# Channel Characteristics of Rail Traffic Tunnel Scenarios Based on Ray-Tracing Simulator

Authors: Jinmeng Zhao; Lei Xiong; Danping He; Jiadong Du
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

The tunnel scenario is a major rail communication scenario. In this paper, the radio channel characteristics of tunnel scenarios with different carrier frequencies, different distances between the transmitter (Tx) and receiver (Rx), and cross sections are simulated with a ray-tracing tool. Key parameters such as path loss, Rician K-factor, root mean square (RMS) delay spread, and angular spread are studied. According to the results, higher frequencies introduce larger path loss and the presence of the vehicle body increases the path loss by about 35 dB in the scenario; at the same time it will also cause the fluctuation and instability of the path loss. Besides, the influence of reflections from the side walls is significant on radio propagation. The channel experiences more severe fading in a narrow tunnel compared with others.


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## Body

## 1. Introduction

The rail traffic communications have experienced a rapid development recently, such as high-speed railway, municipal railway, and urban railway system. The rail traffic scenario is indispensable for both private and public mobile communications. It is widely agreed that the wireless channel model is significant to carry out mobile communications research, system development, and network deployment, and so on [1]. Currently, the Long-Term Evolution Railway (LTE-R) system has been recommended to replace the global system for mobile communication railway (GSM-R) system for high-speed train (HST) communication system as a part of intelligent transportation systems (ITS) [2, 3]. In addition, the research on 5th-Generation wireless systems (5G) based on high-speed railway (HSR) has become a trend to meet the need of transmission capabilities [4–6]. Thus the study on channel models in rail traffic system for new communication system is indispensable.The wireless channel research needs to be carried out for various typical rail traffic scenarios (viaducts, tunnels, cuttings, etc.), considering the significant differences between the rail traffic scenarios and the public network scenarios [7]. Field test and ray tracer (RT) are two well-known methods for implementing channel characterization. Field test in the field of rail traffic is hard, costly, and long-term. RT provides a means of accurately prediction of the wave propagation which is timesaving and convenient. Therefore, RT is widely used in channel modeling for confined environments.Tunnel scenario is one of the most common scenarios, especially in the mountainous and hilly areas. Considering the unique construction, the wireless propagation in tunnel scenarios is different from other HST scenarios which attracts a lot of research interests [8–10]. Leaky cables and Distributed Antenna System (DAS) [11, 12] are mainly two promising methods to provide radio coverage in tunnels. Several tunnel channel models were proposed in recent years, such as ray-tracing model, multimode model, and propagation-graph theory based model [13, 14]. A real multipath propagation model for radio transmission in typical rectangular subway tunnel was presented in [15] using RT to analyze Doppler spread. The three-dimensional (3D) models of six scenario modules for mmWave and THz train-to-infrastructure channels were defined and constructed for the first time in [16], which considered reality obstacle objects. Based on the wideband measurements conducted in the tunnel scenario by using the mobile hotspot network system, the authors in [17] explored key channel characteristics in different HSR scenarios by 3D RT. Besides, suggestions on symbol rate, subframe bandwidth, and polarization configuration were provided to guide the 5G mmWave communication system design in typical HSR scenarios.The aforementioned research summarized that the majority of existing works contribute to modeling methods based on large-scale parameters. However, previous models were analyzed and compared based on field test. The measurements results such as channel impulse response (CIR) are mixed with a variety of factors. In addition, measurements focusing on narrowband single-input single-output (SISO) systems at low frequency band result in missing multipath parameters such as angular spread and Doppler shift. There is still an urgent demand for an accurate complete channel model considering large-scale parameters, small-scale parameters, and spatial parameters [18, 19] for multitype tunnel scenarios in SISO systems or multiple-input multiple-output (MIMO) systems. Based on RT, channel parameters such as the path loss, multipath delay, and angular spread can be obtained exactly and analyzed. This paper provides the simulation results in different type of tunnels at 1.8 GHz. Optimized deployment recommendations are provided for MIMO systems and antenna configuration.The rest of the paper is organized as follows. The existing channel models for the tunnel scenario of 3GPP are introduced in Section2. The defined tunnel scenarios and simulation setup are presented in Section 3. Key parameters such as path loss, Rician K-factor, root mean square (RMS) delay spread, and angular spread in tunnels with different cross sections at different frequencies are analyzed in Section 4. Conclusions are drawn in Section 5.


