Dynamic vehicular channel characteristics analysis and TDL modeling in different scenarios

Abstract

Wireless channel analysis forms the foundation for characterizing channel models. Studying the channel characteristics in different scenarios is significant for reducing interference and enhancing channel stability. In this paper, Vehicle-to-Infrastructure (V2I) channel measurements were conducted in vegetated areas of Beijing and Wuhan at frequencies of 5.9 GHz and 5.8 GHz, respectively, and the dynamic channel characteristics in these two environments were compared. Additionally, a tapped delay line (TDL) model was used to analyze the multipath effects. The results indicate that higher environmental dynamics lead to shorter channel stationarity durations, with measured values of 51.72 ms in Wuhan scenario and 10 ms in Beijing scenario. The RMS delay spread (RMS-DS) is observed to be larger in the Wuhan scenario, with 90% of the values below 168.19 ns, while the corresponding value is 8.48 ns in the Beijing scenario. This paper provides a reference for research in similar environments by comparatively analyzing different channel characteristics and establishing channel models.

Introduction

The development of urbanization has made traffic congestion, frequent accidents, and inefficiency issues more prominent. With the advancement of technologies such as the Internet of Things (IoT), Intelligent Transportation Systems (ITS) have become a key solution to these challenges and an important direction for modern urban development. The Internet of Vehicles (IoV) serves as the core supporting technology of ITS, enabling comprehensive connectivity between vehicles (V2V), vehicles and pedestrians (V2P), vehicles and infrastructure (V2I), and vehicles and networks (V2N) through wireless communication technologies. Vehicular communication is the primary mechanism by which the IoV enables information exchange. Vehicular signal communication relies on electromagnetic wave propagation to transmit data in high-speed, mobile, and highly dynamic environments. However, factors such as high vehicle mobility, obstruction by environmental obstacles, and signal reflection cause the channel to exhibit time-varying and non-stationary characteristics. Therefore, studying and accurately characterizing vehicular channel characteristics is of great significance for improving the communication quality of vehicular networks. In vehicular signal communication, channel characteristics vary depending on the scenario. In recent years, researchers worldwide have analyzed various scenarios across different frequency bands and characteristics.

In terms of research frequency bands, researchers have focused more on the sub-6 GHz bands, such as 3.35 GHz^1–3, 5.9 GHz^4,5, and 5.92 GHz⁶. Unlike other studies on sub-6 GHz bands, articles⁷ and⁸ concentrate on the sub-1 GHz. Huang et al.⁷ conducted measurements in urban and suburban scenarios within the 400–600 MHz frequency range. The measurement results indicate that this band exhibits a smaller path loss exponent and delay spread in urban environments, making it suitable for emerging applications such as 5G, IoT, and emergency communications. An et al.⁸ addressed the needs of emergency communications in mountainous and plateau environments by systematically conducting V2V channel measurements and modeling studies at 376 MHz for the first time, providing important theoretical foundations and experimental data support for the design and optimization of emergency communication systems in mountainous areas. With the development of 5G technology, the demand for high-speed data transmission, and the gradual emergence of the advantages of millimeter-wave bands, researchers have also turned their attention to millimeter-wave frequencies. Extensive channel measurement, modeling, and system performance studies have been carried out in multiple frequency bands such as 22.1–22.4 GHz⁹, 26 GHz¹⁰, 28 GHz, 39 GHz¹¹, and 41 GHz. These efforts aim to take advantage of the large bandwidth characteristics of millimeter waves to achieve ultra-high-speed communication while addressing challenges related to propagation loss, coverage range, and penetration capability.

In research on channel measurements for the IoV, measurement scenarios exhibit high diversity. Researchers have conducted studies in typical environments such as urban roads^4,12, highways^13,14, interchanges⁹, underground parking lots^15,16, intersections^5,17, dense urban areas¹⁸, suburban environments^7,19, and rural environments¹⁰. Current channel studies in forested and wooded areas primarily focus on static point-to-point measurements, while dynamic measurements such as V2V and V2I are relatively limited. Moreover, most measurements in these environments are concentrated in the lower frequency bands of sub-6 GHz and millimeter-wave bands, with fewer studies based on 5.9 GHz. References ⁴ and²⁰ conducted measurements and analyses in urban road environments with linear vegetation and typical forested urban settings, respectively, providing valuable references for V2V channel modeling and system design in vegetated environments. An et al.⁸ and Wang et al.²¹ performed measurements in mountainous plateau environments, specifically in the Ailao Mountains in Yunnan and the mountainous roads of Zhoushan in Zhejiang, respectively, offering references for V2V analysis in similar scenarios.

