Analysis and Modeling of Propagation in Tunnel at 3.7 and 28 GHz

Abstract

In present-day society, train tunnels are extensively used as a means of transportation. Therefore, to ensure safety, streamlined train operations, and uninterrupted internet access inside train tunnels, reliable wave propagation modeling is required. We have experimented and measured wave propagation models in a 1674 m long straight train tunnel in South Korea. The measured path loss and the received signal strength were modeled with the Close-In (CI), Floating intercept (FI), CI model with a frequency-weighted path loss exponent (CIF), and alpha-beta-gamma (ABG) models, where the model parameters were determined using minimum mean square error (MMSE) methods. The measured and the CI, FI, CIF, and ABG model-derived path loss was plotted in graphs, and the model closest to the measured path loss was identified through investigation. Based on the measured results, it was observed that every model had a comparatively lower (n < 2) path loss exponent (PLE) inside the tunnel. We also determined the path loss component's possible deviation (shadow factor) through a Gaussian distribution considering zero mean and standard deviation calculations of random error variables. The FI model outperformed all the examined models as it yielded a path loss closer to the measured datasets, as well as a minimum standard deviation of the shadow factor.

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Computers, Materials & Continua
DOI:10.32604/cmc.2022.023086
Article
Analysis and Modeling of Propagation in Tunnel at 3.7 and 28 GHz
Md Abdus Samad1,2and Dong-You Choi1,*
1Department of Information and Communication Engineering, Chosun University, Gwangju, 61452, Korea
2Department of Electronics and Telecommunication Engineering, International Islamic University Chittagong,
Chittagong, 4318, Bangladesh
*Corresponding Author: Dong-You Choi. Email: dychoi@chosun.ac.kr
Received: 27 August 2021; Accepted: 15 October 2021
Abstract: In present-day society, train tunnels are extensively used as a means
of transportation. Therefore, to ensure safety, streamlined train operations,
and uninterrupted internet access inside train tunnels, reliable wave prop-
agation modeling is required. We have experimented and measured wave
propagation models in a 1674 m long straight train tunnel in South Korea.
The measured path loss and the received signal strength were modeled with the
Close-In (CI), Floating intercept (FI), CI model with a frequency-weighted
path loss exponent (CIF), and alpha-beta-gamma (ABG) models, where
the model parameters were determined using minimum mean square error
(MMSE) methods. The measured and the CI, FI, CIF, and ABG model-
derived path loss was plotted in graphs, and the model closest to the measured
path loss was identified through investigation. Based on the measured results,
it was observed that every model had a comparatively lower (n <2) path loss
exponent (PLE) inside the tunnel. We also determined the path loss com-
ponent’s possible deviation (shadow factor) through a Gaussian distribution
considering zero mean and standard deviation calculations of random error
variables. The FI model outperformed all the examined models as it yielded
a path loss closer to the measured datasets, as well as a minimum standard
deviation of the shadow factor.
Keywords: Path loss; shadow factor; telecommunications; train tunnel; wave
propagation; wireless networks
1Introduction
With the rapidly increasing pace of human lives, there has been an increase in the widespread
usage of tunnels for a variety of purposes, such as transportation, mining of fossil fuels, minerals, and
military operations. Among these types of tunnels, train tunnels play an essential role in present day
life. Consequently, deploying a 5G network inside a tunnel is critical to ensure security and safety,
and to increase the efficiency of train operations [1]. Reliable transmission is required to achieve a
stable and efficient telecommunication facility between the transmitter and receiver. Path loss is an
essential component that may be adversely affected by several elements, such as signal frequency,

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distance from source to destination, environmental conditions, effect of signal fading and weather
conditions [2]. Numerous models of various propagation pathway losses for multiple interferences
and noise-limited settings have been investigated in myriad ways to address the random characteristic
of wireless networks [3].
Nevertheless, knowledge of radio propagation inside a tunnel is essential for setting up the
transmitter and receiver and to actualize the system specifications. For instance, statistical features on
the wireless channel are significant in defining transmitter and receiver characteristics and in budget
link computation, such as the probability density function of the received signal intensity and fade
durations. In addition, the current radio propagation models typically predict the path loss, power
delay profile, or delay spread for specific transmitter and receiver locations [4]. However, it is generally
accepted that the propagation inside a tunnel is distinctly different when compared to other types of
propagation media, such as outdoor, outdoor to indoor, indoor to outdoor, or indoor-to-indoor radio
wave propagation [5]. The fundamental difference in the tunnel is that the radio wave is enclosed by
the blocking surface (of the tunnel) through which the refracted wave cannot reach the receiver, and
as such a propagated signal is received in other cases through a penetration loss at the tunnel blocking
plane. Therefore, the propagation of radio waves inside the tunnel must be investigated independently.
The properties of the wireless propagation channel determine the ultimate performance of a
wireless telecommunication network based on the required quality of service (QoS). Consequently,
a realistic understanding of wireless propagation channels in a tunnel environment is essential. To
date, several studies on communication channels have been conducted in various tunnels [6–8]. In
contrast to open-air propagation, tunnel propagation includes electromagnetic waves in an enclosed
environment [9]. A leaky feeder communication system can be deployed inside confined locations,
in particular inside road or rail tunnels [5]. The cable is leaky in the sense that it includes gaps or
slots in its outer conductor that allow radio signals to leak into or out of the cable along its entire
length. As a result of such signal loss, line amplifiers must be installed at regular intervals to boost
the signal back to acceptable levels that results in significant weight and cost increases [10]. However,
there is a high probability that the cable can be damaged inside the tunnel, resulting in communication
complications in the entire tunnel. Consequently, leaky feeders are not generally deployed inside
tunnels for telecommunication purposes.
Currently, modal expansion in tunnels or corridors is used as a standard approach in wave
propagation analysis [4,11–13]. Given that a tunnel is considered an empty waveguide, the modal
expansion technique can be applied to determine wave propagation. The cross-section of the tunnel
can be represented as the sum of the transverse eigenmodes above the cutoff frequency. However,
this technique becomes ineffective at high frequencies, such as the millimeter wavelength where the
dimensions of the transverse wavelength are far broader, and numerous modes need to be considered.
Radio-wave propagation modeling inside a tunnel can be performed using electromagnetic waves
by numerical methods. However, the numerical approach of finding radio wave propagation inside a
tunnel is complex and requires large computing capacity. Consequently, several simplified techniques
to reduce the computational complexity were proposed in subsequent studies: namely the finite
difference time domain (FDTD) [14], Crank Nicolson (CN) method [15], vector parabolic equation
(VPE) [16,17], scalar parabolic equation (SPE) [17], and uniform theory of diffraction (UTD) [18–20].
Nevertheless, all these simplified techniques are hindered by certain impediments such as: the usage
of the FDTD method is limited to the large-sized tunnel, the CN entails the resolution of sets of
simultaneous equations that might become large enough that dense mesh issues cannot be addressed
efficiently, the VPE technique assumes that fields travel within 30◦in the propagation direction, the

