Networked Control for a Group of Trains ◾ 187
coherent time. For ease of analysis, we assume that each retransmission is independent.
Furthermore, we assume that the ACK transmission is lossless. Fora given FER
p
and
the maximum number of retransmission times
r
, the packet drop rate is
Pp
p
j
r
j
=1 (1 )
=0
1
−−
−
∑
(9.10)
It can be seen from the FER in Figure 9.5 that the packet drop rate due to random
transmission errors is very low for a fair signal-to-noise ratio. In Section 9.4.2, we
will focus on the packet drops introduced by handover.
9.4.2 Packet Drops due to Handover
e onboard STA handovers at the edge of AP’s coverage. In IEEE 802.11, hando-
vers introduce transmission interruptions. e eects of handovers on packet drops
depend on the handover time, the AP coverage area, and the overlapping coverage
area between APs.
9.4.2.1 Handover Time
An active handover scheme is adopted in our CBTC system because it can realize
shorter handover latency. In previous works [33–35], a handover process is divided
into three phases: probing, authentication, and association. Probing delay is the dom-
inant component. Since the data transmission is interrupted when the STA switches
to other channels to scan APs and is resumed after successful negotiation of encryp-
tion keys with the target AP, the four-way handshake of encryption key should also be
included in the analysis of transmission interruption time (handover time).
We develop a software to measure the handover time. A computer is connected
to the backbone network, which has links to all the APs. Another computer is con-
nected to the onboard STA. e ground computer sequentially and periodically
sends data packets to the onboard computer. A unique sequence number is inserted
into each packet. After handover, the onboard computer reorders the received pack-
ets and measures the handover time by counting the number of lost packets.
tnT
ds
ho
=
⋅
(9.11)
where:
t
ho
is the handover time
n
d
is the number of dropped packets
T
s
is the packet sending period
e eld test results of handover time are shown in Figure 9.8, which are obtained
from Beijing Yizhuang Lines.
188 ◾ Advances in Communications-Based Train Control Systems
9.4.2.2 AP’s Coverage Area
e following factors should be considered to plan the AP’s coverage area:
◾ Path loss. In CBTC, the onboard and wayside antennas are installed only
several meters high. e height of the receiving and transmitting antennas
limits the transmission distance to a short range [36]. We use the empirical
equation proposed by Green and Obaidat [37] to anticipate the free-space
path loss. For the
2.4 GHz ISM band, it has
Pdhh
tr
ls
=+ −7.6 40 20
10 10
loglog
(9.12)
where:
P
ls
is the path loss
d
is the distance between the transmitter and receiver
h
t
and
h
r
are the heights of transmitting and receiving antennas,
respectively
◾ Shadow eect. Both the local mean of envelope level Ω
r
and
the local mean of
envelope power Ω
s
obey
log-normal distribution [38].
Ω Ω
rs
rt st st rt==<=<()>,()>,()()/2
2
where:
<>⋅
is the local mean function
rt()
and
st()
are the envelope and envelope power of received signal,
respectively
e dB version of Ω
r
and
Ω
s
obey
Gaussian distribution with the same stan-
dard deviation
σ
Ω
.
e thresholds of the mean envelope power at certain possibilities are
listed in Table 9.1.
◾ Multipath fading. e envelope of the received signal obeys Rayleigh distribu-
tion. e cumulative distribution function of the envelope power of received
signal can be expressed as a function of the fading factor [39].
Fx
s
V
F
() 110
/10
=−
()
exp
(9.13)
where:
Vx
F
=10 /
10
2
log
σ is the fading factor
s
is the envelope power of received signal
σ
is the parameter of Rayleigh distribution
Networked Control for a Group of Trains ◾ 189
When
V
F
<
10
dB
, F
s
(x) ≈
10
/10V
F
e thresholds of the envelope power at certain probabilities are given in
Table 9.2.
◾ Receiver sensitivity. e minimum rate-dependent input levels for receiver to
meet required QoS performance is given in [32]. For
6Mbits/s
data rate, the
minimum sensitivity is
−
82 dB
m
.