When the environment differs, the large-scale and small-scale propagation characteristics of the channel also exhibit significant variations. Current research on channel characteristics primarily focuses on large-scale propagation characteristics such as path loss^5,7,9 and shadow fading⁸, as well as small-scale propagation characteristics including multipath delay spread, angle spread, and Rician K-factor. Both⁵ and⁷ propose dual-slope path loss models based on measured data. Yang et al.⁵ determines the breakpoint distance through geometric relationships, characterizing distinct path loss exponents and shadow fading properties for Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) regions. Huang et al.⁷ introduces a breakpoint distance to differentiate between near-field and far-field regions, incorporating log-normal shadow fading in its modeling. Reference ⁹ introduces an empirical path loss model named “Single-Ridge Bridge (SRB)”, which characterizes the additional propagation loss caused by bridges through a weighted combination of the ”UMi model” (unobstructed conditions) and the ”UMi + Deygout model” (with solid obstacles). The weight coefficients for LoS and NLoS regions were fitted separately based on measurement data. An et al.⁸ analyzed shadow fading and proposed a novel shadow fading correlation model based on a combination of growth and oscillation functions. By introducing multiple fitting parameters, this model more accurately captures the fluctuation characteristics of shadow fading over long distances. Yang et al.⁴ used shadow fading correlation and the Temporary PDP Correlation Coefficient (TPCC) to measure the non-stationarity of the channel. The results indicate that LoS scenarios exhibit a more significant equivalent stationary distance, while OLoS scenarios are more non-stationary. Furthermore, researchers have also conducted studies on channel modeling in other frequencies, such as the free-space optical (FSO)^22,23, and in other scenarios, including integrated satellite-terrestrial relay networks (ISTRNs)²⁴.

As evidenced by the research mentioned above, while numerous scenario-specific measurements and investigations have been conducted, research on forested areas and vegetation-covered urban roads remains relatively limited. Furthermore, during dynamic measurement processes, the link state and channel characteristics continuously vary as the environment between the transmitter (Tx) and receiver (Rx) changes, making the study of dynamic channel properties highly important. However, current research on the dynamic characteristics of channels in forested and vegetation-covered urban road environments is still scarce. Therefore, this paper investigates V2I communications in vegetation-covered urban roads in Wuhan and forested road scenarios in Beijing. A comparative analysis is conducted on the power delay profiles, stationarity time, shadow fading correlation, and delay spread in these two distinct environments. Additionally, path loss models are analyzed for both scenarios. Finally, the tapped delay line (TDL) is employed for channel modeling, the tap parameters of the TDL are extracted, and the variations in tap amplitudes are characterized.

The paper is organized as follows. Section II presents an overview of the measurement campaign, including the measurement system, the measurement parameters, and the considered scenarios. Section III analyzes the channel characteristics of the two scenarios. Section IV employs the TDL model for channel modeling in the Wuhan scenario and derives the tap parameters of the TDL channel model. Section V concludes the paper.

Measurement campaign

Measurement scenarios

The measurements were conducted in two scenarios: Wuhan Yujia mountain (Scenario 1) and Beijing Tanzhe mountain (Scenario 2).

The measurement environments for the two scenarios are shown in Fig. 1a,b. It can be seen that there are many obstacles in Scenario 1. Objects marked by red boxes in the figure, such as guardrails in the road center, streetlights on both sides, utility poles, and vehicles traveling in the same and opposite directions, are all potential obstacles that may affect the channel. Compared with Scenario 1, the environment of Scenario 2 is more spacious with fewer obstacles on the road. However, there are still a small number of streetlights, vehicles, and trees that may affect the channel.

Fig. 1.

