Vehicle-to-Vehicle Channel Characterization Based on Ray- Tracing for Urban Road Scenarios

In this paper, the vehicle-to-vehicle (V2V) channel characteristics in peak hours at the 5.9 GHz band in two typical urban road scenarios, the urban straight road and the intersection, are investigated. The channel characteristics, such as path loss, root mean square (RMS) delay spread, and angular spread, are derived from the ray-tracing (RT) simulations. Due to the low height of antennas at both the transmitter (Tx) and the receiver (Rx), the line of sight (LOS) between the Tx and the Rx will often be obstructed by other vehicles. Based on the RT simulation results, the shadowing loss is modelled by the multimodal Gaussian distribution, and path loss models in both LOS and non-LOS (NLOS) conditions are obtained. And the RMS delay spread in two scenarios can be modelled by the Weibull distribution. In addition, the deployment of an antenna array is discussed based on the statistics distribution of the angular spread.


Introduction
As one of the important parts of an intelligent transportation system (ITS), the V2V communication system allows vehicles to exchange information about the surrounding traffic situation to improve safety, reduce traffic congestion, and provide a comfortable driving experience [1]. It is estimated by the U.S. Department of Transportation (DOT) that V2V communication can address up to 82% of all crashes, saving thousands of lives and billions of dollars. In recent years, V2V communication has attracted more and more attention and has achieved remarkable development.
The channel characteristics are of vital importance in the research, design, and deployment of the V2V communication system. Due to the low antenna height at both the Tx and the Rx, rapid time-varying environments, high mobility of vehicles, relatively short communication distance, diversity of scattering objects, etc., the V2V channel characteristics are significantly different from those in the cellular networks [2].
Many measurement campaigns have been conducted to investigate the V2V channel characteristics over the past few years, and a number of V2V channel models have been proposed. Most campaigns are carried out between the vehicles on the straight road, either in the same direction [3][4][5][6] or in opposite [7,8], and at intersections [9][10][11]. RT simulation technology is also used in [12], where the V2V channel characteristics of an urban intersection environment are analyzed, especially the power delay profile (PDP) and channel gain.
Many studies are carried out in LOS conditions, but some in NLOS conditions caused by large-size vehicles, such as buses, trucks, and vans. In [13], the shadowing effect caused by obstructing vehicles in the V2V channel has been addressed. In [14][15][16], based on the measurement in highways and urban environments, the shadow fading models in LOS and NLOS conditions are established, and it is emphasized that the shadowing loss caused by the surrounding vehicles is about 10 dB. In [17], the V2V communication link is divided into three categories: LOS, LOS blocked by vehicles, and LOS blocked by stationary objects, in which the obstructing vehicles have a more significant impact on the V2V channel. In [14], according to the causes of LOS blockage (vehicles or buildings), the NLOS regions are divided into obstructed LOS (OLOS) and NLOS with lognormal distribution, respectively.
V2V channel characteristics are related to the environment (i.e., urban, suburban, highway, etc.), vehicle speed, and traffic density. During peak hours, urban traffic densities are usually higher and vehicle speeds are usually lower. Due to the mobility of Tx/Rx, the LOS will be blocked and appear in NLOS conditions, which means it is more urgent to investigate the channel characteristics in peak hours. Therefore, in this paper, the V2V channel characteristics of an urban straight road and intersection, e.g., path loss, RMS delay spread, and angular spread, in peak hours at the 5.9 GHz band are investigated based on RT. Channel characteristics in both LOS and NLOS conditions, the probability distribution of LOS in each scenario, and the distribution of shadowing loss and RMS delay spread are modelled. Finally, the RMS angular spread and antenna array deployment are discussed.
The rest of this paper is organized as follows. Section 2 presents the scenario models in urban roads and introduces the RT simulation technology. Section 3 investigates the channel characteristics in both LOS and NLOS conditions. It also includes the probability distribution of LOS in each scenario and the derivation of path loss and modeling of shadow fading in LOS and NLOS conditions. The deployment of an antenna array is also discussed. Conclusions are drawn in Section 4.