## 2. Channel Models

3GPP TSG-RAN WG4 in RAN#66 meeting defined four typical high-speed railway scenarios. A variety of standard channel models in tunnel scenarios were adopted by 3GPP [20–23], like the single tap channel, time delay line (TDL) model, etc.Scenarios 2c and 2g are corresponding to tunnel scenarios covered by leaky cables. The coverage of the Evolved Node B (eNB) is extended by deploying leaky cables in the 2g and 2c scenarios, which is shown in Table1. In scenario 2g, the User Equipment (UE) communicates directly with the leaky cable in the tunnel. The signal is severely attenuated due to the shielding of the train body in this case. In scenarios 2c, relays are set up on the train. The UE achieves two-hop communication with the leaky cable through relay as shown in Figure 1. Since the transmit power gradually attenuates along the leaky cable, RF amplifiers will typically be applied to ensure adequate signal strength. The propagation channel between the in-car relay and the UE does not involve high-speed movement.Table 1
Tunnel scenarios by leaky cables.
Scenarios Description Notation 2c The tunnel is equipped with a leaky cable that communicates with the train’s roof RP and with the UE through the RP Two hop 2g Laying leaky cables in the tunnel to achieve direct coverage of the UE One hopFigure 1
Leaky cable coverage with relay.3GPP R4-154106 proposes a one-tap channel model for leaky cables deployment in the tunnel scenario as shown in Figure2, whereD0 is the distance between two neighbor radiating points; the radiation angle of radiating point is denoted as θ0. It can be assumed that the receiver (Rx) is covered by 8-9 radiation spots. The RF receive signal is(1)rt=∑kxtPkej2πfc-fd,kt+zt=xtej2πfct∑kPke-j2πfd,kt+ztwhere Pk denotes the normalized received power of the kth radiation spot, fd,k is the respective Doppler shift,z(t) is the received noise, andx(t) is the transmitted signal. The power of the fading gain can be modeled as a Rician distribution based on the central limit theorem.Figure 2
Detail illustration of leaky cable.However, this model is only a simplified model. It ignores the reflection component and the scattering component which should be considered in a limited space. Besides, the parameters, such as tunnel size, cross section, internal electromagnetic (EM) properties of tunnel walls, surface roughness, and antenna polarization mode, affect the channel characteristics. RT views radio waves reflected by surfaces of the tunnel. It solves the problem of large workload and poor applicability in field test and also compensates for the inability of the traditional model to provide specific wireless channel parameters, such as amplitude, delay, Doppler shift, and angular spread, which is of great significance for wireless communication systems. It is an effective modeling method to establish a 3D channel model of the rail communication scenarios and analyze the radio signal propagation under different coverage patterns and multiple fading characteristics.


## 3. Scenario Definition and Simulation Setup

### 3.1. Tunnel Scenarios Definition

Given the different geological conditions, the cross section of the tunnel varied in reality. Four typical shapes of cross sections: rectangular, arched, long arched (combined rectangular and semicircular), and semicircular, are shown in Figure3. The side length of rectangular is 6 m intunnel a; the height of arched is 6 m, and the center of circle is 2 m high above the ground intunnel b;tunnel c contains a rectangular whose side length is 4 m and a semicircular whose radius is 2 m; the radius of semicircular is 6 m intunnel d. The number of tunnel surface in the simulation is 4, 10, 9, and 13, respectively. Figure 4 shows the details of the simplified tunnel model referring to the metro tunnel project boundary map provided by the China Railway Fourth Survey and Design Institute Group Co., Ltd. The train model is shown in Figure 5. The 3D tunnel models in this work are built by Google SketchUp. These models are considered in the following simulation analysis.Figure 3
Regular cross sections for tunnels. (a) Rectangular. (b) Arched. (c) Long arched. (d) Semicircular.
(a) (b) (c) (d)Figure 4
Simplified tunnel model (actual scenario).Figure 5
Train model for HST.


