# Analysis of Propagation Characteristics for Various Subway Tunnel Scenarios at 28 GHz

Authors: Chengjian Wang; Wenli Ji; Guoxin Zheng; Asad Saleem
Journal: International Journal of Antennas and Propagation
 (2021)

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## Abstract

In order to meet the higher data transmission rate requirements of subway communication services, the millimeter wave (mmWave) broadband communication is considered as a potential solution in 5G technology. Based on the channel measurement data in subway tunnels, this paper uses ray-tracing (RT) simulation to predict the propagation characteristics of the 28 GHz millimeter wave frequency band in different tunnel scenarios. A large number of simulations based on ray-tracing software have been carried out for tunnel models with different bending radiuses and different slopes, and we further compared the simulation results with the real time measurement data of various subway tunnels. The large-scale and small-scale propagation characteristics of the channel, such as path loss (PL), root mean square delay spread (RMS-DS), and angle spread (AS), for different tunnel scenarios are analyzed, and it was found that the tunnel with a greater slope causes larger path loss and root mean square delay spread. Furthermore, in the curved tunnel, the angle spread of the azimuth angle is larger than that in a straight tunnel. The proposed results can provide a reference for the design of future 5G communication systems in subway tunnels.


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## Body

## 1. Introduction

In the new era of “intelligent railway mobility,” rail transportation communication systems not only need to process critical information, but also need to meet a series of high-data-rate wireless connection services such as on-board high-definition video surveillance [1]. In order to meet the higher data rates, the fifth generation (5G) of mobile communication technology, such as massive multiple-input multiple-output (massive MIMO) and mmWave technology, has been used for rail transit systems [2]. Studying the propagation characteristics of signals in different scenarios and establishing wireless channel models are necessary prerequisites for designing wireless communication systems and transmission technologies [3]. Therefore, studying the propagation characteristics of 5G frequency band signals in subway tunnel scenarios has a vital importance for operators to develop new communication technologies and design appropriate network architectures.Early research on propagation characteristics in tunnel scenarios was mainly focused on empty tunnels and lower frequency bands. In [4], the channel measurements were carried out in a high-speed train tunnel, and the PL and RMS-DS at 2.154 GHz were analyzed. It was found that the RMS-DS in the tunnel is mainly below 50 ns and there exists obvious slow fading in the tunnel. The broadband channel measurements at 980 MHz and 2.450 GHz were carried out on Line 3 of Madrid, Spain, in [5], and the average power and RMS-DS were studied. The research results showed that when the antenna frequency is higher than 2.4 GHz and located in the tunnel close to the station, the multipath effect in the subway environment could be significantly reduced. Through the channel measurement in Beijing Metro Line 14 in [6], the PL, RMS-DS, doppler frequency shift, and channel capacity of the tunnels at 2.4 GHz and 5 GHz were analyzed. It is found that the channel characteristics in the tunnel are highly location dependent. The channel measurements from 2.8 GHz to 5 GHz were carried out in a straight arched tunnel, and the relationship between RMS-DS, AS, and distance were studied in [7]. The measurement results showed that when the transceiver distance is more than 100 m, the RMS-DS showed stabilized performance at 2.5 ns, and when the transceiver distance is around 50 m to 200 m, AS decreased from 10° to 3°. In order to execute channel measurements in subway tunnels, some scholars use ray-tracing method to simulate channel propagation characteristics. In [8, 9], based on measurement and simulation data, PL of straight tunnel and curved tunnel at 2.4 GHz were studied, respectively, and it was found that the radius of curvature of tunnel had a significant influence on channel characteristics. In curved tunnels, there was an additional loss of received power. In [10], channel characteristics in the tunnel under different frequencies, different transceiver distances, and different cross sections were studied based on the RT simulation results. The results showed that the existence of trains would lead to an additional path loss and channel fluctuation. In addition, in the narrower tunnels, tunnel walls had a more significant effect on the AS results. The channel characteristics at 6 GHz in the tunnel are studied based on measurement and simulation data in [11]. It was found that the normal distribution could better fit the received power. The normal distribution and uniform distribution could fit the azimuth angle of arrival (AOA) of all scenarios.For the study of millimeter wave propagation characteristics in tunnels, a channel measurement at 31 GHz was carried out in a subway tunnel of Seoul, South Korea, in [12], and the measurement results showed that the delay spread was less than 60 ns in both straight and curved tunnels. In [13], based on the channel measurement data of Seoul Metro Line 8, the RT model parameters were analyzed comprehensively, and the PL and RMS-DS of the channel in urban, rural, straight, and curved empty tunnel scenarios at 25 GHz were examined quite efficiently. The channel measurements at 28 GHz were carried out in the same short straight experimental tunnel in [14–16]. The correlation between the RMS-DS, K factor, and shadow fading parameters was analyzed, and it was found that the AS decreases with the increase of the transceiver distance in [14]. In [15], the channel capacity of 2 × 2 and 4 × 4 MIMO systems at 28 GHz and the effect of antenna spacing on channel characteristics were studied. In [16], the channel capacity was compared under different polarization modes (horizontal, vertical), and it was found that the capacity of horizontal copolarization is higher than that of vertical copolarization under the assumption of constant signal-to-noise ratio (SNR) in the subway tunnel. The RT method was used to compare the PL and shadow fading parameters of three different antenna settings from 31.5 GHz to 33.5 GHz in straight tunnels with arched cross sections in [17]. A typical straight subway tunnel scene was simulated in [18], and the PL and RMS-DS at 30 GHz were analyzed by using the RT method. In [19], the channel characteristics at 1.4 GHz and 40 GHz in the tunnel were compared based on the simulation results. It was found that when there existed a train in the tunnel, there would be more multipath components, and the propagation characteristics of copolarization and cross polarization performed much differently. Based on the simulation data in [20], the channel characteristics at 37–42.4 GHz in the high-speed railway station was studied, and it was found that the existence of the train had an obvious influence on the AS.In the existing research, there are relatively few studies at 28 GHz in tunnel scenes, and most of them are concentrated in indoor office, urban, and experimental tunnels. There is a lack of measurements and simulation comparison in the real subway tunnel scenarios, especially the tunnel scenes with real time trains. In addition, the influence of the subway train and its complex scatterers on signal propagation is often ignored. In order to fulfill this gap, this paper studies the channel measurement at 28 GHz in a real subway tunnel environment and calibrates the RT material parameters. Referring to the real tunnel environment, the tunnel models and rail models with different curvature radiuses and slopes are designed. According to the real subway train structure, the metro train model with details such as train chairs and train window is designed. In addition, a comprehensive analysis of various subway tunnel channels is carried out to investigate different aspects of channel propagation.The rest of this paper is summarized as follows: Section2 describes the channel measurement in real tunnel environment and RT parameter calibration method. In Section 3, the scenarios and setting of RT simulation are introduced. Section 4 gives the simulation result comparison and complete analysis of channel characteristics. Finally, the conclusion is given in Section 5.