CMC, 2022, vol.71, no.2 3129
SPE can only be used for tunnels with perfect electrical conductor (PEC) walls, and UTD cannot be
used at the junctions where tunnels do not cross perpendicularly.
A widely-accepted path loss model can be implemented in a tunnel using the ray-tracing technique
(RT). However, this technique has several limitations in the implementation and analysis of RT signals.
For example, an implementation through delay line time-domain analysis is minimal if the minimum
delay is less than 8 ns (in which case, it will require a larger bandwidth (BW); for instance, a 1 ns
time delay will require 1 GHz BW) [21]. While an alternative implementation utilizes the shooting and
bouncing RT realization technique, this approach has the impediment of the hypothetical size of the
receiver receiving the propagated ray [22,23]. Another implementation of RT is through 3D ray-tracing
modeling, which has to deal with the challenge of obtaining convergence results as there are numerous
reflections [24].
Consequently, modal expansion, numerical approach, and RT-based techniques of wave propaga-
tion in tunnels have significant challenges. Conversely, a large-scale path loss model was employed for
model wave propagation in the tunnel [25], and the results indicate that large-scale path loss models
could be effective at modelling radio wave propagation inside tunnels. Moreover, large-scale path loss
models have been used to model indoor corridors [26,27] and stairwells [28]. Therefore, we used large-
scale path loss models to model the measured data, and found that the results were satisfactory. This
study makes the following contributions:
•We examined the wave propagation in the newly built train tunnel, called Mangyang Tunnel 2, in
South Korea, and the measured path loss was modeled using the CI, FI, CIF, and ABG models.
•The path loss parameters of the CI, FI, CIF, and ABG models were calculated using the MMSE
optimization technique.
•We analyzed the free space path loss (FSPL) and PLE variations of the CI, FI, CIF, and ABG
models over 3.7 to 28 GHz frequency bands.
•We also modeled the shadow factor using the Gaussian distribution of the studied path loss
models.
The remainder of this paper is organized as follows: Section 2 provides experimental scenarios
and experimental parameter descriptions. Section 3 provides analytical models of CI, FI, CIF, and
ABG models and MMSE-derived optimized parameter calculation procedures. Section 4 discusses
the outcomes obtained from the experimental results. Finally, the conclusions are presented in
Section 5.
2Measurement Experiment
This section describes the measurement technique, soundings, and instruments used for the
experiment, as well as characterizing the equipment used at the transmitter and receiver ends.
2.1 Measuring Tools
This section includes the detailed description of the channel sounder and the scenarios covered
in this measurement experiment. The basic architecture of the experimental scenario is illustrated in
Fig. 1. We utilized the M5183B keysight signal generator at the transmitter end and the keysight
PXI 9393A signal analyzer at the receiver end. The MXG N5183B signal generator can transmit
continuous wave (CW) signals at 9–40 GHz. The PXI 9393A signal analyzer used as the receiver
has a frequency range of 9–30 GHz. Guided horn antennas at the frequency of 3.5 GHz (directional
antenna horn), 28 GHz (directional antenna horn), and 28 GHz tracking antenna system (TAS) were

3130 CMC, 2022, vol.71, no.2
used in the experiment, where the antenna gain was 10, 20, and 20 dBi, respectively. The guided
horn antennas were assembled with horizontal-horizontal co-polarization. The specific computing
operational parameters are listed in Tab. 1. High-frequency bands from RF to microwave frequency
can be generated using the analog signal generator MXG N5183B [29]. Analog signal generation offers
the possibility of adding amplitude, frequency, phase, and pulse modulation to the (CW) transmissions
from the transmitter. Moreover, frequency changeover can be performed using a listing mode with
a switching time of 600 μs. In the sweep mode, the lists change step by step, similar to frequency
switching. The system can produce a low power of approximately—−130 dBm and a maximum power
of approximately +20 dBm. The level of accuracy of the signal generator is approximately ±0.7 dB
(at 10 GHz), and at 1 GHz with a 20 kHz offset, the single-sideband modulation phase noise of the
device is –124 dBc/Hz. In the range of 0.5–64 rad, the signal generator may produce a pulse width of
10 ns and pulse modulation phase deviation in the normal mode. The frequency range of 9 kHz to 9,
4, 14, 18, or 27 GHz was analyzed with this instrument in an extended mode from 3, 6 —50 GHz. The
absolute amplitude accuracy was ±0.13 dB, and the frequency switching was approximately smaller
than 135 μs. The intermodulation of the 3rd order was approximately +31 dBm, and the device showed
a medium noise level of up to −168 dBm/Hz.
Figure 1: Channel sounder architecture
Table 1: Channel specifications and configuration parameters
Parameters 3 GHz 28 GHz 28 GHz
TAS
Operating freq. (GHz) 3.7 28 28
Bandwidth (MHz) 1 1 1
Tx antenna Horn Horn Horn
Rx antenna † 
LNAgain(dB) 575757
System gain (dB) 40 40 40
Tx antenna height (m) 2 2 2
(Continued)