Measurement environments. (a) Scenario 1. (b) Scenario 2.

The measurement routes are shown in Fig.2a, b. In Scenario 1, the Rx was parked at the roadside while the Tx vehicle drove along Yujiashan North Road towards it. In Scenario 2, the Tx was stopped at the roadside while the Rx vehicle drove along the forest road towards the Tx.

Fig. 2.

Driving route of two scenarios. (a) Scenario 1. (b) Scenario 2.

Measurement setup

Before the measurement activity began, a direct calibration method was used to measure the system loss and the cable losses at the Tx and Rx. At the same time, the maximum index value for delay calibration was determined, and satellite signals were used to synchronize the GPS timing at the Tx and Rx. The measurement parameters were individually designed for each scenario to ensure the antennas can receive signals optimally. Although the two scenarios differ in frequency and bandwidth, the radio wave propagation characteristics at 5.9 GHz and 5.8 GHz are highly similar. Moreover, data from different scenarios were processed accordingly to account for these differences.

In measurement 1, the operating frequency of the channel sounder is 5.9 GHz with the bandwidth of 100 MHz. The transmit power is 16 dBm. Both the Tx and Rx are placed inside the measurement vehicle, and the Tx and Rx antennas are installed on the vehicle roof through the sunroof, as shown in Fig.3a. A dual-polarized directional antenna is employed. The heights of the Tx and Rx antennas are 1.57 m and 1.78 m, respectively.

Fig. 3.

Antenna installation drawing of two scenarios. (a) Scenario 1. (b) Scenario 2.

In measurement 2, a signal with a center frequency of 5.8 GHz and a bandwidth of 20 MHz is used. The measurement system, illustrated in Fig. 3b, consists of Rx and Tx antennas, USRP, an RF power amplifier, and a PC control unit. A wide lobe horn antenna is used as the Tx antenna, and an omnidirectional antenna is used as the Rx antenna. The Tx and Rx antennas are mounted at heights of 2.3 m and 1.9 m, respectively. The measurement parameters for the two scenarios are summarized in Table 1.

Table 1.

Measurement parameters.

Measured parameter	Scenario 1	Scenario 2
Center frequency,	5.9 GHz	5.8 GHz
Bandwidth, B	100 MHz	20 MHz
TX antenna gain,	2 dBi	11 dBi
RX antenna gain,	10 dBi	4 dBi
TX antenna height,	1.57 m	2.30 m
RX antenna height,	1.78 m	1.90m
TX power,	16 dBm	16 dBm

Channel characteristic analysis

Stationary time

The Wide-sense Stationary Uncorrelated Scattering (WSSUS) assumption is widely adopted in the analysis of wireless propagation channels. However, this assumption is valid only under limited conditions. The stationarity time plays a crucial role, as it serves as an important parameter by which the validity of the WSSUS assumption can be assessed. If the above assumption holds, the channel statistics become time-independent. Consequently, within a stationarity window, the fading statistics of the channel can be considered to remain more or less constant²⁵.

The stationarity time window images were derived based on the collinearity of the discrete local scattering function (LSF)²⁵. The LSF estimate reads

1

where the delay index, and the Doppler index, respectively. The LSF at and corresponds to the center value of the time-frequency stationarity region. The delay and doppler shift resolutions are given by and , M and N represent the number of time samples and frequency samples in the stationarity region, respectively.

Hence, the collinearity in time is defined as

2

where the symbol denotes the L2 norm of a vector, in the equation (2) the norm operates on , which is the vectorized LSF at a given time instant .

The Collinearity in time results are shown in Fig. 4. Within these figures, the stationarity time windows are marked out with black dashed lines. It can be observed that the stationarity time windows in Scenario 2 are larger than those in Scenario 1. This suggests that the channel conditions in Scenario 2 are more stable during the measurement period compared to Scenario 1. In Fig.4d, the theoretical stationarity time is denoted by . Theoretically, the stationarity time should stabilize to a constant value over a period. The stability of the coherence time is reflected in the distinctness of the stationarity window boundaries, and a more stable stationarity time results in sharper window boundaries. As observed in Fig. 4a, c, the stationarity time in Scenario 1 is more stable compared to Scenario 2 in Fig.4b, d, so the boundaries of its stationarity window are more distinct. Furthermore, longer periods of stationarity correspond to larger stationarity windows. The value of should theoretically stabilize at a constant value of 2.18 s, as indicated by the black line. However, due to the limited number of samples available for estimation in the time domain relative to the measurement duration, the estimated stationarity time exhibits fluctuations.

