Fast simulation of high-speed railway fading channel using finite-state Markov models

Physical Communication 36 (2019) 100825

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Fast simulation of high-speed railway fading channel using finite-state Markov models✩ ∗

Huimin Zhang a , Siyu Lin a , , Hongwei Wang b , Wenjie Li a , Bin Sun b , Shan Yang c a b c

School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China National Research Center of Railway Safety Assessment, Beijing Jiaotong University, China Network Technology Research Institute, China United Network Communications Corporation Limited, China

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Article history: Received 1 January 2019 Received in revised form 20 June 2019 Accepted 14 August 2019 Available online 20 August 2019 Keywords: Channel simulator Finite-state Markov chain High-speed railway communications

a b s t r a c t The design and performance evaluation of the high-speed railway (HSR) communications are inseparable from the accurate and efficient high-speed channel simulator. The variation on path loss, shadowing and fast fading are the key characteristics of HSR channels. Although finite-state Markov chain (FSMC) channel models have been extensively investigated to describe fading channels, most of the previous channel simulators cannot reflect all the above key characteristics. In this paper, we propose a novel FSMC model based on channel simulator with the path loss, shadowing and fast fading in HSR. The accurate closed-form expression of state transition probabilities between channel states is derived to break the simplified assumption of first-order Markov chain. To validate the accuracy of the new FSMC channel simulator, the comparison analysis between the proposed channel simulator and the actual measurements are provided. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The increase in the passengers’ demands for various mobile Internet services stimulates the development of high-speed railway (HSR) communications. However, because of the limited and scarce spectrum resources, as well as poor spectral efficiency caused by the fast fading, the transmission scheme and protocol design of wireless communications for high mobility network have become a hot research area in recent years. Compared with the actual channel measurements which usually have high cost and excessive limitation, channel simulation has key research value because of its high efficiency. Therefore, building an accurate and mathematically tractable channel simulator for HSR communications is indispensable to the evaluation and design of communication systems. The existing high-speed railway channel models in the literature can be categorized as statistical analysis models and packet level channel models. While statistical analysis models are too complicated of simulation, such as WINNER II channel model [1], COST 2100 channel model [2], and tapped delay line channel model [3]. While packet level channel models are gradually widely applied to high-speed channel modeling due to the advantage of simple mathematical expression. A packet level ✩ This work was supported by the Fundamental Research Funds for the Central Universities, China under Grant 2019JBM005. ∗ Corresponding author. E-mail address: [email protected] (S. Lin). https://doi.org/10.1016/j.phycom.2019.100825 1874-4907/© 2019 Elsevier B.V. All rights reserved.

channel model is built by finite-state Markov chain (FSMC) [4]. In [5], the authors propose a state aggregation FSMC model for OFDM systems. However the current packet level models are lack of comprehensive consideration about the effects of both large-scale fading and fast time-varying fading. In this paper, we propose an FSMC based channel simulator for HSR communications with time-varying path loss, shadowing and fast time-varying fading. The impacts on moving speed of the variation on fading channel are incorporated into the proposed channel simulator. The closed-form expression of state transition probability (STP) is derived. And then we verify the accuracy of our proposed simulator by extensive measurements of HSR channels. The proposed channel simulator provides a theoretical basis for the high-level performance analysis and protocol design. The following contributions are provided in this work:

• We propose an accurate and mathematically tractable channel simulator for HSR communications with the effect of path loss, shadowing and fast time-varying fading. • The impacts on moving speed and the number of channel states are considered in the proposed channel simulator. The closed-form expression of STP is derived. • We provide the comparison analysis of the actual channel measurement with the model simulation results to validate the accuracy of the model. The rest of this paper is organized as follows. Section 2 introduces the existing work about channel modeling. Section 3