CMC, 2022, vol.71, no.2 3131
Table 1: Continued
Parameters 3 GHz 28 GHz 28 GHz
TAS
Rx antenna height (m) 1.5 1.5 1.5
Antenna gain 10 20 20
Beam width 45–45◦18–21◦18–21◦
Polarization H H H
Cable loss (dB) 2.3 6.5 6.5
Notes: †Double ridged waveguide horn antenna (typical gain: 10 dBi), 20 dBi WR28
standard waveguide horn antenna, 20 dBi WR28 standard waveguide horn antenna with
a16×2 array system.
2.2 Experiment Description
The measurement experiment site is Mangyang Tunnel 2, located in Mangyang-ri, Giseong-myeon,
Uljin-gun, Gyeongsangbuk-do, South Korea. The newly built tunnel, Mangyang Tunnel 2,isused
for transportation by trains. The experiments were conducted in the tunnel before its opening, and
consequently, safety issues were easily ensured. Some of the measurement attempts are presented
in Figs. 2a–2b. All the equipment and technical support during the measurement experiment was
provided by TA Engineering Inc., South Korea. The organization deployed a physical transmitter
and receiver, a mobile trolley, and other experimental facilities. Mechanical adjustments allow the
transmitter’s antenna to be physically modified. The tunnel geometry at the entrance (of the experiment
starting point) and some of the irregularities in the tunnel structure are shown in Figs. 2c–2d.The
receiver unit was installed on a trolley, which was specially designed for experimental purposes. The
transmitter’s horn antenna was directed toward the central receiver unit, while the receiver trolley was
moved inside the tunnel at regular intervals of 10 m up to 1500 m and then at regular intervals of 20 m
for the rest of the path, and the received signal strength was measured. Thus, the received signal was
measured at a total of 160 places.
2.3 Data Pre-Processing
Path loss is crucial in radio channel models to design the link budget and coverage of wireless
networks. The path loss of a radio link can be calculated as:
PL =PTx −PRx +GTx +GRx −CTx −CRx (1)
where PTx is the transmitted signal power, PRx is the received signal power, GTx and GRx are the gains of
the used antennas, and CTx,CRx are the cable losses at the Tx and Rx ends, respectively. We measured the
received power, and the other gain-related parameters were calculated from the system specifications
and datasheets.
3Path Loss Prediction Models
Absorption and scattering are two primary processes in large-scale signal attenuation. Typically,
path loss and shadowing are used to describe the large-scale signal attenuation. The relationship
between path loss and channel distance is typically characterized by two models: single-frequency
model and multi-frequency model, based on empirical data acquired from channel measurements. The
large-scale CI, FI, CIF, and ABG models have a fixed mathematical structure, and certain parameters

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whose values change according to operational frequency, terrain setting, and environmental factors.
This section determines the propagation parameters using the CI, FI, CIF, and ABG models, which
are discussed in detail in the following subsections.
Figure 2: (a) Receiver movement trolley on the train rail, (b) Transmitter and the receiver together at
an initial measurement, (c) Tunnel geometry at the entrance on one side, and (d) Structural changes
in the tunnel: change in tunnel structure at the points 220, 770, 1000, 1260, 1500 m
3.1 Single Frequency Propagation
3.1.1 Close-In (CI) Model
The Equation for the CI model of wave propagation is:
PLCI(f,d)=L(f,1m)+10nlog10 (d)+SCI
μ,σ[dB] for d ≥1m(2)
where Sis a Gaussian random variable, which means that the random variable can be expressed
through the mean (μ) and standard deviation σin dB, where the mean (μ) is zero, but the standard
deviation (σ) is a non-zero value. The random variable Sshows large-scale channel variations within
a limit (defined by the probability density function) as a result of the shadowing effect [30]. The
free space path loss L(f,1m)is given by 10log10(4πf/c)2for a distance of 1 m, and n is the PLE.
The PLE (n) path loss pattern is determined by the MMSE method that equals the value determined
to the minimum mean square error (by reducing σ) with the original physical anchor point, realized
by the free space power transmitted by the transmitting antenna [31]. To determine the optimum PLE
where the path loss is minimum, Eq. (2) can be rearranged using the MMSE method as
SCI
μ,σ=PLCI(f,d)[dB] −L(f,1m)−10nlog10 (d)for d ≥1m(3)