Fig. 4.

Collinearity in time and stationary time of two scenarios. (a,c) Scenario 1. (b,d) Scenario 2.

The measured stationarity time parameters obtained by statistically analyzing the stationarity time over the entire measurement period are presented in Table 2. It can be observed that the minimum stationarity time for both scenarios does not differ significantly. However, Scenario 2 exhibits larger values than Scenario 1 for both the average stationarity time and the 5% outage probability stationarity time. Furthermore, the stationarity time variance in Scenario 2 is significantly larger than that in Scenario 1. This outcome appears inconsistent with the information conveyed in Fig. 4c, d. This discrepancy likely arises because the vehicle speed in Scenario 2 is higher than in Scenario 1 over the entire period, causing the propagation environment in Scenario 2 to change more rapidly. Based on the data in the table for both scenarios, we tentatively set the stationarity time for Scenario 1 and Scenario 2 to 10 ms. In the measurement environment, we pay more attention to the 5% outtage value. This means that the channel stationarity time has a 95% probability of being greater than this value, and within this time period, the channel is stable. Therefore, based on the data in the table for both scenarios, we tentatively set the stationarity time for Scenario 1 and Scenario 2 as 51.72 ms and 10 ms, respectively. To facilitate subsequent analysis, it can be assumed that the channel environment remains stable within this stationarity time window.

Table 2.

Comparison of stationarity time.

Scenarios	Minimum (ms)	Mean (ms)	Variance (ms)	5% out (ms)
Scenario 1	10.35	558.56	270.95	51.73
Scenario 2	10	924.29	924.29	10

PDP and small scale fading

In wireless communications, the power delay profile (PDP) describes the average power distribution of signals across different paths and propagation delays, while small-scale fading refers to the rapid fluctuations of received signals over very short distances or time periods. Both play crucial roles in channel characteristic analysis.

Figure 5a presents the PDP for Scenario 1. We observe that as the distance between the Tx and Rx decreases, the power of the LoS path received at the Rx increases continuously. This LoS path is marked with a solid ellipse. Numerous reflected paths exist around the LoS path, with multipath delays ranging from 0 to 2500 ns. The reflected paths caused by surrounding objects are indicated by oval dotted line, showing both reflected paths moving farther from the Rx and those approaching the Rx.

Fig. 5.

PDP, AIC and RMS-DS of Scenario 1. (a) PDP. (b) AIC and RMS-DS.

In order to study the small-scale characteristics of the channel, we use a sliding window with a length equal to the stationarity time to eliminate the impact of the large-scale fading on the channel. After using the Akaike Information Criterion (AIC) decision method, the optimal statistical model can be selected from common distributions, including Rician, Rayleigh, Nakagami-m, Weibull, and Lognormal distributions. The best fitting performance can be selected based on the weights of these distributions. A higher AIC weight indicates a better fitting performance. Figure 5b displays the AIC weight and RMS-DS for Scenario 1, while Table 3 presents the best-fit proportions for each distribution. As can be seen from Table 3, among the distributions mentioned above, Rician distribution achieves the highest best-fit proportion at 68.13%. This indicates that the LoS component dominated during the measurement period. However, Nakagami-m, Rayleigh, and Weibull distributions can also be observed. This suggests the presence of signal obstruction during this interval, where objects such as guardrails, road signs, and vehicles in Scenario 1 blocked the signal, generating multipath interference. Consequently, signal propagation experienced obstructed conditions, which is consistent with the information presented in Fig. 5a.

Table 3.

Optimal fitting rate of candidate distributions in Scenario 1.