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describes the system model and fading channel model. The channel model based on FSMC is established in Section 4, and the STP matrix between arbitrary states is derived based on the joint probability density function. The measurement results and the simulation results are shown in Section 5. Finally, we give the conclusions in Section 6. 2. Related work Channel modeling is the basis of the design in wireless communication system. Channel models can be divided into two categories: the statistical analysis model and the packet level channel model. (1) The statistical analysis models focus on the physical propagation characteristics between the transmitter and receiver which are aimed at modeling the actual wireless propagation environment. This kind of models reproduce the wireless signal propagation process by parameters such as time delay, Doppler shift and angle of arrival [6]. Some of the statistical analysis models rely on the configuration of channel matrices and antenna parameters [7, 8], therefore, they always have complex mathematical expressions. The statistical analysis models have poor flexibility and cannot switch freely between line-of-sight and non-line-of-sight channels. They are divided into different scenes [9–13]. Although the statistical analysis models are widely used, they are lack of flexibility. Therefore, statistical analysis models are unsuitable for high-level performance analysis and protocol design. (2) Because of the inadequacies of statistical analysis models, packet level models are proposed which only describe the parameters related to key channel characteristics. The purpose of packet level channel models is for performance analysis and fast channel simulation based on simple mathematical models. From the earliest GEC model [14,15] to the hidden Markov model [16], and then to the FSMC model, Markov has been increasingly used for fast channel simulation. The FSMC model for the fast fading is investigated in [17], and it is suitable for viaduct and terrain cutting scenarios in HSR. The relationship between the different Markov orders and the fading rate of Rician fading is discussed in [18]. In [19], the authors consider about incorporating packet level behavioral aspects in IEEE TGn channel models with the influence of fast fading. Fast fading has a relatively complete mathematical statistical model, so it is widely used in Markov channel modeling. In addition, functional dependence between the Markov STP and steady-state probability (SSP) is found in the slow fading case [20]. The SSP and STP are the key parameters in the Markov model, and a large number of researches have explored their estimation and calculation methods. In [21], the authors use received signalto-noise ratio (SNR) amplitude to approximate STP in Rayleigh fading channels. And in [22], the authors model the fast fading as a Nakagami distribution. However, these works assume that the current channel state just transfers to the adjacent states at the next moment. In fact, the channel states change drastically in high-speed environment, and there is a high probability of cross-state transition. The joint probability density function of the received SNR under fast fading environment is derived which makes channel translation modeling more accurate [23,24]. While the high-order Markov models take into account the influence of multiple moments on the current channel state, it increases the complexity of the model [25]. And many of the proposed models lack the support of actual measurement data [21,22,26]. There are also a lot of related researches in the field of wireless communications which focus on channel modeling, performance analysis and so on [3,22,27–29].

Fig. 1. HSR communication system.

3. System model In this section, we first give a brief description about the traditional radio coverage methods in HSR scenario. Then the basic channel models for large-scale fading and fast time-varying fading are introduced to pave the way for the establishment of the FSMC channel model. 3.1. High-speed railway communication system The linear radio coverage is adopted in HSR train-ground communications. In this case, the received SNR changes periodically when the train proceeds along the track. This means that the received SNR increases during moving forward to serving base station (BS). After passing the BS, the received SNR decreases gradually. In the overlap area, the handover is triggered, then the new period of path loss variation starts. The periodical received SNR of HSR communication system is shown in Fig. 1. 3.2. Channel model In this section, we introduce the channel models as three parts, path loss, shadowing, and fast fading. 3.2.1. Path loss We adopt the traditional multi-slope method to model the effect of path loss, then the received power Pr can be represented as a function of distance Pr (d)

{ =

Pt + L − 10α1 log10 (d/d0 ) d0 ≤ d ≤ dc Pt + L − 10α1 log10 (dc /d0 ) − 10α2 log10 (d/dc ) d > dc (1)

where Pt represents the transmit power in dBm, d0 is the reference distance, dc is the critical distance, α1 and α2 are the path loss exponents. L is a constant which is related to the environment and antenna characteristics, and it is considered to be the free-space path gain at the reference distance d0 [30]

( L = 20log10

λ 4π d0

) (2)

where λ is the wavelength of the signal. Then the average received SNR can be described as

γ¯ (d) = Pr (d) − N0 where N0 represents noise power in dBm.