CMC, 2022, vol.71, no.2 3133
Assuming F=PLCI(f,d)[dB] −L(f,1m),andZ=10log10(d), then the Eq. (2) canwrittenas:
SCI
μ,σ=F−nZ (4)
The standard deviation of the shadow factor can be determined as:
σCI =Σ(SCI
μ,σ)2N=(F−nZ)2N(5)
where Nis the number of Tx-Rx separation distances. Minimizing the shadow factor with standard
deviation σCI is commensurate to reducing the term (F−nZ)2.If(F−nZ)2is reduced, the
derivative of nshould be zero:
d(F−nZ)2dn =2Z(nZ −F)=2Z(nZ −F)=2nZ2−ZF =0 (6)
Therefore, from Eq. (6):
n=FZZ2(7)
Consequently, the lowest standard deviation for the CI model is
σCI
min =(F−nZ)2N(8)
The calculated values of nfor the CI model are listed in Tab. 2.
Table 2: Parameters of the different propagation techniques
Freq.
(GHz)
FSPL PLE (β)γ(b)
CI FI
(α)
CIF ABG
(β)
CI
(n)
FI
(β)
CIF
(n)
ABG
(α)
CIF
(β)
ABG
(γ)
3.7 43.81 48.15 43.81 1.70 1.54
28 61.38 82.97 61.38 59.41 1.61 0.85 1.61 1.15 −0.07 1.05
28 61.38 74.27 61.38 1.51 1.05
3.1.2 Floating-Intercept (FI) Model
TheFIpathlossmodelisexpressedby:
PLFI(d)[dB] =α+10 ·βlog10 (d)+SFI
μ,σ(9)
where αis the f loating-intercept in dB, which is equivalent to the free space path loss, and βis the
slope of the path loss vs. frequency line, which is comparable to the PLE as calculated in the CI model.
The term Sis a Gaussian random variable with zero mean and standard deviation σCI, defining large-
scale signal variations. This method is also utilized in WINNER II [32] and 3GPP standards [33].
Remarkably, Eq. (9) requires two parameters, whereas the CI method requires only a single parameter,

3134 CMC, 2022, vol.71, no.2
PLE (n). Assuming, F=PLFI(d)[dB], and Z=10log10 (d)the minimum shadow factor can be
determined using Eq. (10).
SFI
μ,σ=F−α−βZ(10)
and the SF standard deviation is:
σFI =(SFI
μ,σ)2/N=(G−α−βZ)2/N(11)
The minimum standard deviation σFI was determined based on the minimum value of the term
(G−α−βZ)2/N.AsthetermNis a constant number, it needs to minimize (F−α−βZ)2and,
the same can be achieved by finding the derivative with respect to αand βas follows:
∂(F−α−βZ)2∂α =2(α +βZ−F)=2Nα+βZ−F=0 (12)
∂(F−α−βZ)2∂β =2Z(α +βZ−F)=2αZ+βZ2−ZF=0 (13)
Eqs. (12) and (13) yield:
Nα+βZ−F=0 (14)
αZ+βZ2−ZF =0 (15)
Combining (14) and (15),weget:
α=ZZF −Z2FZ2
−NZ2(16)
β=ZF−NZFZ2
−NZ2(17)
The optimum standard deviation of SF can be achieved by replacing αand βin Eq. (11) with
Eqs. (16) and (17), respectively. The mean values of all vector elements were determined directly in the
dB scale. The calculated values of the term nfor the FI model are listed in Tab. 2.
3.2 Multi-Frequency Propagation
3.2.1 CIF Model
In [3], a multi-frequency method was considered adequate in a closed indoor environment, as
frequency-dependent loss occurs after a distance of 1 m from the transmitter owing to the surrounding
environment. The CI model can be adapted to implement the frequency-dependent path loss exponent
(CIF) that utilizes the same physically driven free space path loss anchor at 1 m as the CI model. The
path loss of the CIF method is calculated by:
PLCIF (f,d)[dB] =L(f,1m)+(n(1−n)+nbf f0)10 ·log(d1m)+SCIF
μ,σ(18)

CMC, 2022, vol.71, no.2 3135
where d(m)is the distance between Tx and Rx greater than 1 m, nis the path loss exponent (PLE)
that describes the dependence of propagation loss in the path (in dB) to the logarithm of the distance
starting at 1 m, and Sis the Gaussian random variable with zero mean and standard deviation σ(dB).
This random variable characterizes the large-scale channel fluctuations due to shadowing, and bis
an optimization parameter that presents the path loss slope of the linear frequency dependence. The
term L(f,1m)is the free-space loss at a distance of 1 m, with fcbeing the center frequency L(dB)=
32.4 +20 log fc(GHz). The symbol f(GHz)is the operating carrier frequency and f0, as the minimum
investigated, is the frequency of operating frequencies [34]. The frequency f0is computed as follows:
f0=
K

k=1
fkNkK

k=1
Nk(19)
where f0is the weighted frequency average of all measurements for each particular scene, that is
determined by considering the product of the sum of all the frequencies, the total number of recorded
data Nkat a specific frequency and antenna scenario, and the corresponding frequency fk, and dividing
that by the total number of measurements (that is, the summation of Nkfrom k=1toK) taken over
all frequencies for that specific scenario and the used transmitter and receiver system.
CIF method: MMSE-based parameters
After changing the side of Eq. (18), if we assume that F=PLCIF(f,d)[dB] −L(f,d0),Z=
10 log(d1m),p=n(1−b),andq=nbf0, we obtain
SCIF
μ,σ=F−Z(p+qf )(20)
The shadow factors’ standard deviation is:
σCIF =SCIF
μ,σ2/N=[F−Z(p+qf )]2/N(21)
Minimizing σCIF is equivalent to minimizing [F−Z(p+qf )]2.When[F−Z(p+qf )]2is
minimized, its derivatives with respect to pand qshould be zero, i.e.,
∂[F−Z(p+qf )]2∂p=2Z(pZ +qZf −F)=2pZ2+qZ2f−ZF=0 (22)
∂[F−Z(p+qf )]2∂q=2Zf (pZ +qZf −F)=2pZ2f+qZ2f2−ZFf =0
(23)
After simplification and combining, we obtain:
p=Z2fZFf −Z2f2ZFZ2f2
−Z2Z2f2(24)
q=Z2fZF −Z2ZFf Z2f2
−Z2Z2f2(25)

