the main noises affecting the quality of outdoor V2I–VLC, and that ${{\sigma }_o}^{ 2}$ is expressed as follows:

According to [33,49], ${\sigma }_{\mathrm{shot}}^2$ and ${\sigma }_{\mathrm{thermal}}^2$ are shown in (5) and (6): where $q$ is the amount of electronic charge; $\eta$ is the photoelectric conversion efficiency of PD; $P_r$ is the average received optical power; $B$ is the system bandwidth; $I_{bg}$ is the received background noise current; $I_2$ is the noise bandwidth factor of background noise; $k$ is the Boltzmann constant; $T_k$ is the absolute temperature; $G$ is the open-loop voltage gain; ${\eta }_c$ is the fixed capacitance per unit area of PD; $\mathsf{\Gamma }$ is the field-effect transistor (FET) channel noise factor; $g_m$ is the FET transconductance; $I_3$ is the FET channel noise current for thermal noise.

In this section, the V2I–VLC path loss expressions for LOS and NLOS links are derived based on the channel modeling in Section 2, and (5) and (9) in [48]. The weather factor and other propagation characteristics are taken into account. In addition, novel closed-form expressions for the average path loss are derived.

Taking the LOS link as an example, the path loss of the proposed outdoor VLC consists of two main components, which are geometric loss and attenuation loss. The geometric loss is caused by the diffusion of emitted rays to areas larger than the PD receiving aperture. The geometric loss between the $j^{th}$ Tx and PD can be expressed as follows: where $D_R$ denotes the aperture diameter of the PD; $\epsilon$ and $\zeta$ are weather-related correction factors [43] (pp. 6892–6894). The attenuation loss is the result of scattering and absorption. It is assumed that most of the scattered photons cannot be captured by the PD and that some of the scattered rays may be received by the PD after reflection. Based on the Beer–Lambert formula and the assumption above, the attenuation loss can be defined as follows: where $c_E$ denotes the extinction coefficient for a given weather type; $D_{LOS,j}^{V_1-PD}{\left({\displaystyle \frac{D_R}{\zeta D_{LOS,j}^{V_1-PD}}}\right)}^{\epsilon /2}$ denotes an additional term proportional to the geometric spread of the light source. In summary, considering the dual Txs of vehicle V₁ and the geometric relation ${\alpha }_j=\arccos {\displaystyle \frac{I_{V_1-PD}}{D_{LOS,j}}}$, the overall path loss of the LOS link can be expressed as follows:

In the proposed V2I–VLC system model, the path loss of the NLOS links is divided into two parts, M and RS, based on the reflected objects. In the same way, the overall path loss of the NLOS links can be expressed as follows: and where $A_M$ and $A_{RS}$ denote the effective areas (assumed to be circular) of M and RS illuminated by the rays, respectively.

The received optical power is an important factor in VLC systems. Consider (1), where $x$ denotes the on-off keying (OOK) symbol corresponding to the intensity modulation-direct detection (IM/DD) scheme and $y$ is the received signal at Rx. Accordingly, the received optical power of the rays arriving at the Rx through the LOS/NLOS link can be expressed as follows: where $P_{t,j}$ corresponds to the emitted power of the $j^{th}$ headlight LED and $h_j$ can be calculated from (2). In the proposed system, $h^{PL\_av}$ denotes the average path loss of the LOS/NLOS link as shown in (12), (13), and (14). Therefore, the power and the total power of the LOS/NLOS link received by Rx from the two Txs can be respectively expressed as follows: and

Channel capacity, as an important metric for performance analysis of communication systems, is the maximum data transmission rate that can be achieved by the communication system. In short-distance and free space optical communication using IM/DD, the average and peak intensity of the transmitted signal is limited [50]. Thus, most of the current research mainly focuses on the bounds of the system capacity, i.e., the emphasis is on deriving the lower/upper bounds [51,52]. In [52], a closed-form expression of channel capacity for VLC systems with high SNR is derived by neglecting the gap between the exact and lower limit values of channel capacity: where $B$ is the bandwidth; $e$ is the natural constant and ${\mathrm{SNR}}_j$ denotes the average received electrical signal-to-noise ratio (SNR) from the $j^{th}$ Tx. For the proposed V2I–VLC system, since the received optical power at Rx can be expressed by (15), ${\mathrm{SNR}}_j$ can be expressed as follows:

Substituting (2) and (21) into (20), the channel capacity of the proposed V2I–VLC system can be obtained as follows:

The outage probability is a key measure of the reliability and stability of a communication system. An outage occurs when the SNR corresponding to all communication links falls below a certain threshold SNR [47].

For the proposed V2I–VLC system, the average received electrical SNR from the $j^{th}$ Tx can be expressed by (21). Define it as follows:

According to the definition of outage probability, and the threshold data transmission rate $C_{th}$, the threshold SNR can be calculated from (21) and (22) as follows:

Consequently, the outage probability of the proposed V2I–VLC system can be expressed as follows: where $R_j$ is shown in (23). Substituting (2) and (3) into (25) and applying the change of variables method for simplification, the closed-form expression for the outage probability is obtained as follows: where $Q(\cdot )$ is the Gaussian Q-function that represents the probability that the value of a Gaussian normal random variable is greater than the standard deviation of $x$, and defined as $Q\left(x\right)={\displaystyle \frac{1}{\sqrt{2\pi }}}{\displaystyle {\int }_x^{\infty }{e}^{\frac{-t^2}{2}}dt}$.

In this subsection, the performance of the proposed V2I–VLC model in terms of path loss is presented. Since the proposed V2I–VLC model is based on short-range communication over LEDs, the path loss has a significant impact on the model. Figure 6 illustrates the path loss under different transmission distances $I_{V_1-PD}$ in LOS and NLOS links given in (12), (13), and (14) for different weather conditions. The simulation curves are also incorporated to confirm the accuracy of the derived closed-form expression for the average path loss. It is worth noting that the negative sign indicates that the path loss is in the form of a penalty. As a result, the path loss in both the LOS and NLOS links increases with the transmission distance, as shown in Figure 6. From the comparison, it is obvious that the LOS and NLOS links have the highest channel gain in clear weather conditions and the worst gain in dense fog conditions. As an example, for $I_{V_1-PD}=50 \mathrm{m}$ in the LOS link, the average path loss value is about −52 dB for clear weather conditions, −53.8 dB for moderate fog conditions, and −55 dB for dense fog conditions. The difference in channel gain between moderate fog and dense fog versus clear weather conditions is 1.8 dB and 3 dB, respectively. In addition, the further V₁ is from Rx (the larger the value of $I_{V_1-PD}$), the larger the difference in channel gain described above. Therefore, the transmission distance and the weather factor have significant impacts on the average path loss of the V2I–VLC.

The average V2I–VLC path loss in different links under dense fog conditions is shown in Figure 7. It is worth noting that the path loss of NLOS-M links is higher than those of NLOS-RS links when the values of $I_{V_1-PD}$ range from 10 to 50 m. However, after 60 m, $P{L}_{av}^{NLOS\_RS}\approx P{L}_{av}^{NLOS\_M}$. It shows that, when V₁ is close to Rx, the reflection effect of the road surface plays the leading role compared to the reflection of the mountain, i.e., most of the optical power received by Rx from the NLOS link is reflected by the road surface. Additionally, when V₁ is far away from Rx, the road surface and mountain reflection have basically the same effect on the performance of V2I–VLC.