(3)

H. Zhang, S. Lin, H. Wang et al. / Physical Communication 36 (2019) 100825

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3.2.2. Shadowing Radio signal usually experiences complex propagation environments along the HSRs. The randomness of channel quality is caused by the buildings, plants, and terrain along the rail track, which is called shadowing. We use the log-normal shadowing model to describe this phenomenon, and then the probability density function (PDF) of received SNR of shadowing is described as

ξ √

(ξ ln (ψ) − µ)2 fψ (ψ) = exp − 2σ 2 σ 2π ψ

(

)

,ψ > 0

(4)

where ξ = 10/ln 10, µ and σ are the mean and the standard deviation of the received SNR in dB, respectively. 3.2.3. Fast fading The Nakagami-m model has been validated to be one of the most common fast fading models. In this work, Nakagami-m distribution is utilized to model the fast fading. Thus the received SNR has the following PDF fx (x) =

( )m m

γ¯

xm−1

(

−mx exp Γ (m) γ¯

) (5)

where γ¯ is the average SNR, m is the Nakagami fading parameter,∫ and Γ (·) is the Gamma function which is defined as ∞ Γ (z) = 0 xz −1 e−x dx. We describe the path loss as a function of the distance between the BS and the train. The randomness of channel fading is related to shadowing and fast fading. To reduce the complexity of modeling and mathematical analysis, we combine the effects of fast fading and shadowing together, so the received signal SNR can be modeled as the lognormal-Nakagami fading as

Fig. 2. Model establishment.

where Γ (·) is the Gamma function.

SNR in each time slot keeps the same, that is, the channel states do not change in each time slot. The received SNR is divided into N non-overlapping SNR intervals as Γn with Γ1 = −∞, ΓN +1 = ∞, (n = 1, 2, . . . , N + 1). The channel state is Sn if γ belongs to [Γn , Γn+1 ). The STP as pn,j is defined as the probability of the channel state that shifts from Sn to Sj . In the proposed FSMC model, the state transitions in one interval are shown in Fig. 3.

4. FSMC Channel model

4.2. Model parameters

FSMC models are applied extensively to describe the variations on wireless channels. In this section, we design a new FSMC channel model considering path loss, shadowing and fast timevarying fading to capture the variations on HSR channel fading. Then we derive the two critical parameters of the proposed FSMC model, SSP and STP.

In the proposed model, the average received SNR γ¯k in each interval is constant, which determines that the SSP of each interval is constant. Also, the STP is related to the SSP of the current interval, so we first consider the SSP for each interval. Under the premise of the given average received SNR, the PDF of received SNR can be rewritten as

4.1. Model establishment

fγ¯k (γ ) =

( )m

γ −mγ exp Γ (m) γ¯ 0 ( ) ξ (ξ ln (γ¯ ) − µ)2 exp − dγ¯ , × √ 2σ 2 σ 2π γ¯

fγ (γ ) =

∫

∞

m

m−1

(

)

γ¯

(6)

The received signal SNR changes periodically due to the linear radio coverage scheme of HSR. According to the feature of HSR coverage, we only focus on the variation in half cell. As shown in Fig. 2, Point A is the nearest position and Point B is the farthest position to the current serving BS in half cell. We only focus on the process when the train moves from point A to point B. We divide the distance between Point A to Point B into K equal non-overlapping intervals, and the distance of each interval is d. The interval number K depends on the range of path loss. To simplify the model, we assume that the average received SNR for each interval is fixed, then we use γ¯k to represent the average received SNR at the kth interval, k = 1, 2, . . . , K . Each interval is further divided into equal non-overlapping time slots, and the duration of each time slots is TF , which should be smaller than the coherent time. We assume that the received

γ m−1 γ exp(−m ) γ¯k Γ (m) γ¯k 0 ξ (ξ ln (γ¯k ) − µ)2 × √ exp(− )dγ¯k . 2σ 2 2πσ γ¯k

∫

∞

(

m

m

)

(7)

To simplify the integral operation, we use the method in [31] to approximate the PDF of the lognormal-Nakagami model to a lognormal distribution. The mean and variance of the approximate lognormal distribution PDF are respectively given by the following equation

µ ˜ = ξ (ψ (m) − ln (m)) + µ

(8)

σ˜ 2 = ξ 2 ζ (2, m) + σ 2

(9)

where ψ (·) is the Euler Psi function, and ζ (·, ·) is the generalized Riemann Zeta function. And ξ = 10/ln 10, µ and σ 2 are the logarithmic mean and the variance, respectively.