### 3.2. Parameters Setup

The simulation parameters should be carefully determined to ensure that the simulation results are accurate and effective and make simulation energy-friendly and timesaving. RT supports a variety of radio wave propagation mechanisms, such as direction, reflection, scattering, diffraction, and transmission. Reflection order means that rays experience up to several times specular reflection from transmitter (Tx) to Rx. The appropriate reflection order is necessary not only to reflect the actual reflectance, but also to avoid a longer simulation time.Based on the above ideas, the channel characteristics under different reflection orders are simulated and analyzed in tunnel scenario in Figure4 with all radio wave propagation mechanisms. The key channel characteristics, such as Rician K-factor, delay spread, angle spread of angle of arrival (AOA), and angle of departure (AOD), are compared, respectively, under different reflection orders range from 6th-9th.When the reflection order is set to higher than 6th, there is rarely a change. In addition, we define(2)PLerrori,j=PLi,f-PLj,fPLj,fwhere the PLi,f is the path loss when the frequency is f and the reflection order is i. The PLerror(i,j) shows the difference rate between ith and jth order in a series of frequencies. The CDF of PLerror is shown in Figure 6. The means of PLerror(8, 9), PLerror(7, 8), and PLerror(6, 7) are 4.26×10-12, 1.9×10-2, and 0.18, respectively. The PLerror(8, 9) is the smallest, ranging from 6.41×10-13 to 1.72×10-11. The PLerror(7, 8) ranges from 4.97×10-5 to 0.12. The PLerror(6, 7) ranges from 1.73×10-4 to 0.53, which is larger than others. As a result, the path loss up to higher than 8th order is hardly change. Thus the 8th order is adopted in simulation due to a tradeoff between computational complexity and precision as shown in Table 2. Considering the fact that the tunnel scenarios are long straight tunnels covered by concrete with no vents and pipes and other obstacles, diffraction is irrelevant here as well as transmission because the Tx is not fixed in the wall.Table 2
Parameters setup.
Parameter Value Frequency 1.8 GHz / 5.8 GHz Transmitting power 25 dBm Antenna(Tx, Rx) Omnidirectional antenna (vertically polarized) Tx location (0, 0, 3) Rx location (x, 0, 5) Reflection order 8 Bandwidth 10 MHz Resolution 1 MHzFigure 6
CDF ofPLerror.Detailed parameters setup is shown in Table2. The frequency is set to 1.8 GHz and 5.8 GHz in order to compare channel characteristics at different frequencies. Signal propagates with 25 dBm of transmitting power. Tx is fixed at one end of the tunnel with the height of 3 m. Rx moves along the x-axis with the height of 5 m. Both of them use vertically polarized omnidirectional antennas. The channel bandwidthB = 10 MHz, and the system time domain resolution Δt= 1/ B. In order to better observe the path with the maximum excess delay max, the number of simulated frequency points Nf should be determined enough [24]:(3)τmax≤Nf×Δtin which, in other words, the frequency domain resolution Δf=B / Nf should be set sufficiently.


## 3.1. Tunnel Scenarios Definition

Given the different geological conditions, the cross section of the tunnel varied in reality. Four typical shapes of cross sections: rectangular, arched, long arched (combined rectangular and semicircular), and semicircular, are shown in Figure3. The side length of rectangular is 6 m intunnel a; the height of arched is 6 m, and the center of circle is 2 m high above the ground intunnel b;tunnel c contains a rectangular whose side length is 4 m and a semicircular whose radius is 2 m; the radius of semicircular is 6 m intunnel d. The number of tunnel surface in the simulation is 4, 10, 9, and 13, respectively. Figure 4 shows the details of the simplified tunnel model referring to the metro tunnel project boundary map provided by the China Railway Fourth Survey and Design Institute Group Co., Ltd. The train model is shown in Figure 5. The 3D tunnel models in this work are built by Google SketchUp. These models are considered in the following simulation analysis.Figure 3
Regular cross sections for tunnels. (a) Rectangular. (b) Arched. (c) Long arched. (d) Semicircular.
(a) (b) (c) (d)Figure 4
Simplified tunnel model (actual scenario).Figure 5
Train model for HST.