## 2. Channel Measurement and RT Parameter Calibration

### 2.1. Channel Measurement

As depicted in Figure1(a), the measurements were conducted in metro Line 7 between Shanghai University and Qihua Rd. in Shanghai, China. The tunnel wall materials are reinforced with concrete. As shown in Figure 1(b), the tunnel can be divided into two sections. One of them is a platform with a length of 28.1 m, and the cross section is rectangular with a height of 5.55 m. Another section is the nonplatform part where the cross section is arched and is 4.96 m high, as shown in Figure 1(c). Along the driving route, there is a straight tunnel with a length of 20 m, a curved tunnel with a length of 100 m, and a long straight tunnel with a length of over 400 m, respectively.Figure 1
The measurement environment: (a) measurement subway tunnel; (b) platform cross section; (c) nonplatform cross section.
(a)(b)(c)The measurement system is illustrated in Figure2. It is mainly composed of Agilent E8257D signal source (transmitter) and Ceyear 4024G spectrum analyzer (receiver). Both transmitting antenna (Tx) and receiving antenna (Rx) are ultra-wideband omnidirectional antennas, and the high-precision rubidium clocks are used to ensure clock synchronization as shown in Figure 3.Figure 2
Measurement system.Figure 3
Ultra-wideband omnidirectional antenna.In the measurements, the transmitter is located at the end of the tunnel platform, close to the tunnel wall, and the height of the transmitting antenna is 3.1 m, as shown in Figure4(a). The receiver is located on the railcar in the center of the tunnel, and the receiving antenna is 2.25 m high. The position of the transmitter remains unchanged, and the measurement distance is 500 m. The input power and the frequency are considered as 10 dBm and 28 GHz, respectively. As the railcar moves, the receiver gradually moves away from the transmitter. We have considered a total of 79 test points, and at each test point, the spectrum analyzer reads and records the received power of the signal. The positions of the transmitting and receiving antennas are shown in Figure 4(b). When the transceiver distance is about 100 m, the sampling interval is 2 m. The interval from 100 m to 300 m is 10 m, and the interval from 300 m to 500 m is 20 m.Figure 4
Transceiver settings in the measurement: (a) the cross section of the measurement tunnel; (b) the positions of Tx and Rx.
(a)(b)


### 2.2. Ray-Tracing Parameter Calibration

Based on the received power from the field measurement, the material property parameters in the RT simulation, such as the material roughness, relative permittivity, and conductivity, can be calibrated. The RT simulation tool used in this article is Wireless Insite (WiSE). The 3D model of the subway tunnel in the measurement is reconstructed, as shown in Figure5. The designs of frequency and positions of antennas in the simulation are the same as in the measurement field. For the concrete and metal materials in simulations, we had set the initial roughness, conductivity, and permittivity and then compared the simulated PL results with the measurement data. According to the compared results, we keep adjusting the parameters until there is a high degree of match between the simulation and measurement results. Figure 6 shows the comparison between the simulated PL and the measurement results after adjusting the material property parameters several times. It can be found that, at most test points, the simulated PL results are very close to the measurement data. Because the field environment is highly complex and there are more reflections, the simulation and measurement results are slightly different at individual test points.Figure 5
3D model of the subway tunnel.Figure 6
Comparison of PL results between measurement and RT simulation at 28 GHz.The classic floating-intercept PL model in [21] is described as follows:(1)PLd=β+10αlgdd0+Xσdb,where α is the slope of the PL model and d0 is the reference transceiver distance, which is 1 m in this paper. β is the model intercept, which represents the PL value when the transceiver distance is the reference distance, and Xσ is a Gaussian random variable with standard deviation of σ. Based on this, PL results of simulation and measurement are fitted, respectively, and their PL models are shown in Figure 6. It can be found that the PL models of the measurement and simulation match well. The parameters of PL models are shown in Table 1, where α and β are basically the same. The comparison results confirm that the RT simulation parameters are very close to the values in the real environment, indicating that the corrected material parameters can be used to simulate the channel propagation characteristics in different subway tunnel environments. At this time, the material parameters are shown in Table 2.Table 1
PL model parameters at 28 GHz.
αβσMeasurement1.401671.37894.4641RT simulation1.415472.21815.5509Table 2
Material property parameters after calibration.
MaterialFrequency (GHz)Relative permittivityConductivity (S/m)Thickness (m)Roughness (m)Tunnel wallConcrete285.310.480.50.005RailMetal 128——0.050.0001


## 2.1. Channel Measurement

As depicted in Figure1(a), the measurements were conducted in metro Line 7 between Shanghai University and Qihua Rd. in Shanghai, China. The tunnel wall materials are reinforced with concrete. As shown in Figure 1(b), the tunnel can be divided into two sections. One of them is a platform with a length of 28.1 m, and the cross section is rectangular with a height of 5.55 m. Another section is the nonplatform part where the cross section is arched and is 4.96 m high, as shown in Figure 1(c). Along the driving route, there is a straight tunnel with a length of 20 m, a curved tunnel with a length of 100 m, and a long straight tunnel with a length of over 400 m, respectively.Figure 1
The measurement environment: (a) measurement subway tunnel; (b) platform cross section; (c) nonplatform cross section.
(a)(b)(c)The measurement system is illustrated in Figure2. It is mainly composed of Agilent E8257D signal source (transmitter) and Ceyear 4024G spectrum analyzer (receiver). Both transmitting antenna (Tx) and receiving antenna (Rx) are ultra-wideband omnidirectional antennas, and the high-precision rubidium clocks are used to ensure clock synchronization as shown in Figure 3.Figure 2
Measurement system.Figure 3
Ultra-wideband omnidirectional antenna.In the measurements, the transmitter is located at the end of the tunnel platform, close to the tunnel wall, and the height of the transmitting antenna is 3.1 m, as shown in Figure4(a). The receiver is located on the railcar in the center of the tunnel, and the receiving antenna is 2.25 m high. The position of the transmitter remains unchanged, and the measurement distance is 500 m. The input power and the frequency are considered as 10 dBm and 28 GHz, respectively. As the railcar moves, the receiver gradually moves away from the transmitter. We have considered a total of 79 test points, and at each test point, the spectrum analyzer reads and records the received power of the signal. The positions of the transmitting and receiving antennas are shown in Figure 4(b). When the transceiver distance is about 100 m, the sampling interval is 2 m. The interval from 100 m to 300 m is 10 m, and the interval from 300 m to 500 m is 20 m.Figure 4
Transceiver settings in the measurement: (a) the cross section of the measurement tunnel; (b) the positions of Tx and Rx.
(a)(b)