Distribution	Lognormal	Nakagami-m	Rician	Rayleigh	Weibull
Probability	0	3.30%	68.13%	8.06%	20.51%

In wireless channel analysis, the Root Mean Square delay spread (RMS-DS) is a crucial parameter in characterizing the temporal dispersion of received signals caused by multipath propagation. It is closely related to the surrounding environment and serves as a critical indicator for evaluating channel frequency-selective fading and small-scale analysis processes. In Fig. 5b, RMS-DS remains relatively low during the 0-17s interval, averaging 34.27 ns. However, between 17-22s, the RMS-DS increases rapidly, averaging 137.05 ns. This significant rise corresponds to the increase in multipath components as the two vehicles approach each other.

The PDP for Scenario 2 is shown in Fig. 6a. A LoS path is evident in the figure. As the distance between the Tx and Rx decreases, the power of the LoS path increases progressively. This LoS channel is annotated with a red solid line in the figure. Compared to Scenario 1, reflected paths are scarcely visible around the LoS path in Scenario 2. In other words, the reflected paths are not prominent. Signal obstruction due to the surrounding environment is a common phenomenon in wireless channel propagation. Based on the AIC results, the measured time periods can be divided into LoS and OLoS time periods, where OLoS refers to obstructed or partially obstructed signals. As shown in Fig. 6b, it can be seen that during period L1, the weight of the Rician distribution is the highest, indicating that the LoS path dominates. In period L2, however, the Rician distribution weight is not high, suggesting that the strength of the LoS path signal is reduced. Consequently, the channel tends to resemble a Rayleigh distribution. Thus, L1 represents a LoS channel between the Tx and Rx, corresponding to the LoS time period. L2 represents a scenario where the signal transmitted from the source is partially or completely obstructed, corresponding to the OLoS period. Based on the segmented calculations described above, the average RMS-DS for the LoS and OLoS time periods are calculated as 6.271 ns and 6.544 ns, respectively. The RMS-DS during the OLoS time period is marginally larger than during the LoS period. This slight difference occurs because obstructions such as surrounding trees in Scenario 2 block the signal, causing it to undergo reflection and scattering, which then generate multipath components, thereby increasing the delay spread.

Fig. 6.

PDP and small-scale analysis of Scenario 2. (a) PDP. (b) AIC and RMS-DS.

Figure 7 show the Cumulative Distribution Function (CDF) of the RMS-DS for the two scenarios. As shown in Fig. 7, 90% of the RMS-DS values remain below 168.19 ns in Scenario 1, while in Scenario 2, 90% of the RMS-DS values are below 8.48 ns. Overall, the RMS-DS in Scenario 1 is significantly higher than that in Scenario 2. This difference arises because Scenario 1 features a more complex propagation environment compared to Scenario 2. Scattering and reflecting from surrounding objects in Scenario 1, such as trees, telegraph poles, guardrails, and moving vehicles on the road, causes an increase in the delay spread of the received signal. Table 4 shows the statistical analysis results of the two scenarios. The variance of Scenario 1 is much larger than that of Scenario 2, indicating that the channel in Scenario 1 changes dramatically and has more interference than in Scenario 2.

Fig. 7.

CDF of two scenarios RMS-DS. (a) Scenario 1. (b) Scenario 2.

Table 4.

Statistical result of RMS-DS.

Scenarios	Mean value (ns)	Variance (ns)	CDF = 50% (ns)	CDF = 75% (ns)	CDF=90% (ns)
Scenario 1	58.36	57.79	36.37	48.95	168.19
Scenario 2	6.39	1.63	5.88	6.89	8.48

Large-scale propagation characteristic

Large-scale signal propagation characteristic plays an important role in the analysis of wireless channels. It refers to the large-scale fading in channel characteristics over factors such as distance, path loss, and shadowing. Large-scale propagation characteristics can be generally described by path loss and shadow fading.

Path loss

As a critical parameter, path loss determines the coverage, operational range, and overall efficiency of wireless communication links. The path loss model is a mathematical model used to predict signal attenuation caused by distance, obstacles, and other factors in the field of wireless communication.