3136 CMC, 2022, vol.71, no.2
In Eqs. (24) and (25), the closed-loop solution of the assumed terms pand qwas derived. The
standard derivation of the shadow factor can be derived by inserting pand qinto Eq. (21).Moreover,
by using the initial definition, p=n(1−b)and q=nbf0the values of nand bcan be calculated. The
calculated values of the CIF model are listed in Tab. 2.
3.2.2 Alpha-Beta-Gamma (ABG) Model
A multi-frequency three-component model called the ABG model contains conditions for describ-
ing the propagated loss at different frequencies depending on the frequency and distance [31,34]. The
path loss of the ABG model is given by Eq. (26):
PLABG(f,d)[dB] =10αlog10(d1m)+β+10γlog10 (f1GHz)+SABG
μ,σ(26)
where αand γare associated with the path length and frequency element of path loss of the link,
fis the frequency in GHz, and βis a parameter utilized as an offset mechanism that does not have
any physical meaning. The parameter S is a Gaussian random variable representing large-scale signal
variations in the mean path loss over distance. The ABG model can be recognized as the annex of
the FI model for multiple frequencies. The MMSE technique can be used to determine the optimum
values of the α,β,andγcoefficients. It can be shown that if γ=0 or 2 and the ABG model is
used for a single frequency, it transforms into an FI model. As a result, the ABG model is a multi-
frequency generalization of the FI, and the FI can also be constructed using a single frequency [35]. In
addition, the ABG model may be simplified to the CI, if αequals 20log(4pi/c),βequals PLE, and γ
equals 2. Given that the ABG model requires three parameters whereas the CI model requires just one
parameter, the CI model is more economical in computing complexity. Moreover, others argue that the
additional two variables in the ABG model provide only a marginal improvement in accuracy [36,37].
The MMSE-based minimum parameter values can be determined by assuming F=PLABG(f,d)[dB],
Z=10log10(d)and P=10log10(f)in Eq. (26), then SF is calculated by
SABG
μ,σ=F−αZ−β−γP(27)
and the SF standard deviation is:
σABG =(SABG
μ,σ)2/N=(F−αZ−β−γP)2/N(28)
To obtain the minimum values of the standard deviation from Eq. (28),(F−αZ−β−γP)2/N
needs to be minimized. Given that N is a constant, to minimize the (F−αZ−β−γP)2, its partial
derivative with respect to α,β,andγshould be zero.
∂(F−αZ−β−γP)2∂α =2Z(αZ+β+γP−F)
=2αZ2+βZ+γZP −ZF=0(29)
∂(F−αZ−β−γP)2∂β =2(αZ+β+γP−F)
=2αZ+Nβ+γP−F=0(30)
∂(F−αZ−β−γP)2∂γ =2P(αZ+β+γP−F)
=2αZP +βP+γP2−PF=0(31)
From Eqs. (29)–(31), it is clear that
αZ2+βZ+γZP −ZF =0 (32)

CMC, 2022, vol.71, no.2 3137
αZ+Nβ+γP−F=0 (33)
αZP +βP+γP2−P=0 (34)
The numeric values of α,β,andγfor the ABG model can be calculated by solving Eq. (35),and
the calculated coefficients of the ABG model are given in Tab. 2.
⎛
⎝
α
β
γ⎞
⎠=⎛
⎝Z2ZZP
ZNP
ZP PP2⎞
⎠
−1⎛
⎝ZF
F
PF ⎞
⎠(35)
4Results and Discussions
4.1 Analysis of the Large-Scale Path Loss Models
Measurement experiments at 3.7 and 28 GHz were conducted to examine the parameters of
long-term path loss models in a train tunnel. The transmitting antenna was directed inwards, and
the receiver, located in the middle of the mobile van, was directed toward the receiving antenna. As
mentioned earlier, three different channels were created at two frequencies (3.7 and 28 GHz) using horn
and TAS antennas. We processed our measured data and produced the visible figures with MATLAB
R2021a. Fig. 3 depicts the coefficients of the models with diverse FSPL and PLE values.
Fig. 3a shows the changes in path loss in the 1674 m long straight train tunnel on a semi-log scale.
A scatter plot was used to depict the measured path losses at various points. The recorded path loss
was fitted using the CI, FI, CIF, and ABG models, all plotted as straight lines. As shown in Fig. 3a,the
ABG model did not fit well with the measured datasets. Except for the ABG model, the other models,
CI, FI, and CIF, are competitive when considering the prediction performance. Additionally, CI, FI,
and CIF models show almost identical path loss predictions at the far end, but a variation appears at
the near end for FI models when compared to the CI and CIF models. At the near end, the FI model
fitted the measured data in contrast to the CI and CIF models. Consequently, at 3.7 GHz frequency,
the FI model fitted the measured dataset with greater efficiency than the other models.
Fig. 3b shows the changes in path loss in the 1674 m long straight train tunnel on a semi-log scale
at a frequency of 28 GHz. While both the CI and CIF models showed good performance at the far end
of the tunnel, they did not perform well at the near end. At a frequency of 28 GHz, the ABG model
did not fit well with the measured dataset, where the ABG model parameters were calculated using
the MMSE-based optimization technique. Of the remaining models, the FI model fitted the measured
dataset with greater efficiency than the CI and CIF models at 28 GHz.
Fig. 3c shows the changes in path loss in the 1674 m long straight train tunnel on a semi-log scale at
a frequency of 28 GHz. The figure shows that the FI model performs well at the 28 GHz TAS receiver
when compared to the CI, CIF, and ABG models. At 28 GHz frequency with the TAS receiver, the
ABG model did not fit well with the measured dataset. The path loss predicted by the FI model fits
well with the measured datasets, and shows higher accuracy at both the near and far ends.