Urban Road Scenario and Ray-
Tracing Simulation 2.1. Urban Road Modeling. The two typical V2V scenarios, urban straight road and intersection, are modelled in the paper. Multiple samples are established in these two scenarios, and Figure 1 takes one sample as an example in each scenario.
2.1.1. Straight Road. Six motor vehicle lanes and two nonmotor vehicle lanes are included. During peak hours, the speed of vehicles is relatively low (25 km/h), and the distance between adjacent vehicles is uniformly distributed between 4 and 10 m, where the distance between adjacent vehicles is defined as the distance from the rear of the front vehicle to the head of the adjacent rear vehicle on the same motor vehicle lane.

Intersection.
The total length of the queues for the vehicles waiting for traffic lights from south to north is 50 m, and the distance between adjacent vehicles is uniformly distributed between 1 and 3 m. While in the same direction, for vehicles that are 50 to 100 m from the zebra crossing and driving into the queues, the distance between adjacent vehicles is uniformly distributed between 4 and 10 m. And the speed of the vehicles in the east-west direction is 25 km/h, and the distance between adjacent vehicles is uniformly distributed between 4 and 10 m, too.

Object
Modeling. The surrounding objects in the V2V scenarios that will affect the radio propagation are considered, such as vehicles, buildings, and trees.   3 Wireless Communications and Mobile Computing medium-sized vehicles, and large vehicles, with the proportions of 89%, 7%, and 4%, respectively [18].
As shown in Figure 2, small-sized vehicles are modelled according to a 3-compartment car, medium-sized vehicles are modelled according to a van, and large-sized vehicles are modelled according to a bus.

Building
Modeling. Urban buildings are modelled as low-rise, multistorey, and medium high-rise buildings, with the height of 7 m, 14 m and 23 m and the proportions of 20%, 50% and 30%, respectively [19], as shown in Figure 3.
And the distribution of buildings presents a commercialresidential-commercial trend. The buildings are arranged with a spacing of 13 m. The distance between a building and the sidewalk is 10 m.  Figure 4. The trunk is modelled as a hexagonal prism, while the crown is modelled as an approximate sphere.
In addition, the electromagnetic parameters of all the materials in the scenario are listed in Table 1. 2.3. Ray-Tracing Simulation. The Tx/Rx antenna is placed on top of the car, with 0.05 m above the roof. For example, the omnidirectional antennas are used, as shown in Figure 5. And the simulation process is as follows.

Straight Road.
A car in the middle lane is selected to simulate the V2V channel characteristics with other cars within 100 m, as shown in Figure 1(a).