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Fig. 3. N - state transitions in one interval.

Therefore, the SNR of the received signal can be simplified as

ξ ˜ (ξ ln (γ ) − µ) exp(− ), γ ≥ 0. √ 2σ˜ 2 σ˜ 2π γ¯k 2

fγ¯k (γ ) =

(10)

According to the definition of the lognormal distribution function, the cumulative distribution function (CDF) can be shown as Fγ¯k (Γn ) = Fγ¯k (γ ≤ Γn ) =

1 2

1

+ erf( 2

ξ ln(Γn ) − µ ˜ ). √ 2 2σ˜

fX (x) = (11)

4.2.1. Steady-state probability The SSP can be calculated as the integral of the PDF corresponding to the SNR intervals as (12). And the CDF is utilized to simplify the integration process [32]

πn =

∫

Γn+1 Γn

fγ¯k (γ )dγ = Fγ¯k (Γn+1 ) − Fγ¯k (Γn ).

(12)

4.2.2. State transition probability Most of the existing methods for calculating the STP are based on the assumption that the state can only transfer to the adjacent states [20,33]. This assumption adapts well to the slow fading channel, or the model that we consider a small number of channel states. However, in the actual HSR communications, the channel is affected by various factors, such as the vehicular speed, external interference and terrain. Therefore, the assumption cannot adapt to the general environments. In this paper, we use the joint probability density function to calculate STPs. The channel states can transfer to any states within a reasonable range at the next moment. In this circumstance, the STP pn,j = Pr (Sl = j|Sl−1 = n) which represents that the probability of the channel state n at time l − 1 to the channel state l at time l can be obtained by double integrating the joint probability density function in any two SNR intervals

∫ Γj+1 ∫ Γn+1 pn,j =

Γj

Γn

f (γ1 , γ2 )dγ1 dγ2

πn

to [Γj , Γj+1 ). Then we give the expression of f (γ1 , γ2 ) which is the PDF of bivariate lognormal distribution. Consider a c-dimensional Gaussian distribution vector X = (X1 , X2 , . . . , Xc )T , where X ∼ N (µ , Σ ), and (·)T represents the transpose of the vector. The PDF of multivariate Gaussian distribution is defined as

(13)

where γ1 and γ2 are the received SNRs of two adjacent time slots. We suppose that γ1 belongs to [Γn , Γn+1 ) and γ2 belongs

(

1

(2π )c /2 |Σ |1/2

exp

−1 2

)

(x − µ)T Σ −1 (x − µ)

(14)

where µ is the c-dimensional mean vector, and Σ is the c × c covariance matrix. Then we consider a c-dimensional lognormal distribution vector Y ≜ (Y1 , . . . , Yc )T with Yi = 10Xi /10 for i = 1, 2, . . . , c. We suppose that the function y = Φ (x ) indicates the 10 ln y relationship between the two variables, and Φ −1 (y ) = ln 10 is the inverse function. Here we use multivariate change of variable theorem to obtain the PDF of multivariate lognormal distribution from multivariate Gaussian distribution PDF which can be represented as fY (yy) = fX (Φ −1 (yy)) ⏐det JΦ −1 (y )⏐

⏐

⏐

(15)

where JΦ −1 (y ) is the Jacobian matrix of the inverse transformation c ⏐ ⏐ ∏ ⏐det JΦ −1 (y )⏐ = j=1

(

10

) (16)

yj ln 10

So the PDF of multiple lognormal distribution can be expressed as c ( ∏

1

fY (y ) =

10

)