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Figure 3: CI, CIF, FI, ABG model, and measured path loss in the tunnel at (a) 3.7 GHz, (b) 28 GHz,
(c) 28 GHz (TAS); (d) FSPL variations at different frequencies developed by CI, FI, CIF, and ABG
models, (e) PLE variations at different frequencies developed by CI, FI, CIF, and ABG models, (f)
Standard deviation of point-to-point variations of received power
4.2 FSPL Variations in Different Propagation Techniques
Fig. 3d shows the variations in FSPL exhibited by the CI, FI, CIF, and ABG models. As the
FSPL of the CI and CIF models is the same, for brevity the CIF model is not depicted in the figure.
The FSPL developed by the ABG model is a constant quantity, as depicted by the straight yellow line
marked by a hexagonal-shaped marker. While the FSPL of the CI model is much lower than that of
the other models, it is evident in Figs. 3a–3c that the CI model did not outperform the FI model at the
frequencies of 3.7, 28, and 28 (TAS) GHz. The FSPL at 28 GHz with the TAS receiver is a different
value, as depicted in the figure by a single red scatter point. Consequently, it is clear that the FI model
has a positive slope of FSPL (even if the single red scatter dot is taken into consideration). Accordingly,
the FSPL obtained using the FI model is consistent with the path loss, as shown in Figs. 3a–3c.
4.3 PLE Variations at Different Frequencies and Models
Fig. 3e shows the variations in PLE with respect to the frequency of the FI, CI, CIF, and ABG
models. The path loss exponent of the CIF and ABG model is constant at 1.6 and 1.1 over frequencies
of 3.7 to 28 GHz, respectively. The remaining two models, CI and FI, exhibit a negative slope. The
PLE points show different CI and FI model trends for the TAS antenna system at the receiver end.

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Evidently, owing to the use of the TAS receiver, the PLE developed through MMSE optimization is
significantly reduced in the CI model, and in the case of the FI model, the PLE for the TAS receiver
increases.
4.4 Point to Point Standard Deviation Variations of Received Power
The point-to-point standard deviation is a valuable tool for investigating the variations in the
received power in different propagation measurement experiments, as reported in [26,38]. Fig. 3f
depicts the variations in the received power measured at different distances in the tunnel at frequencies
of 3.7, 28, and 28 (TAS) GHz. As described earlier, we measured at 160 points inside the tunnel, and
at each point two different frequencies in the S (3.7 GHz) and Ka (28 GHz) bands were used where
the receiver antenna was a horn and TAS.
4.5 Shadow Factor and Multi-Path Components
The shadow factor is calculated as the difference (in dB) between the data points and the trajectory
loss anticipated at a particular distance using the adapted model:
SF(matching)(d,f)[dB]=PLmeas. (d,f)−PL(matching)(d,f)(36)
The shadow factor histograms for CI fitting are shown in Figs. 4a–4c at 3.7, 28, and 28 GHz,
respectively, for the horn, horn, and TAS antenna receiver. Similarly, the shadow factors of the FI
fittings are shown in Figs. 4d–4f,CIFareshowninFigs. 5a–5c,andABGareshowninFigs. 5d–5f,
at 3.7, 28, and 28 GHz for the horn, horn, and TAS antenna receiver, respectively. The shadow factor
follows a Gaussian distribution with zero mean and standard deviation σ, whereby the probability
distribution function (PDF) of the shadow factor is represented by
fX(x)=(1σ√2π)exp(−x22σ2)(37)
Figure 4: Shadow factor of the different propagation models. (a) CI 3 GHz, (b) CI 28 GHz, (c) CI 28
GHz (TAS); (d) FI 3 GHz, (e) FI 28 GHz, (f) FI 28 GHz (TAS)

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Figure 5: Shadow factor of the different propagation models. (a) CIF 3 GHz, (b) CIF 28 GHz, (c) CIF
28 GHz (TAS); (d) ABG 3 GHz, (e) ABG 28 GHz, (f) ABG, 28 GHz (TAS)
As expected, the histograms generally corresponded to a Gaussian distribution. The experimental
mean and standard shadow deviation factors are shown for each Gaussian distribution as a solid red
line. The standard deviation values are listed in Tab. 3.
Table 3: Shadow factor of CI, FI, CIF, and ABG model fitting to the measured data using MMSE
Freq. (GHz) σ(dB)
CI FI CIF ABG
3.7 5.58 5.49 3.91 8.47
28 8.58 5.53 6.53 5.67
28 (TAS) 10.56 4.86 5.40 7.92
5Conclusion
This study focused on developing large-scale channel models that characterize wireless path loss
in train tunnels. As mentioned earlier, there exists some structural changes in the investigated train
tunnel at points 220, 770, 1000, 1260, and 1500 m from the initial measurement position, but no abrupt
changes in the received signal strength was noticed at the receiver end (Figs. 3a–3c). Consequently, the
effects of such smaller structural shape variations on large-scale wave propagation modelling can be
negligible. At every frequency band, the ABG model did not fit well with the measured datasets. While
the CI, CIF, and ABG models showed almost similar performance at a frequency of 28 GHz, at 3.7
GHz frequency the FI model suits the measured data more accurately. The FI model showed consistent
matching results with the measured datasets at a frequency of 28 GHz for both antenna type horn
and the TAS type antenna system. Therefore, the FI model showed better matching performance to