## 2.2. Ray-Tracing Parameter Calibration

Based on the received power from the field measurement, the material property parameters in the RT simulation, such as the material roughness, relative permittivity, and conductivity, can be calibrated. The RT simulation tool used in this article is Wireless Insite (WiSE). The 3D model of the subway tunnel in the measurement is reconstructed, as shown in Figure5. The designs of frequency and positions of antennas in the simulation are the same as in the measurement field. For the concrete and metal materials in simulations, we had set the initial roughness, conductivity, and permittivity and then compared the simulated PL results with the measurement data. According to the compared results, we keep adjusting the parameters until there is a high degree of match between the simulation and measurement results. Figure 6 shows the comparison between the simulated PL and the measurement results after adjusting the material property parameters several times. It can be found that, at most test points, the simulated PL results are very close to the measurement data. Because the field environment is highly complex and there are more reflections, the simulation and measurement results are slightly different at individual test points.Figure 5
3D model of the subway tunnel.Figure 6
Comparison of PL results between measurement and RT simulation at 28 GHz.The classic floating-intercept PL model in [21] is described as follows:(1)PLd=β+10αlgdd0+Xσdb,where α is the slope of the PL model and d0 is the reference transceiver distance, which is 1 m in this paper. β is the model intercept, which represents the PL value when the transceiver distance is the reference distance, and Xσ is a Gaussian random variable with standard deviation of σ. Based on this, PL results of simulation and measurement are fitted, respectively, and their PL models are shown in Figure 6. It can be found that the PL models of the measurement and simulation match well. The parameters of PL models are shown in Table 1, where α and β are basically the same. The comparison results confirm that the RT simulation parameters are very close to the values in the real environment, indicating that the corrected material parameters can be used to simulate the channel propagation characteristics in different subway tunnel environments. At this time, the material parameters are shown in Table 2.Table 1
PL model parameters at 28 GHz.
αβσMeasurement1.401671.37894.4641RT simulation1.415472.21815.5509Table 2
Material property parameters after calibration.
MaterialFrequency (GHz)Relative permittivityConductivity (S/m)Thickness (m)Roughness (m)Tunnel wallConcrete285.310.480.50.005RailMetal 128——0.050.0001


## 3. Channel Propagation Characteristics Based on the RT Method

### 3.1. Simulation Scenarios Description

Referring to the tunnel of Shanghai Line 7, this paper designs tunnel models with a straight tunnel and tunnels with different curvature radiuses and different slopes and sets up a metro train model with reference to trains of Line 7, as shown in Figure7(a).Figure 7
3D models of the subway tunnels and the metro train: (a) 3D models of tunnels; (b) longitudinal section view of the metro train model; (c) cross section view of the metro train model.
(a)(b)(c)All tunnel models designed in this paper are divided into two sections,l1 and l2. The l1 section is a short straight tunnel with a length of 20 m, while l2 section is a tunnel with different structure in different scenarios and has a length of 200 m. As shown in Figure 7(a), l2 of the straight tunnel model is a straight tunnel. In the curved tunnel model, l2 is a curved tunnel with a radius of r, and two r values are designed, 500 m and 300 m, respectively. In the tunnel model with a slope, l2 is an inclined tunnel with a slope of θ, and two θ values are designed, 2° and 3°, respectively. The cross sections of all tunnel models are arched, as shown in Figure 1(c). The metro train model is 24.4 m long, 3 m wide, and 3.8 m high. The interior of the train is shown in Figures 7(b) and 7(c). There are 10 doors, 31 glass windows, 8 chairs, and several vertical handrails inside.This paper considers three types of subway tunnel scenarios: subway tunnel scenarios with different curvature radiuses (Case.2 and Case.3), subway tunnel scenarios with different slopes (Case.4 and Case.5), and subway tunnel scenario with the train (Case.6), as shown in Table3. At the same time, Table 3 shows the length, radius, and slope of the tunnel model for each scenario. Table 4 shows the train model and the dimensions of the internal objects.Table 3
Scenarios and their tunnel models.
ScenarioTunnel modeldl1 (m)dl2 (m)r (m)θ°Metro trainCase.1Straight tunnel20200——WithoutCase.2Curved tunnel 120200500—WithoutCase.3Curved tunnel 220200300—WithoutCase.4Sloped tunnel 120200—2WithoutCase.5Sloped tunnel 220200—3WithoutCase.6Straight tunnel20200——WithTable 4
The metro train model and internal object size.
ModelAmountLength (m)Width (m)Height (m)Train carriage—24.433.8Window (train head)10.0521.2Window (large)221.50.051Window (small)80.50.050.8Train chair82.60.050.9Train handrail170.050.052.6