In the ideal case, the signal strength decays regularly with the increase of distance. The free space path loss can be expressed by the following formula:

3

where is the distance, is the reference distance, and is the path loss exponent, which depends on the environment and typically ranges between 2 and 4. However, in practice, the free space path loss model often does not match actual measurements in most scenarios. To obtain a practical path loss model, additional loss caused by environmental factors must be incorporated based on the specific scenario.

This experiment employed two common models, the one-slope model and the REL model²⁶, to fit path loss models to large-scale samples obtained after filtering out small-scale fading characteristics using a windowing approach. The results are shown in Fig. 8. To more accurately characterize the channel model in the target scenario, the Root Mean Square Error (RMSE) is employed to determine the optimal path loss model. The results indicate that the REL model provides the optimal fit for both scenarios, with RMSEs of 2.80 dB and 3.98 dB, respectively.

Fig. 8.

Path loss model fitting for two scenarios. (a) Scenario 1. (b) Scenario 2.

The path loss of the REL model can be expressed as:

4

In Eq. (4), represents the specular reflection coefficient, and represents the path length difference between the line-of-sight path and the reflected propagation path.

When the distance between Tx and Rx increases, the terrestrial surface may obstruct both line-of-sight and reflected propagation paths. At this point, an additional loss term should be added to correct the PL model. To make the estimation results of the path loss model closer to the actual situation, the REL model based on the one slope model is further adjusted to:

5

where, is

6

is the effective reflection factor, is the shadowing coefficient, and is the divergence coefficient.

Based on the measured data, the parameters obtained from the two scenarios are shown in Table 5 below. From Table 5, we can see that the value of is 0, indicating that there is almost no additional transmission loss due to ground reflection in both scenarios. The parameter exerts a significant effects on the REL model. According to the formula of parameter , the key factors influencing the path loss model in both scenarios are the effective reflection from rough surfaces and the shadowing effect of reflected rays, which are the combined effects of and . In Scenario 1, this occurs primarily through the effective reflection from obstacles like guardrails on the road surface, while in Scenario 2, it results from effective reflection from trees on both sides of the road combined with the shadowing effect on the reflected ray.

Table 5.

REL fitting parameters.

Scenarios				RMSE [dB]
Scenario 1			0	2.80
Scenario 2			0	3.98

As observed in Fig. 8b, the measured path loss is smaller than the fitted REL model curve within the 150-200 m range, exhibiting significant deviation. This anomaly may result from the Tx executing a turning maneuver during this period, transitioning from an obstructed to an unobstructed path between Tx and Rx. The consequent rapid channel improvement likely reduced multipath interference, leading to decreased path loss.

Shadow fading

Shadow fading is a critical parameter for analyzing large-scale propagation properties. It constitutes the dominant mechanism behind slow fading, primarily caused by absorption, reflection, scattering, and diffraction from obstacles between Tx and Rx. Typically, shadow fading follows a zero-mean Gaussian distribution, with its variance closely related to the environment. In this paper, the Gaussian distribution is used to fit the PDF and CDF of shadow fading for two scenarios. As shown in Fig. 9a,b, the shadow fading of both scenarios roughly follows the Gaussian distribution. In Fig. 9c, d, the shadow fading of both scenarios fits well with the Gaussian distribution. The mean values of the shadow fading fitting curves for the two scenarios are dB and 0.146 dB, with variances of 2.80 dB and 3.98 dB, respectively. Scenario 2 exhibits greater shadow fading variance than Scenario 1, likely attributable to its more pronounced road surface undulations and closer proximity to roadside vegetation.

Fig. 9.

Shadow fading PDF and CDF of two scenarios. (a,b) PDF and CDF of Scenario 1 respectively. (b,d) PDF and CDF of Scenario 2 respectively.

Besides the distribution characteristics of shadow fading, shadow fading correlation is another important characteristic in channel analysis. The shadow fading correlation is often measured using distance and is defined as the correlation among the shadow effects of different location from the same Tx. The correlation coefficient of shadow fading can be expressed by the following formula²⁷:

7

where represents the separation distance.