## 3.2. Parameters Setup

The simulation parameters should be carefully determined to ensure that the simulation results are accurate and effective and make simulation energy-friendly and timesaving. RT supports a variety of radio wave propagation mechanisms, such as direction, reflection, scattering, diffraction, and transmission. Reflection order means that rays experience up to several times specular reflection from transmitter (Tx) to Rx. The appropriate reflection order is necessary not only to reflect the actual reflectance, but also to avoid a longer simulation time.Based on the above ideas, the channel characteristics under different reflection orders are simulated and analyzed in tunnel scenario in Figure4 with all radio wave propagation mechanisms. The key channel characteristics, such as Rician K-factor, delay spread, angle spread of angle of arrival (AOA), and angle of departure (AOD), are compared, respectively, under different reflection orders range from 6th-9th.When the reflection order is set to higher than 6th, there is rarely a change. In addition, we define(2)PLerrori,j=PLi,f-PLj,fPLj,fwhere the PLi,f is the path loss when the frequency is f and the reflection order is i. The PLerror(i,j) shows the difference rate between ith and jth order in a series of frequencies. The CDF of PLerror is shown in Figure 6. The means of PLerror(8, 9), PLerror(7, 8), and PLerror(6, 7) are 4.26×10-12, 1.9×10-2, and 0.18, respectively. The PLerror(8, 9) is the smallest, ranging from 6.41×10-13 to 1.72×10-11. The PLerror(7, 8) ranges from 4.97×10-5 to 0.12. The PLerror(6, 7) ranges from 1.73×10-4 to 0.53, which is larger than others. As a result, the path loss up to higher than 8th order is hardly change. Thus the 8th order is adopted in simulation due to a tradeoff between computational complexity and precision as shown in Table 2. Considering the fact that the tunnel scenarios are long straight tunnels covered by concrete with no vents and pipes and other obstacles, diffraction is irrelevant here as well as transmission because the Tx is not fixed in the wall.Table 2
Parameters setup.
Parameter Value Frequency 1.8 GHz / 5.8 GHz Transmitting power 25 dBm Antenna(Tx, Rx) Omnidirectional antenna (vertically polarized) Tx location (0, 0, 3) Rx location (x, 0, 5) Reflection order 8 Bandwidth 10 MHz Resolution 1 MHzFigure 6
CDF ofPLerror.Detailed parameters setup is shown in Table2. The frequency is set to 1.8 GHz and 5.8 GHz in order to compare channel characteristics at different frequencies. Signal propagates with 25 dBm of transmitting power. Tx is fixed at one end of the tunnel with the height of 3 m. Rx moves along the x-axis with the height of 5 m. Both of them use vertically polarized omnidirectional antennas. The channel bandwidthB = 10 MHz, and the system time domain resolution Δt= 1/ B. In order to better observe the path with the maximum excess delay max, the number of simulated frequency points Nf should be determined enough [24]:(3)τmax≤Nf×Δtin which, in other words, the frequency domain resolution Δf=B / Nf should be set sufficiently.


## 4. Simulation Results and Analyses

In this section, the simulation results of tunnel channel characteristics in different cross sections and different frequencies are presented and analyzed. Furthermore, suggestions on optimized deployment are provided.


### 4.1. Large-Scale Parameters

The reliable large-scale channel models are essential to network deployment and optimization. Typically, the path loss is expressed as(4)PLd=A+10nlgd+Xwhere thePL(d) is path loss without small-scale fading and it is a function of the distance between Tx and Rx [25].n is path loss exponent, and X (shadow fading) is the zero-mean Gaussian random variable with standard deviation σ. Figure 7 shows the path loss at 1.8 GHz in different cross sections. In the 0-190 m section, the path loss is nearly the same. However in the 190-500 m section, the path loss intunnel c has a higher path loss than other tunnels. The path loss intunnel c can be divided into two phases, and path loss exponents are 1.96 and 3.62, respectively, which means that there is a breakpoint (d0 = 190.10 m) in this scenario. These tunnel cross sections have the same height, and the width varies in shape and size. The path loss fitting result given in Table 3 indicates that the lateral shape has an important impact on the path loss in the empty tunnel with strong line of sight (LOS) path. The path loss exponent intunnel c is greater than 2 because of the existing breakpoint. The path loss exponents are 1.77, 1.84, and 1.88 intunnel a,d, andb, respectively. Compared with the measurement results in straight arched tunnel [26, 27] and rectangular tunnel [28–30], the value of path loss exponent 1.96 intunnel c is similar to 1.40-2.03 at 954-2000 MHz in straight arched tunnel. Meanwhile, path loss exponent 1.77 intunnel a is similar to 1.65-1.94 at 945-2650 MHz in rectangular tunnel. Simulation results in this paper are basically consistent with the measurement results in previous work.Table 3
Path loss fitting result at 1.8 GHZ.
Parameter A n σ Tunnel a 41.29 1.77 0.74 Tunnel b 39.46 1.88 0.45 Tunnel c 31.82 2.30 1.60 Tunnel d 41.29 1.84 0.60Figure 7
Path loss in different tunnel cross sections at 1.8 GHz.Figure8 shows the received power at different frequencies intunnel c. As the frequency increases, the received power decreases. When the distance between Tx and Rx equals 50 m, the received power at 1.8 GHz is 11 dB higher than that at 5.8 GHz. Received power has larger fluctuation, and deeper fading is prone to occur in higher frequency. Based on the similar simulation scenario and parameters setup, the same conclusion is also reflected on the simulation results at three different typical carrier frequencies, i.e., 900 MHz, 2.45 GHz, and 5.75 GHz in [31]. Table 4 shows the fitting parameters at different frequencies. The path loss exponent is 2.31 at 1.8 GHz, while the path loss exponent is less than 2 at higher frequency. Results confirm that the frequency band has a strong impact on the wireless propagation.Table 4
Path loss fitting result intunnel c.
Parameter A n σ 1.8 GHz 31.82 2.31 1.60 5.8 GHz 51.51 1.78 1.45Figure 8
Received power at different frequencies intunnel c.For the tunnel with train, the path loss result in selected locations is shown in Figure9. Rx is fixed on the head of train when the train gradually moves away from the Tx. The obstruction and reflection of the train make the received signal experience longer distance and greater attenuation. The corresponding number of arriving rays reduces sharply. The path loss increases by 35.58 dB with the presence of the vehicle body. The result shows that the path loss in the empty tunnel scenario rises more steadily. Suggestions are given that the antenna deployment in reality scenarios should make sure of the existence of LOS path between Tx and Rx. Moreover, antenna placement is selected carefully to make the blocking effect of the train as small as possible for which further researches are needed.Figure 9
Path loss in empty tunnel and tunnel with train.