### 3.2. Simulation Settings

In the simulation, the frequency of the transmitting and receiving antennas is set to 28 GHz, the bandwidth is 100 MHz, both the transmitting and receiving antennas are omnidirectional antennas, and the input power is 10 dBm.The position settings of the receiving and transmitting antennas in the three scenarios are also different, as shown in Figure8. In tunnel scenarios with different curvature radiuses and slopes (Case.1–Case.5), as shown in Figure 8(a), the transmitting antenna is located in the center of the tunnel cross section with a height of 2.48 m. The first receiving antenna is 10 m away from the transmitting antenna, and then a receiving antenna is placed every 5 m until the transceiver distance of 210 m. There are a total of 41 receiving positions, and all receiving antennas are located in the center of the cross section of the tunnel with a height of 2.48 m. In the tunnel scene with the train (Case.6), as shown in Figure 8(b), the transmitting antenna is close to the left tunnel wall, 2.5 m away from the midline of the tunnel cross section and 3 m high. In Case.6, three positions of receiving antennas are considered, all located in the midline of the tunnel cross section. Rx1 is located at the top of the train and is 4.3 m high. Rx2 is located in front of the train and is 1.8 m high. Rx3 is located inside the carriage and is 4.3 m high. At a distance of 15 m, the subway train starts moving away from the transmitting antenna, and the simulations are carried out every 5 m until the train moves to a distance of 200 m from the transmitting antenna.Figure 8
Transceiver antenna position settings: (a) transceiving antennas’ settings in Case.1–Case.5; (b) transceiving antennas’ settings in Case.6.
(a)(b)In the RT simulation, this paper considers four materials: concrete, metal, glass, and plastic. Table5 shows the parameter settings of all materials. The parameters of concrete and metal 1 use the calibration results in Section 2.2, and other material parameter settings use the values recommended by ITU (International Telecommunication Union)-R P.2040 [22]. In addition, we set the number of reflections to 15, the number of transmission to 2, the spacing of rays to 0.1° and assume that no more than 100 rays are received.Table 5
Parameter settings of all materials.
ObjectMaterialFrequency (GHz)Relative permittivityConductivity (S/m)Thickness (m)Roughness (m)Tunnel wallConcrete285.310.480.50.005RailMetal 128——0.050.0001CarriageMetal 228——0.050WindowsGlass286.270.230.030ChairsPlastic28——0.050


## 3.1. Simulation Scenarios Description

Referring to the tunnel of Shanghai Line 7, this paper designs tunnel models with a straight tunnel and tunnels with different curvature radiuses and different slopes and sets up a metro train model with reference to trains of Line 7, as shown in Figure7(a).Figure 7
3D models of the subway tunnels and the metro train: (a) 3D models of tunnels; (b) longitudinal section view of the metro train model; (c) cross section view of the metro train model.
(a)(b)(c)All tunnel models designed in this paper are divided into two sections,l1 and l2. The l1 section is a short straight tunnel with a length of 20 m, while l2 section is a tunnel with different structure in different scenarios and has a length of 200 m. As shown in Figure 7(a), l2 of the straight tunnel model is a straight tunnel. In the curved tunnel model, l2 is a curved tunnel with a radius of r, and two r values are designed, 500 m and 300 m, respectively. In the tunnel model with a slope, l2 is an inclined tunnel with a slope of θ, and two θ values are designed, 2° and 3°, respectively. The cross sections of all tunnel models are arched, as shown in Figure 1(c). The metro train model is 24.4 m long, 3 m wide, and 3.8 m high. The interior of the train is shown in Figures 7(b) and 7(c). There are 10 doors, 31 glass windows, 8 chairs, and several vertical handrails inside.This paper considers three types of subway tunnel scenarios: subway tunnel scenarios with different curvature radiuses (Case.2 and Case.3), subway tunnel scenarios with different slopes (Case.4 and Case.5), and subway tunnel scenario with the train (Case.6), as shown in Table3. At the same time, Table 3 shows the length, radius, and slope of the tunnel model for each scenario. Table 4 shows the train model and the dimensions of the internal objects.Table 3
Scenarios and their tunnel models.
ScenarioTunnel modeldl1 (m)dl2 (m)r (m)θ°Metro trainCase.1Straight tunnel20200——WithoutCase.2Curved tunnel 120200500—WithoutCase.3Curved tunnel 220200300—WithoutCase.4Sloped tunnel 120200—2WithoutCase.5Sloped tunnel 220200—3WithoutCase.6Straight tunnel20200——WithTable 4
The metro train model and internal object size.
ModelAmountLength (m)Width (m)Height (m)Train carriage—24.433.8Window (train head)10.0521.2Window (large)221.50.051Window (small)80.50.050.8Train chair82.60.050.9Train handrail170.050.052.6


## 3.2. Simulation Settings

In the simulation, the frequency of the transmitting and receiving antennas is set to 28 GHz, the bandwidth is 100 MHz, both the transmitting and receiving antennas are omnidirectional antennas, and the input power is 10 dBm.The position settings of the receiving and transmitting antennas in the three scenarios are also different, as shown in Figure8. In tunnel scenarios with different curvature radiuses and slopes (Case.1–Case.5), as shown in Figure 8(a), the transmitting antenna is located in the center of the tunnel cross section with a height of 2.48 m. The first receiving antenna is 10 m away from the transmitting antenna, and then a receiving antenna is placed every 5 m until the transceiver distance of 210 m. There are a total of 41 receiving positions, and all receiving antennas are located in the center of the cross section of the tunnel with a height of 2.48 m. In the tunnel scene with the train (Case.6), as shown in Figure 8(b), the transmitting antenna is close to the left tunnel wall, 2.5 m away from the midline of the tunnel cross section and 3 m high. In Case.6, three positions of receiving antennas are considered, all located in the midline of the tunnel cross section. Rx1 is located at the top of the train and is 4.3 m high. Rx2 is located in front of the train and is 1.8 m high. Rx3 is located inside the carriage and is 4.3 m high. At a distance of 15 m, the subway train starts moving away from the transmitting antenna, and the simulations are carried out every 5 m until the train moves to a distance of 200 m from the transmitting antenna.Figure 8
Transceiver antenna position settings: (a) transceiving antennas’ settings in Case.1–Case.5; (b) transceiving antennas’ settings in Case.6.
(a)(b)In the RT simulation, this paper considers four materials: concrete, metal, glass, and plastic. Table5 shows the parameter settings of all materials. The parameters of concrete and metal 1 use the calibration results in Section 2.2, and other material parameter settings use the values recommended by ITU (International Telecommunication Union)-R P.2040 [22]. In addition, we set the number of reflections to 15, the number of transmission to 2, the spacing of rays to 0.1° and assume that no more than 100 rays are received.Table 5
Parameter settings of all materials.
ObjectMaterialFrequency (GHz)Relative permittivityConductivity (S/m)Thickness (m)Roughness (m)Tunnel wallConcrete285.310.480.50.005RailMetal 128——0.050.0001CarriageMetal 228——0.050WindowsGlass286.270.230.030ChairsPlastic28——0.050