◾ Eective isotropic radiated power (EIRP). In Europe and China, the maximum
EIRP for
2.4
GH
z
ISM band is
100 mW
(
G
t
<
10 dBi).
EIRP
ti
=+ −
PG P
tt
(9.14)
where:
P
t
is the output power of transmitter
G
t
is the antenna gain in dBi
P
ti
is the insertion loss between transmitter and antenna
A fading margin is reserved in link budge for shadow fading and multipath
fading to ensure the probability that the power of received signal at the edge
of AP’s coverage area exceeds the receiver’s sensitivity and is above a given
threshold. e received signal power is
PPPP
GP
rr
=−−− +−
EIRP
ls sf mf ri
(9.15)
where:
P
r
is the received power at the cell’s edge
P
sf
is the power loss induced by shadow fading
P
mf
is the power loss due to multipath fading
G
r
is the gain (in dBi) of receiving antenna
P
ri
is the insertion loss at the receiver
Table 9.2 Threshold of the Envelope Power at Certain
Probabilities
V
F
(in dB) −23 −16
−13 α
8
P(s ≤ V
F
⋅ σ
2
)
0.005 0.025 0.05
Table 9.1 Threshold of the Mean Envelope Power
atCertain Possibilities (σ
Ω
= 8 dB)
x (in dB) −20.6 −15.7
−13.2 α
8
P(Ω
p
≤ x)
0.005 0.025 0.05
190 ◾ Advances in Communications-Based Train Control Systems
e selected parameters for AP’s coverage plan are listed in Table 9.3. e curves of
dierent probabilities that the received power at a given distance exceeds a certain
level are depicted in Figure 9.6. As shown in the gure, when the cell coverage
range is less than
200 m
, the probability that the power of received signal would
exceed
−
82 dB
m
is above
95%
.
0 50 100 150 200 250 30
0
−100
−80
−60
−40
−20
0
20
Distance (m)
Received power (dBm)
90% edge probability
95% edge probability
99% edge probability
Figure 9.6 Probabilities that the received power at a given distance exceeds
certain levels.
Table 9.3 Parameters for
APCoverage Plan
Parameters Value α
8
EIPR (dBm) 17
h
t
(m) 4.5
h
r
(m) 5
G
r
(dBi) 10
P
ri
(dB) 4
Networked Control for a Group of Trains ◾ 191
9.4.2.3 Overlapping Coverage Area
We propose a method to determine the overlapping coverage area of APs in
CBTC. As illustrated in Figure 9.7, APs are linearly deployed along the track. Two
directional antennas are installed and connected to each wayside AP and to each
onboard STA. At rst, the STA associates with AP1. At point “a,” the STA detects
the signal of AP2. At point “b,” the strength of signal from AP2 exceeds that from
AP1. e STA initiates a handover. Normally, the STA sends de-association frame
to the original AP to release resources after successfully negotiating encryption keys
with the objective AP. e STA should complete the whole handover process before
running out of the coverage area of AP1. e length of overlapping coverage area
must satisfy the following:
ddd
ov ab bc
=+
ddvt
mab bc mh
=≥⋅
(9.16)
where:
d
ov
is the length of the overlapping coverage area
d
ab
is the distance between point “a” and “b”
d
bc
is the distance between point “b” and “c”
v
m
is the maximum train speed
t
mh
is the longest handover time
e eld test results on handover time are given in Figure 9.8. e rarely appeared
(
<%1
) overlong
t
ho
are removed as bad values. It is assumed that
t
mh
ms
=180 . In
the design of AP’s overlapping coverage area, a maximum train speed of
200 km/h
is considered for CBTC’s future applications, and
d
ov
m
=20 .
9.4.2.4 Rate of Packet Drops Introduced by Handovers
Based on AP’s coverage range, overlapping coverage area, and the handover time,
we can get the rate of packet drops introduced by handover. Suppose that there
acb
VOBC STA
AP1 AP2
Figure9.7 Overlapping coverage area of APs.
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