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the measured datasets than the other models in all measuring scenarios. Given that a lower standard
deviation of the shadow factor in the wave propagation model was expected in this case, the FI model
yielded shadow factors of 5.49, 5.53, 4.86 at frequencies of 3.7, 28, and 28 GHz (TAS) receivers,
respectively. The shadow factors yielded by the FI model are almost the lowest (except for CIF at 3.7
GHz) among all models, as shown in Tab. 3. A minimum shadow factor indicates that the probable
error introduced in the model will also be minimal. Additionally, we checked that the point-to-point
standard deviation of the received power by the FI model is also minimum among all models, which
has not been shown here for brevity. Hence, it can be concluded that the FI model produced more
acceptable propagation losses in the tunnel. Based on this investigation, it is assumed that the FI model
can predict wave propagation loss in similarly structured train tunnels.
Acknowledgement: The authors would like to thank TA Engineering Inc., South Korea, for assisting
with the wave propagation measurement experiments.
Funding Statement: The authors received no specific funding for this study.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding
this study.
References
[1] Z.Hu,W.Ji,H.Zhao,X.Zhai,A.Saleemet al., “Channel measurement for multiple frequency bands in
subway tunnel scenario,” International Journal of Antennas and Propagation, vol. 2021, pp. 1–13, 2021.
[2] K. Haneda, L. Tian, H. Asplund, J. Li, Y. Wang et al., “Indoor 5G 3GPP-like channel models for office
and shopping mall environments,” in Proc. 2016 IEEE Int. Conf. on Communications Workshops,Kuala
Lumpur, Malaysia, pp. 694–699, 2016.
[3] T. S. Rappaport, Y. Xing, G. R. MacCartney, A. F. Molisch, E. Mellios et al., “Overview of millimeter wave
communications for fifth-generation (5G) wireless networks—with a focus on propagation models,” IEEE
Transactions on Antennas and Propagation, vol. 65, no. 12, pp. 6213–6230, 2017.
[4] A. Hrovat, G. Kandus and T. Javornik, “A survey of radio propagation modeling for tunnels,” IEEE
Communications Surveys & Tutorials, vol. 16, no. 2, pp. 658–669, 2014.
[5] A. Seretis, X. Zhang, K. Zeng and C. D. Sarris, “Artificial neural network models for radiowave propagation
in tunnels,” IET Microw. Antennas Propag., vol. 14, no. 11, pp. 1198–1208, 2020.
[6] J.Li,Y.Zhao,J.Zhang,R.Jiang,C.Taoet al., “Radio channel measurements and analysis at 2.4/5 GHz
in subway tunnels,” China Communications, vol. 12, no. 1, pp. 36–45, 2015.
[7] X. Zhang and C. D. Sarris, “Statistical modeling of electromagnetic wave propagation in tunnels with rough
walls using the vector parabolic equation method,” IEEE Transactions on Antennas and Propagation,vol.
67, no. 4, pp. 2645–2654, 2019.
[8] L. Rapaport, G. A. Pinhasi and Y. Pinhasi, “Millimeter wave propagation in long corridors and tunnels—
theoretical model and experimental verification,” Electronics, vol. 9, no. 5, pp. 707, 2020.
[9] J. Boksiner, C. Chrysanthos, J. Lee, M. Billah, T. Bocskor et al., “Modeling of radiowave propagation in
tunnels,” in Proc. MILCOM 2012–2012 IEEE Military Communications Conf., Orlando, FL, USA, pp. 1–6,
2012.
[10] M. Liénard and P. Degauque, “Wideband analysis of propagation along radiating cables in tunnels,” Radio
Science, vol. 34, no. 1, pp. 113–122, 1999.
[11] X. Zhang, N. Sood, and C. D. Sarris, “Fast radio-wave propagation modeling in tunnels with a hybrid vector
parabolic equation/waveguide mode theory method,” IEEE Transactions on Antennas and Propagation,vol.
66, no. 12, pp. 6540–6551, 2018.
[12] S. F. Mahmoud, “Wireless transmission in tunnels with non-circular cross section,” IEEE Transactions on
Antennas and Propagation, vol. 58, no. 2, pp. 613–616, 2010.