## 4. Simulation Results and Analysis

### 4.1. Subway Tunnel Scenarios with Different Curvature Radiuses (Case.1, Case.2, and Case.3)

The simulation results are executed according to (1), and the PL models of Case.1, Case.2, and Case.3 are achieved, as shown in Figure 9. The PL model parameters are shown in Table 6. It can be found that, with the decrease of the tunnel curvature radius, the PL value at the same transceiver distance increases. This is because the smaller the tunnel curvature radius is, the sooner the line-of-sight (LOS) component of the signal will disappear, and the more the attenuation of the non-line-of-sight (NLOS) component will increase. When the curvature radius is 500 m, the slope of the PL model is close to that of the PL model of free space. In addition, the slope of the floating-intercept PL model of the straight tunnel is smaller than that of the indoor environment in [23] and the urban environment in [24] at 28 GHz. This is mainly because the waveguide effect of the tunnel reduces the power attenuation. Moreover, the obstacles in the subway tunnel are fewer than those in the indoor or urban environment, which reduces the obstruction to signal propagation.Figure 9
PL models of Case.1, Case.2, and Case.3.Table 6
PL model parameters of Case.1, Case.2, and Case.3.
ScenarioαβσCase.11.253964.32270.4357Case.22.064753.48872.4111Case.32.628545.67472.8547The expression for calculating the RMS-DS in [25] is as follows:(2a)t¯=∑i=1NPitiP,(2b)tRMS−DS=∑i=1Npiti2P−t¯2,where P represents the received power at this point and Pi and ti are the received power and time delay of the i-th path, respectively. Based on this, the RMS-DS results of Case.1, Case.2, and Case.3 can be obtained, as shown in Figure 10, and the statistical parameters are shown in Table 7. It can be found that the RMS-DS mean of Case.3 is the largest while the RMS-DS mean of Case.1 is the smallest. This is because, with the decrease of the tunnel curvature radius, multipath signals need to go through more reflections before they can be received, leading to the increase of path difference between multipath signals and the increase of RMS-DS.Figure 10
RMS-DS of Case.1, Case.2, and Case.3.Table 7
RMS-DS statistical parameters of Case.1, Case.2, and Case.3.
ScenarioMean value (ns)Standard deviation (ns)Maximum value (ns)Case.10.61270.28161.9904Case.20.96200.28701.9904Case.31.00660.38401.9904The relationship of estimating the angle spread (AS) in [26] is as follows:(3a)θAS=−2ln∑i=1NejθiPnP,(3b)μθ=arg∑i=1NejθiPi,where P is the received power at this point; Pi and θi are the received power and the direction of arrival or departure of the i-th path, respectively; and μθ is the power weighted mean angle. Based on this, the AS of Case.1, Case.2, and Case.3 can be obtained. In Figure 11, ASA, ESA, ASD, and ESD are the AS of the azimuth angle of arrival (AOA), the elevation angle of arrival (EOA), the azimuth angle of departure (AOD), and the elevation angle of departure (EOD) for each scenario. The AS statistical parameters of Case.1, Case.2, and Case.3 are shown in Table 8. It can be found that both the ASA and the ASD of Case.1, Case.2, and Case.3 are about 10°. When the transceiver distance exceeds 15 m, the ASA and ASD of Case.2 and Case.3 are greater than those of Case.1. The reason is that, in curved tunnels, multipath signals need to be reflected more times before they can be received, leading to the increase of AS. Both the ESA and the ESD of Case.1, Case.2, and Case.3 are about 15°. When the transceiver distance is less than 100 m, both the ESA and the ESD of Case.1, Case.2, and Case.3 decrease monotonously, and those of Case.2 and Case.3 are smaller than those of Case.1. When the transceiver distance is more than 100 m, the ESA and ESD of Case.1, Case.2, and Case.3 gradually tend to be the same. Until the transceiver distance is 150 m, they are basically the same. It can be seen that the curvature radius of the tunnel has a more obvious influence on the AS of azimuth angle than that of elevation angle.Figure 11
AS of Case.1, Case.2, and Case.3: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 8
AS statistical parameters of Case.1, Case.2, and Case.3.
ScenarioMean value (°)Standard deviation (°)Maximum value (°)ASACase.12.27360.87276.0414Case.24.13020.74856.0414Case.34.37340.93646.4141ESACase.13.99802.803012.7750Case.22.93882.659112.7750Case.32.95932.535912.7750ASDCase.12.30520.85156.0413Case.24.25360.76266.0413Case.34.62550.80166.6207ESDCase.13.94612.840412.7749Case.22.95142.650512.7749Case.32.85692.573912.7749


