164 ◾ Advances in Communications-Based Train Control Systems
where:
γ
2
()Dd−
is the receive SNR from AP
2
at the location where the distance is
()Dd−
from AP
2
γ
1
()
d is the receive SNR from AP
1
with the distance of d
α
A
,
β
A
,
α
B
, and
β
B
are dened as same as in Equation 8.3 with channel DoF A
and B, respectively
e channel DoF applying zero forcing coding of MIMO multiplexing transmis-
sion is 2(
NM−+1
) for two antennas, where N is the number of receive antennas
and M is the number of transmitting stations at the same time. And the DoF is
4(
NM−+1
) when applying STBC transmission for two antennas. When the
number of antennas is four at the receiver, the DoF is 8(
NM−+1
) with STBC
transmission, and it is 2(
NM−+1
) when multiplexing transmission is applied [27].
Suppose that the target packet error rate is 10
–2
, we can calculate the target BER
using Equation 8.4. In the hando scenario, the channel DoF of the communica-
tion link between the train and the previous AP is 8, and it is 2 for the link between
the train and the candidate AP where the hando signaling and data packets are
transmitted simultaneously. e required SNR from AP
2
is bigger than from AP
1
even with the same MCS level because the channel DoF of the link between AP
2
and the MS is dierent.
Given the two dierent required SNRs from the two APs, the received power
from the two APs can be calculated by Equations 8.12 and 8.13. en the dis-
tance from the optimal hando location to the serving AP can be calculated from
Equation 8.3:
dDD
=− +
[]
/1 10
/(10
*)
SNR
diff
PL
(8.16)
where:
d is the distance from the optimal hando location to the previous AP
D is the inter-site distance between the two adjacent APs
SNR
di
is the SNR dierence between the required SNR with DoF= 8 and
DoF=2
PL is the path loss factor of the signal attenuation
8.4.3 Error-Free Period
Because hando only happens at the predetermined position in the MAHO
scheme, the number of handos is always 1. erefore, the average error-free period
can be obtained directly:
TD
v
ef
=
/
(8.17)
where:
D is the inter-site distance between the successive APs
v is the average moving speed of the train
Novel Handoff Scheme with MIMO ◾ 165
To analyze the error-free period of traditional hando schemes, we suppose the
triggering condition of existing schemes are as follows [30]:
1. e received signal strength at the candidate AP is greater than that of the
serving AP by a hysteresis of h dB.
2. e average received signal strength at the serving AP is below an absolute
threshold value T dBm.
e hando will be triggered only when both the conditions are met. Because
the hando triggering positions are random due to the random receiving signal
quality caused by the stochastic fading, it is dicult to calculate the instanta-
neous transmission interruption period in the hando algorithms. To analyze
and compare the hando performance of existing “break-before-make” hand-
o scheme with our MAHO scheme, we will calculate the error-free period in
average.
To get the error-free period of the communication system, we rst calculate the
number of handos when the MS moves from the serving AP to the next AP. e
distance between the adjacent APs is divided into equal small intervals of length
d
s
.
Suppose that the hando will initiate at the end of each interval. Let
Pk
ho
()
be the
hando probability that when the MS is at the nth interval,
P
12
be the probability
of the association changing from AP
1
to AP
2
,
P
21
be the probability of the associa-
tion changing from AP
2
to AP
1
,
Pk
1
()
be the probability that the MS associates with
AP
1
, and
Pk
2
()
be the probability that the MS associates with AP
2
. ese probabili-
ties are calculated recursively as follows:
Pk Pk PP
kP
ho
() (1)(1)
1122 21
=− +−
(8.18)
Pk Pk Pk Pk P
11 12 221
() (1)1 () (1)=−−
[]
+−
(8.19)
Pk Pk Pk Pk P
22 21 112
() (1)1 () (1)
=−−
[]
+−
(8.20)
where
kD
d
=
1,2,...,
s
/ and
P
1
(0
)1=
and
P
2
(0)=
0
are the initial values. e number
of the handos from the serving AP to the next AP is the sum of the
Pk
ho
()
by
k
. In
the calculation of
Pk
ho
()
, if
P
12
and
P
21
are available, the results are obtained recur-
sively. And then
P
12
and P
21
are calculated as follows [30]:
Pk Pkdhxd h
PddTxd h
kk
kk
12 1
() {( )|(}
{( )| () }
≈<−≥−×
<<
−
−
(8.21)
Pk Pxdhxd h
PbdTxd h
kk
kk
21 1
() {( )( }
{( )| () }
≈> ≤×
<>
−
|
(8.22)
e number of handos
N
HO
is the sum of the hando probability for all k’s at the
hando points:
166 ◾ Advances in Communications-Based Train Control Systems
NP
k
k
HO ho
=
∑
()
(8.23)
e hando latency, at the level of 100ms [25], is much less than the inter-
val between the handos. When calculating the average error-free transmis-
sion period, it can be neglected. erefore, the average error-free transmission
period is
T
D
vN
ef
HO
=
×
(8.24)
where:
v
is the average moving speed of the train
8.4.4 FER of the Handoff Signaling
e SNR in dB at the receiver can be calculated as
SN
RN
F
MAHO MAHO N
=−−
PP
(8.25)
where:
P
MA
HO
is the received power in dBm at the hando location and can be calcu-
lated by Equation 8.12
P
N
is the power of the noise in dBm
NF is the noise gure in dB at the receiver
e bit error rate of the hando signaling can be calculated by Equation 8.3 with
the channel DoF of 8, and then the FER of the hando signaling can be obtained
by Equation 8.4.