Intersection.
A car waiting for the traffic light near the zebra crossing in the north-south direction is selected, to simulate the V2V channel characteristics with other cars within around 100 m, as shown in Figure 1 As a technique to predict radio propagation characteristics, RT is based on electromagnetic theory, geometrical optics (GO) theory, and uniform theory of diffraction (UTD). It is assumed that the radio wave propagates in the plane wave, whose far-field propagation characteristics can be simplified to a ray model to describe all propagation paths from Tx to Rx, and the geometry and dielectric properties of scattering objects in the scenario need to be modelled.
The RT simulator employed in this study is developed by Beijing Jiaotong University. It is composed of a V2V RT simulator [20] and an UWB THz RT simulator [21]. Recently, this RT simulator is extended to a high-performance computing (HPC) cloud-based platform (CloudRT). More details of this platform can be found in [22] as well as via http:// raytracer.cloud. This RT simulator has been validated by a large number of measurements from frequencies below the 6 GHz [1,20] to 300 GHz band [21,23]. With a Web browser, MATLAB, and SketchUp installed, users can prepare the needed models, configure/trigger simulation tasks, and download results.
RT can identify all possible rays between Tx and Rx, whose propagation modes include LOS, reflection, scattering, and diffraction. After a coherent superposition of all determined rays, the final output of the ray-based model is the time-variant CIR hðτ, tÞ ∈ ℂ M R ·M T , which completely characterizes the frequency-selective channel for each Tx/Rx link for the M T and M R transmit and receive antennas, respectively. We can express the CIR for single-input single- where the kth MPC is described by the amplitude a k ðtÞ, the delay τ k ðtÞ, and the phase shift φ k ðtÞ at time t. NðtÞ and f denote the number of MPCs for each time instant and the carrier frequency, respectively. Based on the predicted CIR, additional characteristics like the PDP and RMS delay spread can be derived. The simulation parameters are listed in Table 2, where the reflection order is defined as the maximum number of   Wireless Communications and Mobile Computing reflections that can be determined by the RT model based on the image method. Specular reflections are calculated recursively up to a desired order, but considering the complexity of the environment, only reflections up to order three are practical due to the limit of computational effort. In addition, the directive scattering (DS) model [24] which is widely used in optics is selected to calculate the power and direction of the scattering path in the platform.

Channel Characteristics
In this section, based on RT simulation technology, the channel characteristics in the straight road and intersection are discussed in peak hours.

LOS and NLOS.
It can be seen from Figure 6(a), in the straight road scenario, as the Tx-Rx distance increases from 10 m to 90 m, the LOS probability falls from 100% to 40%. As shown in Figure 6(b), the LOS probability in the intersection scenario has a similar trend. However, the LOS probability in different regions (from south to north, from north to south, and in east-west direction) is slightly different. For cars driving from north to south, if there are medium-sized or large-sized vehicles in the east-west direction in front of the Tx, LOS will be blocked. However, the distance between adjacent vehicles is relatively short in peak hours, which results in about 4-6 vehicles in the east-west direction ahead of the Tx. In addition, considering the proportion of vehicles (the probability of the appearance of medium-sized and

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large-sized vehicles appearing in urban roads is 11%), according to probability theory, the probability of more than one large-and medium-sized vehicle in these 4-6 vehicles, that is, the probability of LOS blockage, will be more than 40%, which means that the probability of LOS in that area will be less than 60%.    it can be seen that more reflecting objects (i.e., buildings and trees) exist near the Tx and Rx in the intersection scenario, so more multipath contributions (MPCs) can be provided when the Tx and the Rx are obstructed. According to ITU-R P.1411 [25], the radio propagation within 1 km is mainly affected by buildings and trees. Since most of the short-range wireless signal transmission is in the city and suburb, the influence of buildings is particularly important. The height of transmitters is near ground level, which leads to more interaction with objects in the close neighbor surroundings [26]. Figure 8 shows the path loss in the straight road scenario and the intersection scenario with LOS and NLOS conditions in terms of the Tx-Rx distance. The path loss in dB is roughly linear with the logarithmic distance in LOS conditions. In NLOS conditions, the shadowing loss caused by vehicle occlusion can exceed 20 dB even in the short Tx-Rx distance about 10 m, which is consistent with the conclusion in [13].