(2π )c /2 |Σ |1/2 j=1 yj ln 10 ( ( )T ( )) −1 10 ln y −1 10 ln y × exp −µ Σ −µ 2

ln 10

ln 10

(17)

where µ is the mean vector, Σ is the covariance matrix, and ρ is the correlation coefficient. We only need a 2-dimensional vector for the joint probability density function, therefore the PDF of 2-dimensional lognormal

H. Zhang, S. Lin, H. Wang et al. / Physical Communication 36 (2019) 100825

5

Fig. 5. Path loss fitting.

Fig. 4. Measurement scenario.

distribution is showed as follows f (y1 , y2 ) =

ξ2 2π σ1 σ2 y1 y2

√

ξ ln y −µ

1−ρ

2

exp(

ξ ln y −µ

−q 2(1 − ρ 2 )

)

ξ ln y −µ

(18) ξ ln y −µ

2 2 2 1 1 2 2 1 1 2 ) +( ) − 2ρ ( )( ). where q = ( σ1 σ2 σ1 σ2 Finally, we use (12) to calculate SSPs and STPs are drived from (13).

5. Performance evaluation To validate the accuracy of the proposed FSMC based HSR channel simulator, we perform extensive channel measurements in the Hefei–Nanjing and Hefei–Wuhan high-speed lines. In this section, we first introduce the measurement campaign, and then derive the channel parameters of FSMC model according to the measurement data. Then the accuracy of proposed FSMC based HSR channel simulator is validated by the experimental results from measurements. 5.1. Measurement Campaign In our measurements, existing BSs are utilized as the transmitters. The carrier frequency and bandwidth of BSs are 930 MHz and 200 KHz, respectively. The transmitting power is 43 dBm and the dual-polarization directional antennas, with 17 dBi gain, 65◦ horizontal and 6.8◦ vertical beamwidths are mounted on towers and connected to the signal transmitters with feeder cable. The receiving antennas used by the measurement system are omnidirectional antennas with 4 dBi gain, 80◦ vertical beamwidth and located in the middle part of the train, on top of the carriage at a height of 30 cm above the roof. The measurement scenario is shown in Fig. 4. The ESPI test receiver with maximum 10 K sample rate is utilized to collect measurements data. The measurement locations and train speed are collected via Global Positioning System (GPS) receiver and the distance sensor deployed on the wheel of the locomotive, respectively. To investigate the effects of moving speed on the temporal channel statistical characteristic, the trains move at different speed modes. 5.2. Parameters selection The model proposed in this paper takes into account path loss, shadowing and fast fading, so we should select the appropriate parameters firstly. The three parts of the fading effect should be separated before we process measurement data. First, the 40-wavelength sliding window is used to average the original measurement data for separating the large-scale fading

and fast fading [34]. Then shadowing and path loss are separated by linear regression fitting. As we mentioned earlier, we use linear regression to determine the parameters of the path loss. We get the best fitting results with α1 = 2.412, α2 = 5.668, d0 = 40 m and dc = 400 m as we mentioned at (1). The path loss fitting result is shown in Fig. 5. The removal of path loss from large-scale fading leaves shadowing, and the shadowing can be modeled as a Gaussian distribution with the mean µ= −1.1029 and variance σ 2 = 9.0024. Then, by matching the Nakagami channel model with measurement data, we find that the Nakagami fading parameter m = 3 can be accepted. To simplify the mathematical complexity of the model, we divide the whole length into K = 100 intervals. The time slot duration is selected as TF = 1 ms, which is smaller than the coherence time of the HSR channel to ensure that the channel state is basically unchanged in one time slot. In the actual measurement scenario, the carrier frequency of the signal is 930 MHz, and the parameters of this HSR channel can be calculated as 0.423/fd ≈ 1.4 ms [35]. Also the transmission time slot of LTE system is 1 ms. So the value of 1 ms not only matches with the LTE system, but also meets the requirements of the channel model in this paper. In addition, we get the correlation parameter ρ by autocorrelation coefficient method. 5.3. Model validation To validate the accuracy of the proposed channel simulator with different vehicular speeds and the number of states, the comparison analysis of three sets of parameters are provided.

