Modeling of the Wireless Channels in Underground Tunnels ◾ 75
of the candidate models and select the model with the smallest value of AICc. e
candidate models in this chapter include Rice, Rayleigh, and Nakagami.
Because our channel model is related to the distance between the transmitter
and the receiver, the tunnel should be divided into intervals. Assume that there are
L
intervals, and we apply AICc for each candidate model in every interval. As a result,
we can select the most appropriate model based on the frequency of the minimum
AICc value of dierent candidate models. In order to obtain enough data for each
interval and ensure the accuracy of the model, we set the length of each interval as 40
wavelengths of WLANs [18], and then there are 100 intervals. Based on the frequen-
cies of AICc of dierent distributions in the real eld measurements, we observe that
the Nakagami distribution provides the best t compared to Rayleigh and Rician
distributions as shown in Figure 4.4. As a result, we can dene
p
()γ
as the Nakagami
distribution.
After the distribution of the signal strength is obtained, according to [17], we
can derive the distribution of SNR:
p
l
l
l
l
l
l
l
l
ll l
()
()
1
γ
µγ
γµ
µµ
µ
µγ γ
=
−
−
Γ
e
/)
(
(4.13)
where:
γ
l
is the SNR of the received signal in the
l
th interval
γ
l
is the mean of SNR in the
l
th interval
µ
l
is the fading factor of Nakagami distribution in the
l
th interval
Γ()⋅
is the gamma function
0.0
Nakagami RicianRayleigh
0.1
0.2
0.3
Relative frequency
0.4
0.5
Figure4.4 Frequencies of AICc selecting a candidate distribution.
76 ◾ Advances in Communications-Based Train Control Systems
In fact, µ
l
can be calculated when applying AICc through the maximum likelihood
estimator for each interval.
4.4 Real Field Measurement: Results
and Discussions
In this section, we compare our FSMC model with real eld test results to illustrate
the accuracy of the model. e eects of dierent parameters in the proposed model
are discussed. e number of states in our model is rst set as four. We also use eight
states to study the eects of the number of states on the accuracy of the proposed
model. In order to obtain the eects of distance intervals on the model, we choose
the intervals as 5, 10, 20, 50, and 100 m. We perform measurements in the tunnel of
Beijing Subway Changping Line for 20 times so that enough data can be captured.
e accuracy of the FSMC model is veried through another set of measurement data.
Based on the measurement data, Equations 4.8–4.10 and 4.13, we derive the
thresholds
{,
0,1,2,...,
}Γ
n
nN=
of SNR in each distance interval. Tables 4.2 and4.3
demonstrate the thresholds of the SNR levels at the location of 100 m for dierent
intervals, where we divide SNR into four and eight levels. As the distance intervals
are dierent, the range of SNR is dierent and it brings dierent thresholds, which
can provide a more accurate model.
After we get the thresholds, we can get the state probabilities and the state tran-
sition probabilities from the real eld data. Table 4.4 illustrates the state transition
probabilities of the FSMC model and the measurement data at the same location
(35–40 m), when there are four states and the distance interval is 5 m. We can
observe that the sum of the transition probability of each channel state does not
equal to 1. is is because, in the measurement data, there are some state transitions
that do not happen in adjacent states, such as transitions from state 1 to state3.
However, in our FSMC models, for the sake of simplicity, we assume that states can
Table 4.2 Thresholds of SNR Levels (Four Levels) at the Location of
100m for Different Intervals
Interval 5 m 10 m 20 m 50 m 100 m
Range [95,100] [90,100] [80,100] [50,100] [0,100]
First threshold 24 22 22 22 22
Second threshold 27.98 26.90 27.73 29.53 33.22
Third threshold 32.03 31.44 32.89 35.39 44.01
Fourth threshold 36.31 36.02 38.14 41.22 57.00
Fifth threshold 41 41 44 48 78
Modeling of the Wireless Channels in Underground Tunnels ◾ 77
only transit to the adjacent states. erefore, in Table 4.4, we only consider state
transitions between adjacent states. Consequently, the sum of the transition prob-
ability of each state of the measurement data does not equal to 1. Nevertheless, it
is very close to 1, which means that our assumption is realistic for practical tunnel
channels in CBTC systems.