Path Loss.
Considering that NLOS conditions will have a great impact on the path loss, in order to improve the accuracy, the path loss model, shown in (2), is used in LOS and NLOS conditions, independently, and the fitting parameters are shown in Table 3.
where A is the interception, d is the Tx-Rx distance (unit: m), n is the path loss exponent, and L a and L b are the shadowing loss in the LOS and NLOS conditions, respectively. Due to the obvious linear variation of the path loss in LOS conditions, both n and A are fitted in LOS conditions based on the minimum mean squared error (MMSE). In the two scenarios, the waveguide effect occurs because of a set of waves reflected by the buildings on both sides of the road like valleys. Thus, the path loss exponent n in the straight road and the intersection are slightly smaller than those in the free space path loss (FSPL) model (n = 2). Moreover, the phenomenon (n < 2) has also been found in many other studies [4,[27][28][29]. And the difference of n and A in the two scenarios is very small.
The probability density function (PDF) of the shadowing loss and fitting results in the straight road scenario and the intersection scenario with LOS conditions is shown in Figure 9. It should be noted that the change trend of simulated data is approximately monotonically increasing, which is similar to special cases of Weibull distribution. Reference [30] points out that the Weibull distribution is a better fit over all empirical data than the Nakagami distribution in V2V channels. The PDF of the Weibull distribution is defined as where λ > 0 denotes the scale parameter and k > 0 denotes the shape parameter. And the cumulative distribution In this paper, we need to modify the value of x by substituting the value of the maximum shadowing loss minus the shadowing loss; the fitting parameters of the Weibull distribution are presented in Table 4. The λ in the intersection is larger than that in the straight road, which shows that the probability of different shadowing loss values in the intersection with LOS conditions is more uniform. In the intersection, although the influence of multipaths at different locations is diversified, the effect of MPCs is more consistent in the distribution of the shadowing loss. The differences in the shadowing loss in LOS conditions are mainly attributed to the different participations of multipaths on the direct LOS path.
The PDFs of the shadowing loss and fitting results in the straight road scenario and the intersection scenario with NLOS conditions are shown in Figure 10. Observed from data fitting, it is more in line with the multimodal Gaussian distribution, which is the superposition of three Gaussian distributions, corresponding to different compositions of multipath components, and can well describe the statistics of the shadowing loss, whether there is a straight road or a crossroad. Fitting parameters of the shadowing loss are shown in Table 4. The multimodal Gaussian distribution is defined as where u 1 , u 2 , and u 3 are the mean values of the Gaussian distribution from left to right and σ 1 , σ 2 , and σ 3 are the corresponding standard deviations.
The mean value of the first Gaussian distribution of shadowing loss is 4.02 dB (straight road)/6.55 dB (intersection). This is mainly due to the existence of the single bounce reflections from the side of buildings and vehicles. Moreover, due to the larger value of a, the probability of the first Gaussian distribution is the largest. In [17,31], it is reported that, in the absence of LOS, most of the power is received by single bounce reflections from physical objects. The measurement results in the urban road in [14] at the 5.6 GHz band show that the shadowing loss caused by obstructing vehicles follows the Gaussian distribution, and the mean value of the shadowing loss is about 7 dB, which is basically consistent  with the mean value of the first Gaussian distribution of the shadowing loss in this paper.
The mean value of the second Gaussian distribution of the shadowing loss in the straight road is 16.94 dB, with a low probability. It is mainly caused by multiple reflections from the vehicles.
The mean value of the second Gaussian distribution of the shadowing loss in the intersection and the third Gaussian distribution of the shadowing loss in the straight road is 34.48 dB (straight road)/37.06 dB (intersection). The rays are composed of a large number of scattering paths with a relatively low power from trees, buildings, and vehicles.
The mean value of the third Gaussian distribution of the shadowing loss in the intersection is 63.6 dB. It only appears when the Rx is driving in the east-west direction, extremely far away from the intersection and obstructed by many medium-sized or large-sized vehicles, resulting in only a small number of scattering paths existing, with lower power.

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Wireless Communications and Mobile Computing Reference [9] points out that the path loss is high when the vehicles are far away from the intersection, with few physical objects actually providing propagation rays. In NLOS conditions, the strength of the received power is dependent on the availability of the reflection and scattering coming from buildings and trees, which may account for the main received power. In the absence of a large fraction of these reflections and scattering, the second Gaussian distribution or the third Gaussian distribution of the shadowing loss will appear.