• Three channel states, train speed v = 40 m/s. This is the most basic model. The three-state FSMC model represents the channel states corresponding to good, normal, and poor channel qualities. • Eight channel states, train speed v = 40 m/s. We set up more states in the model. The channel model with the appropriate number of channel states can describe the variation on fading channel accurately. • Eight channel states, train speed v = 100 m/s. The high speed is considered to show that the effect of fast timevarying on temporal characteristics of HSR channel. We show that the proposed model can be applied into different speed scenarios. Then the proposed model results will be compared to the measured data by SSP and STP. Also we evaluate the accuracy of our simulator by level crossing rate (LCR) and average fading rate (AFD).

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Fig. 6. Steady-state probability with different number of states. The lines indicate the model results, and the point marks indicate the statistical results of the measurement data.

5.3.1. Verification of steady-state probability Fig. 6 shows the SSPs with three states and eight states, respectively. We can see that the FSMC model results fit well with the measurement results. The SSPs of three-state FSMC are showed in Fig. 6(a). The SNR interval is Γ2 = 3 dB and Γ3 = 20 dB. The probability of State 3 decreases with the increase of the interval index, this is because that the average received SNR gradually decreases as the train moves away from the BS. In contrast, the probability of State 1 increases. The sum probability of the three channel states occurring in the same time slot equals to 1, so the probability of State 2 increases at the front part and then decreases. Next, we divide the channel into more states. Fig. 6(b) shows the SSPs of eight-state Markov. The model results also match well to the measurement results. The states are divided equally with Γ2 = −5 dB, Γ8 = 30 dB, then we can observe more channel states in each time slot. Similar to the results of the first set of parameters, the probability of State 8 which indicates the best channel quality decreases with the increase of interval index, while the probability of State 1 which indicates the worst channel quality increases. 5.3.2. Verification of state transition probability Furthermore, we focus on the STPs of the channel states. Here we use three settings for comparison. Fig. 7 shows the STPs in the case of three-state FSMC with v = 40 m/s. We can track the channel changes over all the intervals through the STPs. We note that there are some gaps for the STPs between model and measurement results at some intervals in Fig. 7. Within these intervals, the corresponding SSPs are very low in Fig. 6, thus we can ignore the gaps in these intervals. As we see the channel states mostly transfer to the adjacent states, so p1,3 and p3,1 cannot be clearly observed in Fig. 7. Another reason is that the SNR intervals of the three-state Markov channel model

Fig. 7. State transition probability with 3 states (v = 40 m/s). The lines indicate the model results, and the point marks indicate the statistical results of the measurement data.

are wide, so the probabilities of cross-state transitions are very low. We further divide the entire SNR into eight states. The STPs of eight-state Markov with v = 40 m/s and v = 100 m/s are shown in Fig. 8. For the FSMC channel model, each state has eight transitions at the next slot, which means that there are sixty-four elements in the state transition matrix. For simplicity, we chose the 25th, 44th and 90th intervals to show the state transitions. This is because that the three intervals represent three typical locations, which are corresponding to the location near the BS, the middle location of the half cell and the cell boundary. Fig. 8 shows the good agreement of the proposed model and the measurement results. The State 1 to 4 are almost non-existent in the 25th interval as shown in Fig. 8(a) and (d). When the interval index is small, the average received signal power is large, so we ignore the states which belong to the small SNR. In the middle location of half cell, there are many channel states that can be observed in the 44th interval as shown in Fig. 8(b) and (e). And in the 90th interval, channel states mainly stay at State 1 to 4 as shown in Fig. 8(c) and (f). The fading parameter m varies as the train at different locations, therefore, there are gaps between the model

H. Zhang, S. Lin, H. Wang et al. / Physical Communication 36 (2019) 100825

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Fig. 8. State transition probability with 8 states (v = 40 m/s).