### 4.2. Subway Tunnel Scenarios with Different Curvature Radiuses (Case.1, Case.4, and Case.5)

Based on (1), the PL models of Case.1, Case.4, and Case.5 can be achieved, as shown in Figure 12. The PL model parameters of Case.1, Case.4, and Case.5 are shown in Table 9. It can be found that, as the slope increases, the intercept of the PL model increases. This is mainly because when the transceiver distance is less than 20 m in the tunnel scenario with a larger slope, the signal is reflected more times from the transmitting to the receiving side, leading to a faster attenuation rate of the NLOS component, and this makes the path loss larger. It is worth noting that, with the increase of the transceiver distance, the influence of slope on the propagation of the NLOS component decreases, so the attenuation rate of the NLOS component becomes slow and gradually becomes consistent with that of the straight tunnel. When the transceiver distance is 200 m, the PL values of Case.1, Case.4, and Case.5 have been found to be very close.Figure 12
PL models of Case.1, Case.4, and Case.5.Table 9
PL model parameters of Case.1, Case.4, and Case.5.
αβσCase.11.253964.32270.4357Case.41.206766.97990.5148Case.51.177768.39460.6725The RMS-DS results of Case.1, Case.4, and Case.5 are shown in Figure13, and the statistical parameters are shown in Table 10. It can be found that the RMS-DS mean values of Case.4 and Case.5 scenarios are larger than that of Case.1. The main reason is that, with the increase of tunnel slope, the path difference between multipath signals becomes larger, leading to the increase of RMS-DS. After the transceiver distance is more than 150 m, the RMS-DS values of Case.4 and Case.1 are almost the same. This shows that the multipath component difference caused by the distance between the transmitter and the receiving antenna can be ignored when the transceiver distance is large, which is consistent with the conclusion of that in [27].Figure 13
RMS-DS of Case.1, Case.4, and Case.5.Table 10
RMS-DS statistical parameters of Case.1, Case.4, and Case.5.
Mean value (ns)Standard deviation (ns)Maximum value (ns)Case.10.61270.28161.9904Case.40.73080.31791.9925Case.50.83990.26101.9953The AS results of Case.1, Case.4, and Case.5 are shown in Figure14, and the statistical parameters are shown in Table 11. It can be found that the AS in the tunnel shows a downward trend with the increase of the transceiver distance, which is similar to the conclusion in [14]. When the transceiver distance is about 50 m, the AS values of Case.4 and Case.5 are both smaller than that of Case.1. This means that when the distance between receiving and transmitting antennas is relatively close, in the tunnel with slope, some multipath signals experience more reflection, resulting in increased loss, so they cannot be received, and the AS decreases. When the transceiver distance is more than 150 m, the AS values of three scenarios tend to be the same. This proves that the influence of slope on signal propagation is reduced when the transceiver distance is far.Figure 14
AS of Case.1, Case.4, and Case.5: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 11
AS statistical parameters of Case.1, Case.4, and Case.5.
ScenarioMean value (°)Standard deviation (°)Maximum value (°)ASACase.12.27360.87276.0414Case.42.29060.82046.0478Case.52.17630.95086.0559ESACase.13.99802.803012.7750Case.43.86572.038012.7804Case.53.99931.871112.7873ASDCase.12.30520.85156.0413Case.42.53970.86206.0478Case.51.87750.86716.0560ESDCase.13.94612.840412.7749Case.43.63112.013212.7803Case.54.12231.884512.7874


### 4.3. Subway Tunnel Scenario with the Train (Case.6)

In Case.6, the PL results of Rx at different positions are shown in Figure15. Throughout the measurement distance, the PL of Rx2 is always less than those of Rx1 and Rx3. This is because Rx2 is located in front of the train driver’s cab and can receive the signals reflected from the tunnel walls and the surface of the train. The PL of Rx3 is always the highest, mainly because Rx3 is located inside the metro train carriage. When the signal reaches the receiving end, it needs to penetrate the train windows, resulting in extra energy loss. When the transceiver distance is 200 m, the loss through the train windows is about 15 dB. The PL model parameters of Rx1, Rx2, and Rx3 are shown in Table 12. It can be found that the PL results of Rx1 and Rx2 gradually tend to be the same with the increase of the transceiver distance, indicating that the influence of the train on signal propagation gradually decreases with the increase of the transceiver distance.Figure 15
PL model of Rx1, Rx2, and Rx3 in Case.6.Table 12
PL model parameters of Rx1, Rx2, and Rx3 in Case.6.
αβσRx11.280069.33390.2606Rx21.347865.45810.4733Rx31.434478.13280.6242The RMS-DS results of Rx1, Rx2, and Rx3 are shown in Figure16, and the RMS-DS statistical parameters are shown in Table 13. The average value of the RMS-DS of Rx3 is significantly greater than those of Rx1 and Rx2. This is mainly because Rx3 can receive the signals reflected from the rear of the train, which increases the path difference between multipath signals. Further, it can be seen that when the antenna is located inside the carriage, the reflection environment is more complicated. The RMS-DS of Rx2 is slightly larger than that of Rx1, mainly because Rx2 can receive the signals reflected by the surface of the train.Figure 16
RMS-DS of Rx1, Rx2, and Rx3 in Case.6: (a) RMS-DS of Rx1 and Rx2; (b) RMS-DS of Rx3.
(a)(b)Table 13
RMS-DS statistical parameters of Rx1, Rx2, and Rx3 in Case.6.
Mean value (ns)Standard deviation (ns)Maximum value (ns)Rx10.87220.20021.1010Rx21.29170.18112.0691Rx318.763918.275070.9541The AS results of Rx1, Rx2, and Rx3 are shown in Figure17, and the statistical parameters are shown in Table 14. When the transceiver distance is more than 60 m, the AS of Rx1 and Rx3 gradually tends to be the same. This is because, with the increase of transceiver distance, the signals reflected from the rear of the carriage become weaker and weaker, leading to a consistent multipath signal distribution of Rx1 and Rx3. However, Rx2 can always receive the strong signals reflected from the train surface, so the AS of arrival of Rx2 is always larger than those of Rx1 and Rx3. In addition, with the increase of the transceiver distance, the ASD and ESD of Rx1, Rx2, and Rx3 tend to be the same.Figure 17
AS of Rx1, Rx2, and Rx3 in Case.6: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 14
AS statistical parameters of Rx1, Rx2, and Rx3 in Case.6.
Rx positionMean value (°)Standard deviation (°)Maximum value (°)ASARx12.11790.47082.8648Rx25.74711.072910.4650Rx33.28831.74609.1013ESARx12.68730.78456.3774Rx29.01752.892024.3014Rx33.58552.232712.3933ASDRx11.99940.34792.6501Rx23.27480.94724.8599Rx33.25851.23867.1010ESDRx13.09970.71044.2279Rx23.10501.906912.4340Rx32.51690.83464.5651