3142 CMC, 2022, vol.71, no.2
[13] C. Zhou, “Ray tracing and modal methods for modeling radio propagation in tunnels with rough walls,”
IEEE Transactions on Antennas and Propagation, vol. 65, no. 5, pp. 2624–2634, 2017.
[14] M. M. Rana and A. S. Mohan, “Segmented-locally-one-dimensional-FDTD method for EM propagation
inside large complex tunnel environments,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 223–226,
2012.
[15] M. Levy, “Parabolic equation framework,” in Parabolic Equation Methods for Electromagnetic Wave Prop-
agation, Michael Faraday House, Six Hills Way, Stevenage, SG1 2AY, UK: The Institution of Engineering
and Technology, pp. 4–19, 2000.
[16] R. Martelly and R. Janaswamy, “An ADI-PE approach for modeling radio transmission loss in tunnels,”
IEEE Transactions on Antennas and Propagation, vol. 57, no. 6, pp. 1759–1770, 2009.
[17] A. V. Popov and N. Y. Zhu, “Modeling radio wave propagation in tunnels with a vectorial parabolic
equation,” IEEE Transactions on Antennas and Propagation, vol. 48, no. 9, pp. 1403–1412, 2000.
[18] Y. Hwang, Y. P. Zhang and R. G. Kouyoumjian, “Ray-optical prediction of radio-wave propagation
characteristics in tunnel environments. 1. Theory,” IEEE Transactions on Antennas and Propagation,vol.
46, no. 9, pp. 1328–1336, 1998.
[19] Y. P. Zhang and Y. Hwang, “Theory of the radio-wave propagation in railway tunnels,” IEEE Transactions
on Vehicular Technology, vol. 47, no. 3, pp. 1027–1036, 1998.
[20] C. Zhou, R. Jacksha and M. Reyes, “Measurement and modeling of radio propagation from a primary
tunnel to cross junctions,” in Proc. 2016 IEEE Radio and Wireless Symposium (RWS), Austin, TX, USA,
pp. 70–72, 2016.
[21] H. Qiu, J. M. Garcia-Loygorri, K. Guan, D. He, Z. Xu et al., “Emulation of radio technologies for railways:
A tapped-delay-dine channel model for tunnels,” IEEE Access, vol. 9, pp. 1512–1523, 2021.
[22] F.Hossain,T.K.Geok,T.A.Rahman,M.N.Hindia,K.Dimyatiet al., “An efficient 3-D ray tracing
method: Prediction of indoor radio propagation at 28 GHz in 5G network,” Electronics,vol.8,no.3,pp.
286, 2019.
[23] S.-H. Chen and S.-K. Jeng, “SBR image approach for radio wave propagation in tunnels with and without
traffic,” IEEE Transactions on Vehicular Technology, vol. 45, no. 3, pp. 570–578, 1996.
[24] C.-H. Teh, B.-K. Chung and E.-H. Lim, “An accurate and efficient 3-d shooting-and- bouncing-polygon
ray tracer for radio propagation modeling,” IEEE Transactions on Antennas and Propagation, vol. 66, no.
12, pp. 7244–7254, 2018.
[25] S. Li, Y. Liu, L. Lin, Z. Sheng, X. Sun et al., “Channel measurements and modeling at 6 GHz in the tunnel
environments for 5G wireless systems,” International Journal of Antennas and Propagation, vol. 2017, pp.
1513038, pp. 1–15, 2017.
[26] I. D. S. Batalha, A. V. R. Lopes, J. P. L. Araujo, B. L. S. Castro, F. J. B. Barros et al., “Indoor corridor and
office propagation measurements and channel models at 8, 9, 10 and 11 GHz,” IEEE Access,vol.7,pp.
55005–55021, 2019.
[27] N. O. Oyie and T. J. O. Afullo, “Measurements and analysis of large-scale path loss model at 14 and 22
GHz in indoor corridor,” IEEE Access, vol. 6, pp. 17205–17214, 2018.
[28] Y. Shen, Y. Shao, L. Xi, H. Zhang and J. Zhang, “Millimeter-wave propagation measurement and modeling
in indoor corridor and stairwell at 26 and 38 GHz,” IEEE Access, vol. 9, pp. 87792–87805, 2021.
[29] Keysight Technologies Inc., Technical Overview: Selecting a Signal Generator. [Online]. Available: https://
www.keysight.com/kr/ko/assets/7018-03356/technical-overviews/5990-9956.pdf (Accessed on August 23,
2021).
[30] T. S. Rappaport, “The cellular concept–system design fundamentals,” in Wireless Communications: Princi-
ples and Practice, vol. 2. Upper Saddle River, NJ, USA: Prentice-Hall, 1996.
[31] G. R. MacCartney, J. Zhang, S. Nie and T. S. Rappaport, “Path loss models for 5G millimeter wave
propagation channels in urban microcells,” in Proc. 2013 IEEE Global Communications Conf., Atlanta,
GA, USA, pp. 3948–3953, 2013.

CMC, 2022, vol.71, no.2 3143
[32] J. Meinilä, P. Kyösti, T. Jämsä and L. Hentilä, “WINNER II channel models,” in Radio Technologies and
Concepts for IMT-Advanced, 1st ed., 1 Fusionopolis Walk, Solaris South Tower, Singapore, Wiley, pp.
39–92, 2010.
[33] J. M. Meredith,“Spatial channel model for multiple input multiple output (MIMO) simulations,” Te ch -
invite, Tech Rep. TR, vol. 25, pp. 1–42, 2012. [Online]. Available: https://www.etsi.org/deliver/etsi_
tr/125900_125999/125996/11.00.00_60/tr_125996v110000p.pdf.
[34] S. Piersanti, L. A. Annoni and D. Cassioli, “Millimeter waves channel measurements and path loss models,”
in Proc. 2012 IEEE Int. Conf. on Communications, Ottawa, ON, Canada, pp. 4552–4556, 2012.
[35] G. R. Maccartney, T. S. Rappaport, S. Sun and S. Deng, “Indoor office wideband millimeter-wave
propagation measurements and channel models at 28 and 73 GHz for ultra-dense 5G wireless networks,”
IEEE Access, vol. 3, pp. 2388–2424, 2015.
[36] T. S. Rappaport, G. R. MacCartney, M. K. Samimi and S. Sun, “Wideband millimeter-wave propagation
measurements and channel models for future wireless communication system design,” IEEE Transactions
on Communications, vol. 63, no. 9, pp. 3029–3056, 2015.
[37] S. Sun, T. A. Thomas, T. S. Rappaport, H. Nguyen, I. Z. Kovacs et al., “Path loss, shadow fading, and
line-of-sight probability models for 5G urban macro-cellular scenarios,” in Proc. 2015 IEEE Globecom
Workshops, San Diego, CA, USA, pp. 1–7, 2015.
[38] A. V. R. Lopes, I. S. Batalha and C. R. Gomes, “Large-scale analysis and modeling for indoor propagation
at 10 GHz,” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 19, no. 2, pp.
276–293, 2020.