For traditional hando schemes, the hando may happen at random locations,
so the FER of the hando signaling cannot be obtained directly. To get the FER of
the hando signaling, same as in Section 8.4.3, we rst get the probabilities
Pk
1
()
and
Pk
2
()
that the MS associates with AP
1
and AP
2
, respectively, when the MS is
at position k. e BER of the hando signaling at position k can be calculated as
follows:
PkPk Pk
b_ho
BE
RB
ER() () ()
1122 21
=× +×
(8.26)
where:
BE
R
12
is the BER of hando signaling which switches from AP
1
to AP
2
at posi-
tion k
BE
R
21
is the BER from AP
2
to AP
1
e denitions of
Pk
1
()
and
Pk
2
()
are given in Equations 8.19 and 8.20. en the
average BER of the hando signaling is
Novel Handoff Scheme with MIMO ◾ 167
P
Pk Pk
N
k
b_ho
HO
BE
RB
ER
=
×+×
[]
∑
1122 21
() ()
(8.27)
where
N
HO
is the number of hando as dened in Equation 8.23. With the
P
b_h
o
,
the FER of the hando signaling can be calculated by using Equation 8.4.
8.4.5 Impacts on Ongoing Data Sessions
When the hando happens, the MIMO transmission will switch to multiuser mul-
tiplexing mode from the STBC diversity mode, which will degrade the BER perfor-
mance. As the data packets and hando signaling are transmitted simultaneously
by multiplexing, to guarantee the target FER, the receive SNR has to be increased,
which will decrease the range of AP’s coverage.
Another method to guarantee the FER performance is to adopt more robust
MCS level when hando happens. Because the hando latency is in the level of
100ms, the throughput loss in the hando procedures due to the decrease of the
data rate is neglectable. In this chapter, to simplify the analysis, we only consider the
rst case where no adaptive modulation and coding (AMC) schemes are adopted.
8.5 Simulation Results and Discussions
In this section, the simulation results on the hando performance are given, which
include the packer error rates of the hando signaling, hando latency, error-free
period, and the FER of hando signaling with dierent data rates.
8.5.1 Analysis of the Handoff Latency
In the MAHO scheme, the hando procedure runs concurrently with data trans-
mission and does not interrupt normal data transmission. e hando delay can
not describe the hando performance exactly because the hando procedure does
not interrupt data transmission in our scheme. However, concurrent transmission of
data packets with hando signaling will increase the probability of the packet loss
and then will increase the transmission delay of data packets due to the retransmis-
sion. erefore, we have the delay increments of packet transmission when hand-
o (DIH) happens as the hando performance measure. For “break-before-make”
hando schemes, the DIH value is the same as the hando latency. e parameters
used in the calculations are shown in Table 8.1.
Figure8.5 shows the latency performance comparisons between the proposed
MAHO scheme and the “break-before-make” hando scheme. e hando latency
of traditional hando schemes are calculated as in Equation 8.10, and the DIH is
the dierence of the hando latency that the multiplexed transmission is usedin
168 ◾ Advances in Communications-Based Train Control Systems
Table 8.1 Simulation Parameters
Notations Value Notations Value
T
DIFS
38μs [2]
Distance between two APs 600m
T
SIFS
20μs [2]
Transmit power at AP and MS 30mW [25]
T
ACK
16μs [2]
Insertion loss at AP 9dB
aSlottime
9μs [2]
Insertion loss at MS 7dB
aCWmin 15 [2] The height of the antenna at AP 4m
T
wait
1000ms [6] The height of the antenna at MS 4m
mChTime 10ms Standard deviation of shadow
fading
5dB
t
Auth
40ms [16] Correlation distance of shadow
fading
25m
Antenna gain at AP 13.5dBi Antenna gain at MS 9.5dBi
0 5 10 15
20
0
50
100
150
200
250
E
b
/N
0
(dB)
Delay increment due to handoff (ms)
Break-before-make handoff scheme
MAHO scheme
Figure8.5 Latency performance improvements of the MAHO scheme.
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