### 4.2. Small-Scale Parameters

Small-scale parameters have an important impact in wireless communication system design and analysis. Rician K-factor, RMS delay spread, and angular spread are key parameters to describe the small-scale characteristics. Table5 shows the K-factor and RMS delay spread in different tunnel scenarios.Table 5
Small scale parameters.
Parameter Mean K-factor[dB] Percentage of K<25 dB Mean delay spread [ns] 95 % of delay spread range[ns] Tunnel a 13.7 88% 0.47 0.31-0.76 Tunnel b 14.98 86% 0.37 0.09-0.75 Tunnel c 10.82 94.8% 0.33 0.17-0.66 Tunnel d 14.46 87% 0.40 0.16-0.80


#### 4.2.1. Rician K-Factor

Rician K-factor is defined as the radio of the power of LOS path to the power of non-line-of-sight (NLOS) paths [32]. Figure 10 shows K-factor at 1.8 GHz and CDF of K-factor at all the snapshots. Figure 10(a) depicts that the simulation section can be divided into two parts; K-factor fluctuates severely in part one (0-100 m) and then decreases smoothly in part two (100-500 m). In the first 50 m, the fading is weak, but, after that, the fading is increasingly serious whatever the tunnel scenario is. Table 5 demonstrates that 94.8% of K-factor in all the snapshots intunnel c is lower than 25 dB, but there is about 88% of K-factor lower than 25 dB in other tunnel scenarios as shown in Figure 10(b). The mean K-factor of tunnel scenarios is around 13.49 dB larger than the result 11.5 dB of empirical cluster characteristics extracted for tunnel scenarios at 2.14 GHz [33]. Since the path loss increases with frequency, LOS path experiences a deeper fading at 2.14 GHz. In conclusion, channel characteristics intunnel c experience a severe fading than others.Figure 10
(a) Rician K-factor at 1.8 GHz. (b) CDF of Rician K-factor at all the snapshots.
(a) (b)


#### 4.2.2. RMS Delay Spread

Figure11 shows that RMS delay spread at 1.8 GHz and CDF of RMS delay spread at all the snapshots.Tunnel a is the rectangular tunnel (W6 m × H6 m), andtunnel c is the long arched tunnel (W4 m × H6 m). The most apparent difference betweentunnel a andtunnel c is their widths. RMS delay spread intunnel a is larger than that intunnel c along the simulation section. In Table 5, we notice that RMS delay spread is lower than 0.8 ns in at least 95% at all the snapshots, and the maximum RMS delay spread is 1.18 ns. The results in Table 5 illustrate that 95% of the RMS delay spreads at all the snapshots intunnel a andtunnel c are 0.45 ns and 0.49 ns, respectively, which is narrow compared with other scenarios. On the other hand, mean RMS delay spread is the largest intunnel a, and the weighted average of the delay spread intunnel c is the smallest. As a result, the channel intunnel c experiences a more stable fading. The RMS delay spread varies in ns because of fewer obstacles in empty tunnel, which is similar to the measurement results of delay spread 2-27 ns in mine tunnels [34].Figure 11
(a) RMS delay spread at 1.8 GHz. (b) CDF of RMS delay spread at all the snapshots.
(a) (b)