Figure 10 shows the shadow fading correlation coefficients calculated based on measurement data from two scenarios. The Kim model, Zhang model, Shengkui model, and Extended Kim model⁸ are employed to characterize the correlations and the fitting model formulas are as follows:

8

9

10

11

In the above formula, - and - are fitting parameters of the corresponding models, where also represents the separation distance. Table 6 shows the specific values of fitting parameters and RMSE for the shadow fading correlation in two scenarios. It can be concluded from the table that the best fitting model for both scenarios is the Extended Kim model, with the smallest RMSE values of 0.0474 and 0.0394, respectively.

Fig. 10.

Shadow fading autocorrelation fitting of two scenarios. (a) Scenario 1. (b) Scenario 2.

Table 6.

Shadow fading correlation parameters of typical models.

	Kim model			Zhang model			Zhou model
Scenario			RMSE			RMSE			RMSE
Scenario 1	0.127	14.999	0.054	0.100	0.107	0.056	1.000	5.000	0.059
Scenario 2	14.438	8.145	0.082	2.110	99.997	0.108	1.000	0.200	0.107
	Extended Kim model
Scenario									RMSE
Scenario 1	0.119	15.000	0.376	-0.190	0.377	-0.854	-0.142		0.047
Scenario 2	18.584	8.109	-0.822	-0.082	-0.822	-0.226	-0.506		0.039

The decorrelation distance of shadow fading represents the degree of variation in the spatial dimension. It can be used to estimate how shadow fading changes over space. This decorrelation distance is generally defined as the distance at which the autocorrelation coefficient of shadow fading decreases from its maximum value to . It also serves as the equivalent stationary distance based on shadow fading. Table 7 shows the decorrelation distance values of shadow fading. The decorrelation distance of Scenario 1 is , which is much smaller than that of Scenario 2 at . This indicates that the channel environment in Scenario 1 is unstable, and environmental obstructions have exacerbated the non-stationarity of the V2I channel, resulting in a smaller decorrelation distance.

Table 7.

Shadow fading decorrelation levels under different scenarios.

Scenarios	Frequency (GHz)	Decorrelation distance d(1/e) (m)	Decorrelation distance d(1/e) []
Scenario 1	5.9	0.10	2
Scenario 2	5.8	5.07	98

TDL channel model

Tap Delay Line (TDL) is commonly used modeling methods for multipath channels²⁸. TDL is suitable for narrowband channel modeling, with relatively low multipath resolution, and serves as a mathematical model for simulating multipath channels. The TDL model defines several discrete multipaths, each with corresponding delays and energy attenuation to represent channel variations, as illustrated in Fig.11.

Fig. 11.

Schematic diagram of TDL.

When the signal reaches the receiver, due to obstacles, ground reflection, and scattering, each path arrives at the receiver with different time delays and power. Therefore, multipath can be represented by impulses with different time delays and power, and the received signal can be expressed as

12

where W represents the number of multipaths, represents the gain of the w path, represents the phase of the w path, and represents the delay of the w path, n(t) represents noise.

From the PDP of Scenario 1, it can be observed that numerous distinct multipath components exist clustered around LoS path. Therefore, a multipath extraction algorithm can be applied to Scenario 1 to establish a TDL channel model. Based on the stationarity time, the CIR data is processed and windowed. Then, the APDP after windowing is subjected to a multipath extraction algorithm²⁹ to extract the number, delay, and power of the multipath components (MPCs). The local maximum method is used to extract the multipaths for each window, and the results of the multipath extraction are shown in Fig. 12. As shown in Fig. 12, the number of multipaths in each window is mostly 16 or less. Specifically, windows containing 16 or fewer MPCs account for 94.5% of all cases. Therefore, the number of taps is set to 16.

Fig. 12.

Multipath variation with the number of windows.

For each window described above, the tap amplitudes are extracted. During this extraction, only taps with significant relative energy are retained. Subsequently, tap indices are assigned to the extracted taps within each window. As a matter of fact, due to the mobility of the transmitter and the constant changes in its surrounding environment, the channel exhibits non-stationary characteristics. Consequently, the number of multipaths varies across different windows, with multipaths appearing and disappearing. A binary switch-like variable indicator function is adopted, where state 1 denotes MPC existence (tap active) and state 0 signifies MPC absence (tap inactive). At this point, the TDL channel can be represented as shown in Fig. 13.