RMS Delay Spread.
The RMS delay spread is defined as [32] where P n and τ n denote the power and the excess delay of the n-th ray, respectively; N is the number of rays; and the mean delay τ is defined by Figure 11 shows the RMS delay spread in the straight road scenario and the intersection scenario with LOS and NLOS conditions. And the corresponding CDFs and PDFs are shown in Figures 12 and 13.
The The standard deviations of the RMS delay spread are 29.32 ns in the straight road and 41.66 ns in the intersection. The standard deviation in the intersection is larger than that in the straight road. The result illustrates that the surrounding scatterers in the intersection have a more significant impact on the V2V radio channel.
It can be observed that the RMS delay spread in LOS conditions is much smaller than that in NLOS conditions. The RMS delay spread in most locations is close to 0 ns, which indicates that MPCs with a large delay suffer greater attenuation.
Moreover, the RMS delay spread in the intersection is larger than that in the straight road. MPCs will be involved, and the Rx can receive more reflection and scattering paths from the surrounding buildings and trees, even from some distant buildings, as shown in Figures 6(b) and 6(d), which leads to a greater RMS delay spread.
Generally, the statistical characteristics of the RMS delay spread can be modelled as a Gaussian distribution [33,34]. However, as can be seen from Figure 12, the Gaussian distribution is not applicable, so we use the Weibull distribution to model it. The results are presented in Table 5. A larger λ in the straight road indicates the extent to which the RMS delay spread variation is greater.

RMS Angular
where P n and θ n denote the power and angle (azimuth/elevation angle of arrival/departure) of the n-th ray, respectively, and N is the number of rays.

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In the V2V channel, the angle of arrival and the angle of departure are equivalent. Therefore, only the RMS angular spread of departure is discussed. Figure 14 shows the CDFs of the Azimuth Spread of Departure (ASD) and Elevation Spread of Departure (ESD) in the straight road and the intersection.
ESDs are almost 0°which indicate that the directions of the rays are almost parallel to the ground. The MPCs from the top of the buildings on both sides experience greater attenuation. The LOS path and the reflection paths from the buildings at the same height as the car contribute the main energy.
The median values of ASDs are 8.55°in the straight road and 8.68°in the intersection. 90% of ASDs are less than 32°in  the straight road and 56°in the intersection. The ASDs in the intersection are larger than those in the straight road. The objects involved in the radio wave propagation in the straight road are arranged along both sides of the road, resulting in a relatively weak reflection and scattering paths. The RMS angular spreads of the azimuth angle are larger than those of the elevation angle, illustrating that the low correlation and higher multiple-input multiple-output (MIMO) gain can be improved when the antenna arrays are placed horizontally at the Tx locations.

Conclusion
Based on RT simulation technology, the V2V channel characteristics at the 5.9 GHz band are investigated. The two V2V scenarios, urban straight road and intersection, 13 Wireless Communications and Mobile Computing including road models, vehicle models, building models, and tree models, are established. RT simulation results show that the LOS probability nearly linearly decreases with the Tx-Rx distance, and the shadowing loss caused by obstructing vehicles can exceed 20 dB even in the short Tx-Rx distance. The shadowing loss can be well characterized by the multimodal Gaussian distribution. Thus, the path loss models in the LOS and NLOS conditions are obtained. Furthermore, the distributions of the RMS delay spread in the two scenarios are obtained and are modelled by the Weibull distribution. Finally, the deployment of antenna arrays is discussed based on the statistics distribution of the angular spread.
In the past, the shadowing effect caused by obstructing vehicles is usually modelled as one Gaussian-correlated variable. However, different blocking levels, as we have observed, have different effects on shadow fading, which have largely been ignored. More importantly, we propose a multimodal Gaussian distribution to describe the shadowing loss, and the division of the multimode depends on the difference of multipath components caused by different blocking levels.
In the future work, based on RT simulation, we will carry out the research on V2V channel characteristics of specific scenarios and measurement campaigns to verify the RT simulation results and make the results more convincing.

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.