### 4.3. Spatial Parameters

The RMS angular spreads intunnel c and CDF of angular spreads are shown in Figure 12. ASA, ESA, ASD, and ESD are angular spreads of the azimuth angle of arrival, the elevation angle of arrival, the azimuth angle of departure, and elevation angle of departure, respectively. Figure 11 illustrates that ESA, ASD, and ESD decrease slowly as the Rx moves far away from Tx, and they are lower than 10.20∘ at all the snapshots. The means of ASA, ESA, ASD, and ESD are 51.25∘, 0.67∘, 1.63∘, and 0.95∘, respectively. 99% of ESA, ASD, and ESD are less than 5∘. However, ASA varies differently compared with others. It gradually increases and the max ASA is 123.90∘ when the distance between Tx and Rx reaches 500 m. Angular spread in straight tunnel scenario in work [17] varies similarly, in which ASD becomes larger as the distance of Tx and Rx increases and others decrease at the same time. ASA is greater than others in the majority of the snapshots, which indicates that the impact of reflections from the side walls is significant on radio propagation. Multiantennas can be considered to implement a MIMO system so that the system capacity can be increased by achieving diversity and multiplexing. Besides, directional antennas can be deployed to drop the ASA and reduce the impact of Doppler spread on the channel.Figure 12
Tunnel c scenario. (a) RMS angular spread at 1.8 GHz. (b) CDF of RMS angular spread at all the snapshots.
(a) (b)Simulation results reveal that ASA, ESA, ASD, and ESD vary similarly intunnels b,c, andd. The ASA is compared intunnels b,c, andd as shown in Figure 13. The maximum of ASA intunnels b,c, andd is 65.8∘, 123.9∘, and 73.8∘, respectively. It is obvious that ASA intunnel c is larger than that intunnel d, whereas ASA intunnel b is the lowest at the majority of snapshots. This observation indicates that spatial fading is affected by the cross section. Furthermore, the side walls have a more significant impact on the channel in a narrow tunnel than a wider one.Figure 13
ASA intunnels b,c, andd.


## 4.1. Large-Scale Parameters

The reliable large-scale channel models are essential to network deployment and optimization. Typically, the path loss is expressed as(4)PLd=A+10nlgd+Xwhere thePL(d) is path loss without small-scale fading and it is a function of the distance between Tx and Rx [25].n is path loss exponent, and X (shadow fading) is the zero-mean Gaussian random variable with standard deviation σ. Figure 7 shows the path loss at 1.8 GHz in different cross sections. In the 0-190 m section, the path loss is nearly the same. However in the 190-500 m section, the path loss intunnel c has a higher path loss than other tunnels. The path loss intunnel c can be divided into two phases, and path loss exponents are 1.96 and 3.62, respectively, which means that there is a breakpoint (d0 = 190.10 m) in this scenario. These tunnel cross sections have the same height, and the width varies in shape and size. The path loss fitting result given in Table 3 indicates that the lateral shape has an important impact on the path loss in the empty tunnel with strong line of sight (LOS) path. The path loss exponent intunnel c is greater than 2 because of the existing breakpoint. The path loss exponents are 1.77, 1.84, and 1.88 intunnel a,d, andb, respectively. Compared with the measurement results in straight arched tunnel [26, 27] and rectangular tunnel [28–30], the value of path loss exponent 1.96 intunnel c is similar to 1.40-2.03 at 954-2000 MHz in straight arched tunnel. Meanwhile, path loss exponent 1.77 intunnel a is similar to 1.65-1.94 at 945-2650 MHz in rectangular tunnel. Simulation results in this paper are basically consistent with the measurement results in previous work.Table 3
Path loss fitting result at 1.8 GHZ.
Parameter A n σ Tunnel a 41.29 1.77 0.74 Tunnel b 39.46 1.88 0.45 Tunnel c 31.82 2.30 1.60 Tunnel d 41.29 1.84 0.60Figure 7
Path loss in different tunnel cross sections at 1.8 GHz.Figure8 shows the received power at different frequencies intunnel c. As the frequency increases, the received power decreases. When the distance between Tx and Rx equals 50 m, the received power at 1.8 GHz is 11 dB higher than that at 5.8 GHz. Received power has larger fluctuation, and deeper fading is prone to occur in higher frequency. Based on the similar simulation scenario and parameters setup, the same conclusion is also reflected on the simulation results at three different typical carrier frequencies, i.e., 900 MHz, 2.45 GHz, and 5.75 GHz in [31]. Table 4 shows the fitting parameters at different frequencies. The path loss exponent is 2.31 at 1.8 GHz, while the path loss exponent is less than 2 at higher frequency. Results confirm that the frequency band has a strong impact on the wireless propagation.Table 4
Path loss fitting result intunnel c.
Parameter A n σ 1.8 GHz 31.82 2.31 1.60 5.8 GHz 51.51 1.78 1.45Figure 8
Received power at different frequencies intunnel c.For the tunnel with train, the path loss result in selected locations is shown in Figure9. Rx is fixed on the head of train when the train gradually moves away from the Tx. The obstruction and reflection of the train make the received signal experience longer distance and greater attenuation. The corresponding number of arriving rays reduces sharply. The path loss increases by 35.58 dB with the presence of the vehicle body. The result shows that the path loss in the empty tunnel scenario rises more steadily. Suggestions are given that the antenna deployment in reality scenarios should make sure of the existence of LOS path between Tx and Rx. Moreover, antenna placement is selected carefully to make the blocking effect of the train as small as possible for which further researches are needed.Figure 9
Path loss in empty tunnel and tunnel with train.