## 4.1. Subway Tunnel Scenarios with Different Curvature Radiuses (Case.1, Case.2, and Case.3)

The simulation results are executed according to (1), and the PL models of Case.1, Case.2, and Case.3 are achieved, as shown in Figure 9. The PL model parameters are shown in Table 6. It can be found that, with the decrease of the tunnel curvature radius, the PL value at the same transceiver distance increases. This is because the smaller the tunnel curvature radius is, the sooner the line-of-sight (LOS) component of the signal will disappear, and the more the attenuation of the non-line-of-sight (NLOS) component will increase. When the curvature radius is 500 m, the slope of the PL model is close to that of the PL model of free space. In addition, the slope of the floating-intercept PL model of the straight tunnel is smaller than that of the indoor environment in [23] and the urban environment in [24] at 28 GHz. This is mainly because the waveguide effect of the tunnel reduces the power attenuation. Moreover, the obstacles in the subway tunnel are fewer than those in the indoor or urban environment, which reduces the obstruction to signal propagation.Figure 9
PL models of Case.1, Case.2, and Case.3.Table 6
PL model parameters of Case.1, Case.2, and Case.3.
ScenarioαβσCase.11.253964.32270.4357Case.22.064753.48872.4111Case.32.628545.67472.8547The expression for calculating the RMS-DS in [25] is as follows:(2a)t¯=∑i=1NPitiP,(2b)tRMS−DS=∑i=1Npiti2P−t¯2,where P represents the received power at this point and Pi and ti are the received power and time delay of the i-th path, respectively. Based on this, the RMS-DS results of Case.1, Case.2, and Case.3 can be obtained, as shown in Figure 10, and the statistical parameters are shown in Table 7. It can be found that the RMS-DS mean of Case.3 is the largest while the RMS-DS mean of Case.1 is the smallest. This is because, with the decrease of the tunnel curvature radius, multipath signals need to go through more reflections before they can be received, leading to the increase of path difference between multipath signals and the increase of RMS-DS.Figure 10
RMS-DS of Case.1, Case.2, and Case.3.Table 7
RMS-DS statistical parameters of Case.1, Case.2, and Case.3.
ScenarioMean value (ns)Standard deviation (ns)Maximum value (ns)Case.10.61270.28161.9904Case.20.96200.28701.9904Case.31.00660.38401.9904The relationship of estimating the angle spread (AS) in [26] is as follows:(3a)θAS=−2ln∑i=1NejθiPnP,(3b)μθ=arg∑i=1NejθiPi,where P is the received power at this point; Pi and θi are the received power and the direction of arrival or departure of the i-th path, respectively; and μθ is the power weighted mean angle. Based on this, the AS of Case.1, Case.2, and Case.3 can be obtained. In Figure 11, ASA, ESA, ASD, and ESD are the AS of the azimuth angle of arrival (AOA), the elevation angle of arrival (EOA), the azimuth angle of departure (AOD), and the elevation angle of departure (EOD) for each scenario. The AS statistical parameters of Case.1, Case.2, and Case.3 are shown in Table 8. It can be found that both the ASA and the ASD of Case.1, Case.2, and Case.3 are about 10°. When the transceiver distance exceeds 15 m, the ASA and ASD of Case.2 and Case.3 are greater than those of Case.1. The reason is that, in curved tunnels, multipath signals need to be reflected more times before they can be received, leading to the increase of AS. Both the ESA and the ESD of Case.1, Case.2, and Case.3 are about 15°. When the transceiver distance is less than 100 m, both the ESA and the ESD of Case.1, Case.2, and Case.3 decrease monotonously, and those of Case.2 and Case.3 are smaller than those of Case.1. When the transceiver distance is more than 100 m, the ESA and ESD of Case.1, Case.2, and Case.3 gradually tend to be the same. Until the transceiver distance is 150 m, they are basically the same. It can be seen that the curvature radius of the tunnel has a more obvious influence on the AS of azimuth angle than that of elevation angle.Figure 11
AS of Case.1, Case.2, and Case.3: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 8
AS statistical parameters of Case.1, Case.2, and Case.3.
ScenarioMean value (°)Standard deviation (°)Maximum value (°)ASACase.12.27360.87276.0414Case.24.13020.74856.0414Case.34.37340.93646.4141ESACase.13.99802.803012.7750Case.22.93882.659112.7750Case.32.95932.535912.7750ASDCase.12.30520.85156.0413Case.24.25360.76266.0413Case.34.62550.80166.6207ESDCase.13.94612.840412.7749Case.22.95142.650512.7749Case.32.85692.573912.7749


## 4.2. Subway Tunnel Scenarios with Different Curvature Radiuses (Case.1, Case.4, and Case.5)

Based on (1), the PL models of Case.1, Case.4, and Case.5 can be achieved, as shown in Figure 12. The PL model parameters of Case.1, Case.4, and Case.5 are shown in Table 9. It can be found that, as the slope increases, the intercept of the PL model increases. This is mainly because when the transceiver distance is less than 20 m in the tunnel scenario with a larger slope, the signal is reflected more times from the transmitting to the receiving side, leading to a faster attenuation rate of the NLOS component, and this makes the path loss larger. It is worth noting that, with the increase of the transceiver distance, the influence of slope on the propagation of the NLOS component decreases, so the attenuation rate of the NLOS component becomes slow and gradually becomes consistent with that of the straight tunnel. When the transceiver distance is 200 m, the PL values of Case.1, Case.4, and Case.5 have been found to be very close.Figure 12
PL models of Case.1, Case.4, and Case.5.Table 9
PL model parameters of Case.1, Case.4, and Case.5.
αβσCase.11.253964.32270.4357Case.41.206766.97990.5148Case.51.177768.39460.6725The RMS-DS results of Case.1, Case.4, and Case.5 are shown in Figure13, and the statistical parameters are shown in Table 10. It can be found that the RMS-DS mean values of Case.4 and Case.5 scenarios are larger than that of Case.1. The main reason is that, with the increase of tunnel slope, the path difference between multipath signals becomes larger, leading to the increase of RMS-DS. After the transceiver distance is more than 150 m, the RMS-DS values of Case.4 and Case.1 are almost the same. This shows that the multipath component difference caused by the distance between the transmitter and the receiving antenna can be ignored when the transceiver distance is large, which is consistent with the conclusion of that in [27].Figure 13
RMS-DS of Case.1, Case.4, and Case.5.Table 10
RMS-DS statistical parameters of Case.1, Case.4, and Case.5.
Mean value (ns)Standard deviation (ns)Maximum value (ns)Case.10.61270.28161.9904Case.40.73080.31791.9925Case.50.83990.26101.9953The AS results of Case.1, Case.4, and Case.5 are shown in Figure14, and the statistical parameters are shown in Table 11. It can be found that the AS in the tunnel shows a downward trend with the increase of the transceiver distance, which is similar to the conclusion in [14]. When the transceiver distance is about 50 m, the AS values of Case.4 and Case.5 are both smaller than that of Case.1. This means that when the distance between receiving and transmitting antennas is relatively close, in the tunnel with slope, some multipath signals experience more reflection, resulting in increased loss, so they cannot be received, and the AS decreases. When the transceiver distance is more than 150 m, the AS values of three scenarios tend to be the same. This proves that the influence of slope on signal propagation is reduced when the transceiver distance is far.Figure 14
AS of Case.1, Case.4, and Case.5: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 11
AS statistical parameters of Case.1, Case.4, and Case.5.
ScenarioMean value (°)Standard deviation (°)Maximum value (°)ASACase.12.27360.87276.0414Case.42.29060.82046.0478Case.52.17630.95086.0559ESACase.13.99802.803012.7750Case.43.86572.038012.7804Case.53.99931.871112.7873ASDCase.12.30520.85156.0413Case.42.53970.86206.0478Case.51.87750.86716.0560ESDCase.13.94612.840412.7749Case.43.63112.013212.7803Case.54.12231.884512.7874