In this subsection, the received optical power performance corresponding to the proposed V2I–VLC propagation model is discussed. Figure 8 gives the received optical power in different links under moderate fog conditions based on (16), (17), and (18). It can be seen that the received optical power is highly correlated with the average path loss, and they are directly proportional to each other. Thus, the trends of the received optical power curves shown in Figure 8 are consistent with those in Figure 7. Meanwhile, in the total received power at Rx, the received optical power from the LOS link is much larger than the received optical power from the two NLOS links. In addition, when V₁ is at a close distance from Rx, under the same conditions, the NLOS power caused by the reflection from RS is larger than that caused by the reflection from M. This is mainly due to the fact that the NLOS propagation distance of the rays reflected by the road surface ($D_{NLOS,j}^{V_1-RS}$ and $D_{NLOS,j}^{RS-PD}$) is smaller than the NLOS propagation distance of the rays reflected by the mountain ($D_{NLOS,j}^{V_1-M}$ and $D_{NLOS,j}^{M-PD}$) during the light propagation process. Additionally, when V₁ and Rx become gradually farther away from each other, the received optical power of the two NLOS links is also basically the same because the propagation distances of the rays are not very different.

The total received optical power of the V2I–VLC system, based on (19) as well as the simulation curves under different weather conditions, are presented in Figure 9. It can be seen that the total received optical power is the largest in clear weather conditions and the smallest in dense fog conditions. Moreover, the further the distance between V₁ and Rx, the larger the difference in total received optical power. For example, when $I_{V_1-PD}=10 \mathrm{m}$, the total received optical power in dense fog conditions is only about 12.5% lower than it is in clear weather conditions. However, when $I_{V_1-PD}=100 \mathrm{m}$, the ratio reaches 76.2%. This is due to the fact that, the further away V₁ is from Rx and the worse the weather conditions are, the more the light from the headlights is affected, making the performance of the V2I–VLC worse as well.

In this subsection, the channel capacity performance corresponding to the proposed V2I–VLC propagation model is discussed. Figure 10 illustrates the relationship between the channel capacity (maximum data rate) and the transmission distance based on (22), and also the simulation curves. First, it achieves the highest capacity at all transmission distances in clear weather conditions due to better average path loss performance compared to foggy weather. Second, transmission distance has a great impact on the channel capacity of the proposed V2I–VLC propagation model. For example, under clear weather conditions, the channel capacity at $I_{V_1-PD}=20 \mathrm{m}$ is about 87.4% lower than the channel capacity at $I_{V_1-PD}=10 \mathrm{m}$. Additionally, when $I_{V_1-PD}=40 \mathrm{m}$ (compared to $I_{V_1-PD}=10 \mathrm{m}$), this ratio reaches 98.9%. Furthermore, with the increasing transmission distance, the effect of weather conditions on the channel capacity becomes less significant. For instance, Figure 10 shows that when $I_{V_1-PD}=10 \mathrm{m}$, the channel capacity of the moderate and dense fog is about 18.6 Mb/s and 21.9 Mb/s lower than that of the clear weather, but, when $I_{V_1-PD}=20 \mathrm{m}$, the difference is only 3.6 Mb/s and 5.0 Mb/s. It reveals that, for the proposed V2I–VLC propagation model, the transmission distance is a more influential factor than the weather conditions in terms of the performance of the channel capacity.

Figure 11 shows the relationship between the outage probability and transmission distance, based on (26), and the simulation curves. From (26), it can be seen that the received optical power is highly correlated with the threshold SNR, which is a function of the threshold data transmission rate. Therefore, the threshold of the data transmission rate has a great influence on the outage performance of the V2I–VLC system. Figure 11a,b depict the outage performance when the threshold is 200 kb/s and 500 kb/s, respectively. It is observed that the higher the threshold data transfer rate is set, the higher the outage probability under the same weather and transmission distance conditions. For example, for the same moderate fog conditions and $I_{V_1-PD}=30 \mathrm{m}$, the outage probability at a threshold data transfer rate of 200 kb/s is about $5.1\times {10}^{-3}$, and 0.11 at 500 kb/s. In addition, it can also be seen from Figure 11 that the outage probability increases rapidly as the transmission distance increases. When considering the weather factor, the outage probability curves for different weather conditions are relatively close to each other, regardless of whether the threshold data transmission rate is 200 kb/s or 500 kb/s. The results indicate that weather conditions have less impact on the outage performance compared to transmission distance.