## 4.2. Small-Scale Parameters

Small-scale parameters have an important impact in wireless communication system design and analysis. Rician K-factor, RMS delay spread, and angular spread are key parameters to describe the small-scale characteristics. Table5 shows the K-factor and RMS delay spread in different tunnel scenarios.Table 5
Small scale parameters.
Parameter Mean K-factor[dB] Percentage of K<25 dB Mean delay spread [ns] 95 % of delay spread range[ns] Tunnel a 13.7 88% 0.47 0.31-0.76 Tunnel b 14.98 86% 0.37 0.09-0.75 Tunnel c 10.82 94.8% 0.33 0.17-0.66 Tunnel d 14.46 87% 0.40 0.16-0.80


### 4.2.1. Rician K-Factor

Rician K-factor is defined as the radio of the power of LOS path to the power of non-line-of-sight (NLOS) paths [32]. Figure 10 shows K-factor at 1.8 GHz and CDF of K-factor at all the snapshots. Figure 10(a) depicts that the simulation section can be divided into two parts; K-factor fluctuates severely in part one (0-100 m) and then decreases smoothly in part two (100-500 m). In the first 50 m, the fading is weak, but, after that, the fading is increasingly serious whatever the tunnel scenario is. Table 5 demonstrates that 94.8% of K-factor in all the snapshots intunnel c is lower than 25 dB, but there is about 88% of K-factor lower than 25 dB in other tunnel scenarios as shown in Figure 10(b). The mean K-factor of tunnel scenarios is around 13.49 dB larger than the result 11.5 dB of empirical cluster characteristics extracted for tunnel scenarios at 2.14 GHz [33]. Since the path loss increases with frequency, LOS path experiences a deeper fading at 2.14 GHz. In conclusion, channel characteristics intunnel c experience a severe fading than others.Figure 10
(a) Rician K-factor at 1.8 GHz. (b) CDF of Rician K-factor at all the snapshots.
(a) (b)


### 4.2.2. RMS Delay Spread

Figure11 shows that RMS delay spread at 1.8 GHz and CDF of RMS delay spread at all the snapshots.Tunnel a is the rectangular tunnel (W6 m × H6 m), andtunnel c is the long arched tunnel (W4 m × H6 m). The most apparent difference betweentunnel a andtunnel c is their widths. RMS delay spread intunnel a is larger than that intunnel c along the simulation section. In Table 5, we notice that RMS delay spread is lower than 0.8 ns in at least 95% at all the snapshots, and the maximum RMS delay spread is 1.18 ns. The results in Table 5 illustrate that 95% of the RMS delay spreads at all the snapshots intunnel a andtunnel c are 0.45 ns and 0.49 ns, respectively, which is narrow compared with other scenarios. On the other hand, mean RMS delay spread is the largest intunnel a, and the weighted average of the delay spread intunnel c is the smallest. As a result, the channel intunnel c experiences a more stable fading. The RMS delay spread varies in ns because of fewer obstacles in empty tunnel, which is similar to the measurement results of delay spread 2-27 ns in mine tunnels [34].Figure 11
(a) RMS delay spread at 1.8 GHz. (b) CDF of RMS delay spread at all the snapshots.
(a) (b)


## 4.2.1. Rician K-Factor

Rician K-factor is defined as the radio of the power of LOS path to the power of non-line-of-sight (NLOS) paths [32]. Figure 10 shows K-factor at 1.8 GHz and CDF of K-factor at all the snapshots. Figure 10(a) depicts that the simulation section can be divided into two parts; K-factor fluctuates severely in part one (0-100 m) and then decreases smoothly in part two (100-500 m). In the first 50 m, the fading is weak, but, after that, the fading is increasingly serious whatever the tunnel scenario is. Table 5 demonstrates that 94.8% of K-factor in all the snapshots intunnel c is lower than 25 dB, but there is about 88% of K-factor lower than 25 dB in other tunnel scenarios as shown in Figure 10(b). The mean K-factor of tunnel scenarios is around 13.49 dB larger than the result 11.5 dB of empirical cluster characteristics extracted for tunnel scenarios at 2.14 GHz [33]. Since the path loss increases with frequency, LOS path experiences a deeper fading at 2.14 GHz. In conclusion, channel characteristics intunnel c experience a severe fading than others.Figure 10
(a) Rician K-factor at 1.8 GHz. (b) CDF of Rician K-factor at all the snapshots.
(a) (b)