## 4.3. Subway Tunnel Scenario with the Train (Case.6)

In Case.6, the PL results of Rx at different positions are shown in Figure15. Throughout the measurement distance, the PL of Rx2 is always less than those of Rx1 and Rx3. This is because Rx2 is located in front of the train driver’s cab and can receive the signals reflected from the tunnel walls and the surface of the train. The PL of Rx3 is always the highest, mainly because Rx3 is located inside the metro train carriage. When the signal reaches the receiving end, it needs to penetrate the train windows, resulting in extra energy loss. When the transceiver distance is 200 m, the loss through the train windows is about 15 dB. The PL model parameters of Rx1, Rx2, and Rx3 are shown in Table 12. It can be found that the PL results of Rx1 and Rx2 gradually tend to be the same with the increase of the transceiver distance, indicating that the influence of the train on signal propagation gradually decreases with the increase of the transceiver distance.Figure 15
PL model of Rx1, Rx2, and Rx3 in Case.6.Table 12
PL model parameters of Rx1, Rx2, and Rx3 in Case.6.
αβσRx11.280069.33390.2606Rx21.347865.45810.4733Rx31.434478.13280.6242The RMS-DS results of Rx1, Rx2, and Rx3 are shown in Figure16, and the RMS-DS statistical parameters are shown in Table 13. The average value of the RMS-DS of Rx3 is significantly greater than those of Rx1 and Rx2. This is mainly because Rx3 can receive the signals reflected from the rear of the train, which increases the path difference between multipath signals. Further, it can be seen that when the antenna is located inside the carriage, the reflection environment is more complicated. The RMS-DS of Rx2 is slightly larger than that of Rx1, mainly because Rx2 can receive the signals reflected by the surface of the train.Figure 16
RMS-DS of Rx1, Rx2, and Rx3 in Case.6: (a) RMS-DS of Rx1 and Rx2; (b) RMS-DS of Rx3.
(a)(b)Table 13
RMS-DS statistical parameters of Rx1, Rx2, and Rx3 in Case.6.
Mean value (ns)Standard deviation (ns)Maximum value (ns)Rx10.87220.20021.1010Rx21.29170.18112.0691Rx318.763918.275070.9541The AS results of Rx1, Rx2, and Rx3 are shown in Figure17, and the statistical parameters are shown in Table 14. When the transceiver distance is more than 60 m, the AS of Rx1 and Rx3 gradually tends to be the same. This is because, with the increase of transceiver distance, the signals reflected from the rear of the carriage become weaker and weaker, leading to a consistent multipath signal distribution of Rx1 and Rx3. However, Rx2 can always receive the strong signals reflected from the train surface, so the AS of arrival of Rx2 is always larger than those of Rx1 and Rx3. In addition, with the increase of the transceiver distance, the ASD and ESD of Rx1, Rx2, and Rx3 tend to be the same.Figure 17
AS of Rx1, Rx2, and Rx3 in Case.6: (a) ASA; (b) ESA; (c) ASD; (d) ESD.
(a)(b)(c)(d)Table 14
AS statistical parameters of Rx1, Rx2, and Rx3 in Case.6.
Rx positionMean value (°)Standard deviation (°)Maximum value (°)ASARx12.11790.47082.8648Rx25.74711.072910.4650Rx33.28831.74609.1013ESARx12.68730.78456.3774Rx29.01752.892024.3014Rx33.58552.232712.3933ASDRx11.99940.34792.6501Rx23.27480.94724.8599Rx33.25851.23867.1010ESDRx13.09970.71044.2279Rx23.10501.906912.4340Rx32.51690.83464.5651


## 5. Conclusions

Based on the RT simulation method, this paper studies the propagation characteristics at 28 GHz in a variety of subway tunnel scenarios. The actual measurement data is used to calibrate the property parameters of the materials in order to execute simulations. In addition, tunnel models with different curvature radiuses, different slopes, and a train are established. The PL, RMS-DS, and AS results of three different tunnel scenarios are analyzed. The main results are as follows:(1)
For subway tunnel scenarios with different curvature radiuses, with the increase of transceiver distance, in tunnels with a smaller radius, the LOS component of the signal will disappear earlier, and the attenuation of NLOS components will accelerate, resulting in the increase of PL and RMS-DS. The curvature radius of the tunnel has a more obvious effect on the AS of the arrival angle. The smaller the curvature radius of the tunnel is, the larger the ASA and ASD will be.(2)
On the premise of conforming to the subway tunnel construction standards, for subway tunnel scenarios with different slopes, the difference of slopes will have a significant impact on the channel characteristics within a transceiver distance of 100 m. The tunnel with a larger slope will have larger PL and RMS-DS results. When the transceiver distance is about 50 m, the ASA and ESA in the subway tunnel with a slope are obviously smaller than those in the straight tunnel. When the transceiver distance is more than 150 m, the influence of the slope on channel characteristics gradually decreases.(3)
For the subway tunnel scenario with the metro train, when the receiving antenna is located in front of the train, it can receive the signals reflected by the train surface, so the PL is smaller, and the RMS-DS, ASA, and ESA are all increased. When the receiving antenna is located inside the carriage, the energy loss caused by the signal penetrating the train window is about 15 dB. Because the signals reflected from the rear of the train can be received, the multipath distribution is more complicated, and the RMS-DS is significantly larger than those in other scenarios.These results can provide reference for the design of 5G communication systems in subway tunnels for future challenges.



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*Source: 7666624-2021-09-27.xml*