Fig. 13.

TDL model with “switch”.

The non-stationary characteristics of the mobile channel can be described using a Markov chain, where the existence and disappearance of taps can be described using a first-order Markov chain. The defining characteristic of the first-order Markov chain is its memoryless property, indicating that the future state depends only on the current state. The definition of the Markov chain is as follows:

13

denotes the probability of the tap state transitioning from to , where ’0’ represents the tap being closed and ’1’ represents the tap being open, with and . denotes the transition probability matrix, and represents the steady-state probability matrix.

The TDL model expression after adding a switch is shown below:

14

where denotes the tap index, represents the gain of the path, represents the phase of the path, represents the delay of the path, and is used to control the switch of the path, n(t) represents noise.

The TDL tap parameter table based on segmented extraction is shown in Table 8. For simplicity in description, only the steady-state probability is shown in the table.

Table 8.

TDL 16-Tap parameter.

Tap	Normalized delay (ns)	Linear normalization power	Normalized power (dB)
1	0	1.0000	0.0000	1
2	20	0.2811		1
3	40	0.0759		0.9950
4	80	0.0087		0.9849
5	130	0.0044		0.9598
6	150	0.0068		0.9296
7	170	0.0056		0.8657
8	220	0.0048		0.8091
9	240	0.0014		0.7648
10	260	0.0012		0.6633
11	280	0.0011		0.5678
12	330	0.0010		0.4271
13	360	0.0008		0.3166
14	400	0.0012		0.2412
15	680	0.0020		0.1457
16	710	0.0006		0.1005

Statistical analysis of the obtained tap amplitudes and taps for each snapshot, as shown in Figs.14, 15 and Table 9, reveals that both fit well with the log-normal distribution.

Fig. 14.

Amplitude lognormal distribution fitting of taps.

Fig. 15.

RMS delay spread fitting of taps.

Table 9.

Lognormal distribution fitting parameter of taps.

Type	Lognormal distribution parameters
	Mean ()	Standard deviation ()
Amplitude		1.778
RMS-DS	3.5951	0.4760

As shown in Fig.16, the RMS delay spread distributions from the tap model and the measured data are similar. Additionally, the K-S statistic and the KL divergence are adopted as two metrics to evaluate the simulation results. The KL divergence is used to assess the similarity between two distributions, similarly to the K-S statistic, and it is commonly employed for the validation of TDL models. indicates a good match between the simulated data and the measured data. The calculated values of the K-S statistic and KL divergence are 0.2 and 1.31, respectively. From these results, it can be observed that there is a discrepancy between the simulated and measured delay characteristics, which requires further follow-up optimization and improvement.

Fig. 16.

Tap and measured data fitting comparison.

Conclusion

This study conducted channel measurements in two forest road scenarios at the 5.9 GHz and 5.8GHz respectively, with a focus on analyzing the PDP, large-scale propagation characteristics, stationarity time, and small-scale fading characteristics. Through stationarity time analysis, it can be observed that the stationarity time in Scenario 1 is generally larger than that in Scenario 2. In the scenario with the larger stationarity time, 90% of the RMS-DS values are below 168.19 ns, and the decorrelation distance is . In contrast, in the scenario with the smaller stationarity time, 90% of the RMS-DS values are below 8.48 ns, and the decorrelation distance is . It is found that the path loss models for both scenarios closely match the REL model, and the shadow fading correlation models fit well with the Extended Kim model. In addition, this paper develops a TDL channel model for scenario 1, extracts the tap parameters, performs corresponding analysis, and evaluates the output results of the model. Although the study is conducted in the forest road environment, the analysis revealed that compared to linear roadside vegetation, moving vehicles and inherent roadside scatterers such as guardrails have more significant impacts on the channel characteristics. Future work will involve investigating the TDL model across different scenarios and frequency bands based on measured data.

Author contributions

C. Li, W. Chen and J. Yu were involved with the conception of the research. Z. Zhang and S. Luo executed the study and collected the data. B. Zhang gave writing and revision suggestions. All authors contributed to drafing the article.

Funding

This document is the results of the research project funded in part by the NSFC (no. 52102399).

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.