## 4.2.2. RMS Delay Spread

Figure11 shows that RMS delay spread at 1.8 GHz and CDF of RMS delay spread at all the snapshots.Tunnel a is the rectangular tunnel (W6 m × H6 m), andtunnel c is the long arched tunnel (W4 m × H6 m). The most apparent difference betweentunnel a andtunnel c is their widths. RMS delay spread intunnel a is larger than that intunnel c along the simulation section. In Table 5, we notice that RMS delay spread is lower than 0.8 ns in at least 95% at all the snapshots, and the maximum RMS delay spread is 1.18 ns. The results in Table 5 illustrate that 95% of the RMS delay spreads at all the snapshots intunnel a andtunnel c are 0.45 ns and 0.49 ns, respectively, which is narrow compared with other scenarios. On the other hand, mean RMS delay spread is the largest intunnel a, and the weighted average of the delay spread intunnel c is the smallest. As a result, the channel intunnel c experiences a more stable fading. The RMS delay spread varies in ns because of fewer obstacles in empty tunnel, which is similar to the measurement results of delay spread 2-27 ns in mine tunnels [34].Figure 11
(a) RMS delay spread at 1.8 GHz. (b) CDF of RMS delay spread at all the snapshots.
(a) (b)


## 4.3. Spatial Parameters

The RMS angular spreads intunnel c and CDF of angular spreads are shown in Figure 12. ASA, ESA, ASD, and ESD are angular spreads of the azimuth angle of arrival, the elevation angle of arrival, the azimuth angle of departure, and elevation angle of departure, respectively. Figure 11 illustrates that ESA, ASD, and ESD decrease slowly as the Rx moves far away from Tx, and they are lower than 10.20∘ at all the snapshots. The means of ASA, ESA, ASD, and ESD are 51.25∘, 0.67∘, 1.63∘, and 0.95∘, respectively. 99% of ESA, ASD, and ESD are less than 5∘. However, ASA varies differently compared with others. It gradually increases and the max ASA is 123.90∘ when the distance between Tx and Rx reaches 500 m. Angular spread in straight tunnel scenario in work [17] varies similarly, in which ASD becomes larger as the distance of Tx and Rx increases and others decrease at the same time. ASA is greater than others in the majority of the snapshots, which indicates that the impact of reflections from the side walls is significant on radio propagation. Multiantennas can be considered to implement a MIMO system so that the system capacity can be increased by achieving diversity and multiplexing. Besides, directional antennas can be deployed to drop the ASA and reduce the impact of Doppler spread on the channel.Figure 12
Tunnel c scenario. (a) RMS angular spread at 1.8 GHz. (b) CDF of RMS angular spread at all the snapshots.
(a) (b)Simulation results reveal that ASA, ESA, ASD, and ESD vary similarly intunnels b,c, andd. The ASA is compared intunnels b,c, andd as shown in Figure 13. The maximum of ASA intunnels b,c, andd is 65.8∘, 123.9∘, and 73.8∘, respectively. It is obvious that ASA intunnel c is larger than that intunnel d, whereas ASA intunnel b is the lowest at the majority of snapshots. This observation indicates that spatial fading is affected by the cross section. Furthermore, the side walls have a more significant impact on the channel in a narrow tunnel than a wider one.Figure 13
ASA intunnels b,c, andd.


## 5. Conclusion

In this paper, the radio channel characteristics of several tunnel scenarios were simulated with RT. The channel characteristics in different carrier frequencies and tunnel cross sections were analyzed. The key parameters, such as path loss, Rician K-factor, RMS delay spread, and angular spread were simulated and analyzed. The presence of the vehicle body introduces additional 35 dB of the path loss, which leads to the fluctuation and instability of the channel. K-factor changes severely when the distance between Tx and Rx is smaller than 100 m and then decreases smoothly in far region. The channel has short delay spread (1.18 ns) due to strong LOS and the limited space. The side walls have a significant influence on radio propagation especially in a narrow tunnel. Therefore, the conclusion can be drawn that the channel experiences a severe and stable fading in long arched tunnels compared to other tunnel scenarios. The other parameters (i.e., Doppler spread, coherence time, antenna polarization, etc.) and leaky cable for coverage will be studied in the future work.



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*Source: 9284639-2018-08-01.xml*