Figure 4.5 shows the simulation results generated from our FSMC model and
the experimental results from real eld measurements. We can observe the great
agreement between them. Next, we derive the mean square error (MSE) to mea-
sure the degrees of approximation, shown in Figure 4.6, where the
y
-axis is the
Table 4.4 State Transition Probabilities of the FSMC
ModelandtheMeasurement Data with Four States and 5 m Interval
attheLocation(35–40 m)
FSMC Model Measurement Data
p
kk,1−
p
kk,
p
kk,1+
p
kk,1−
p
kk,
p
kk,1+
k = 1 – 0.91 0.08 – 0.91 0.08
k = 2 0.043 0.86 0.086 0.041 0.86 0.09
k = 3 0.024 0.85 0.12 0.024 0.85 0.11
k = 4 0.023 0.96 – 0.023 0.97 –
Table 4.3 Thresholds of SNR Levels (Eight Levels) at the Location
of100mfor Different Intervals
Interval 5 m 10 m 20 m 50 m 100 m
Range [95,100] [90,100] [80,100] [50,100] [0,100]
First threshold 24 22 22 22 22
Second threshold 25.99 24.53 25.00 26.16 27.87
Third threshold 27.98 26.90 27.73 29.50 33.22
Fourth threshold 29.99 29.18 30.33 32.50 38.50
Fifth threshold 32.03 31.43 32.89 35.38 44.01
Sixth threshold 34.13 33.69 35.47 38.25 50.04
Seventh threshold 36.31 36.01 38.14 41.22 57.00
Eighth threshold 38.59 38.43 40.95 44.41 65.68
Ninth threshold 41 41 44 48 78
78 ◾ Advances in Communications-Based Train Control Systems
0 100 200 300 400 50
0
0
10
20
30
40
50
60
70
80
Distance (m)
SNR (dB)
Simulation results
Experimental results
Figure4.5 Simulation results generated from the FSMC model and experimental
results from real eld measurements.
Shark-fin
antenna
Feeder line
Feeder
line
Test vehicle
WLAN test
Serial port
(displacement)
Single chip
Velocity
Velocity sensor
MS
Yagi
antenna
AP
Ethernet
(signal strength)
Figure4.6 MSE between the FSMC model and the experimental data with four
states and eight states.
Modeling of the Wireless Channels in Underground Tunnels ◾ 79
MSE between the FSMC results and the measurement results, and the
x
-axis is
the interval distance (5, 10, 20, 50, and 100 m). As we can see from Figure 4.6,
when the distance interval increases, the MSE also increases, which means that the
accuracy of the model decreases. Moreover, we can also observe that the MSE of the
FSMC model with four states is larger than that with eight states. e number of
states in the FSMC model plays a key role in the accuracy. Nevertheless, when the
distance interval is 5 m, the MSE dierence is small for the four-state FSMC model
(0.032) and eight-state FSMC model (0.028). From this gure, we can see that the
FSMC model with four states and 5 m distance interval can provide an accurate
enough channel model for tunnel channels in CBTC systems.
4.5 Conclusion
Modeling the tunnel wireless channels of urban rail transit systems is important in
designing the wireless networks and evaluating the performance of CBTC systems.
In this chapter, we have proposed an FSMC model for tunnel channels in CBTC
systems. As the train location is known in CBTC systems, the proposed FSMC
channel model takes train locations into account to have a more accurate channel
model. e distance between the transmitter and the receiver is divided into inter-
vals, and an FSMC model is designed in each interval. e accuracy of the proposed
model has been illustrated by the simulation results generated from the proposed
model and the real eld measurements. In addition, we have shown that the num-
ber of states and the distance interval have impacts on the accuracy of the proposed
FSMC model.
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