Fig. 9. State transition probability with 8 states (v = 100 m/s).

and the measurement results. We can also see that the channel states mainly transfer to the same or adjacent states at next moment, but the situation of cross-state transition cannot be ignored when the number of states increase from 3 to 8, such as p3,5 = 0.0296 shown in Fig. 8. Fig. 9 shows the STPs when the train moves with the speed of 100 m/s. The model results are also close to the measurement results at high speed. With the increase of train speed, the probabilities of cross-state transition also increase, for example, the p3,5 = 0.1387 in Fig. 9(e) is higher than p3,5 = 0.0296 in Fig. 8(e). This is because that the correlation coefficient between adjacent time slots decreases. The comparison results show that the proposed FSMC model can capture the transition of the channel states accurately at both low and high speed. 5.3.3. Simulator validation Finally, we show the LCR and AFD of the generated FSMC channel simulator and measurement data in Fig. 10. As we see

that the second-order characteristic parameters of the generated FSMC channel and the measurement data match well in most cases. We find that the difference between the simulator and the measurement exist in the case of high and low SNR. The reason is that within these high or low SNR intervals, the amount of eligible data is insufficient, which results in the deviation of statistical results. We consider that the deviation also comes from the mathematical approximation process and the linear fitting process. 6. Conclusion In this paper, the FSMC channel model which considers the large-scale fading and fast time-varying fading channel is established. The model can accurately represent the characteristics and variation on the channel when the train move through the whole cell with different speeds. The proposed channel simulator based on FSMC of HSR is a useful tool for performance analysis and protocol design of HSR communications.

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Fig. 10. LCR and AFD of the FSMC vehicular channel model and measurement data.

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Huimin Zhang received the B.E. degree from China University of Mining and Technology, Xuzhou, China, in 2017. She is currently working toward the M.E. degree in Beijing Jiaotong University, Beijing, China. Her current research interests are in the field of wireless channel modeling.

Wenjie Li received the B.C. degree from North China Electric Power University, Baoding, China, in 2018, and she is currently working toward the M.E. degree in Beijing Jiaotong University, Beijing, China. Her current research interests focus on edge computing of vehicle networking.

Siyu Lin received the B.E. and Ph.D. degrees from Beijing Jiaotong University, Beijing, China, in 2007 and 2013, respectively, both in electronic engineering. From 2009 to 2010, he was an Exchange Student with the Universidad Politecnica de Madrid, Madrid, Spain. From 2011 to 2012, he was a Visiting Student with the University of Victoria, Victoria, BC, Canada. He is currently an associate professor with Beijing Jiaotong University. His main research interest is performance analysis and channel modeling for wireless communication networks. He received the First Class Award of Science and Technology in Railway in 2017.

Bin Sun received the B.E. and M.E. in 2004 and 2007, both from Beijing Jiaotong University, Beijing, China. From 2007 to 2015, worked as a R&D manager for a high-tech enterprise, engaged in product research and development in the fields of mobile communication, broadband wireless communication and information. Participated in the compilation of the interfaces and application system industry standards related to GSM-R/LTE-R. His main research interest are simulation modeling, testing and evaluation technology for broadband mobile communication system.

Hongwei Wang received the B.S. and Ph.D. degrees in electronics and information engineering from Beijing Jiaotong University, Beijing, China, in 2008 and 2014, respectively. He was a visiting Ph.D. student with Carleton University, Ottawa, ON, Canada. He is currently a faculty member with Beijing Jiaotong University. His research interests include trainCground communication technologies in communication-based trainCground communication systems and cognitive control in trainCground communication systems.

Shan Yang received the B.E. from Jilin University, Jilin, China in 2005, and Master, Ph.D. degrees from Beijing Jiaotong University, Beijing, China, in 2008 and 2013, respectively, both in electronic engineering. From 2010 to 2012, he was a visiting student with the University of New Brunswick, Fredericton, NB, Canada. He is currently a senior engineer with China United Network Communications Corporation Limited. His main research interest is big data analysis and smart sustainable city construction.