phs【秋张吧吧】

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Electronics and Communications in Japan, Part 1, Vol. 82, No. 4, 1999
Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J81-B-II, No. 4, April 1998, pp. 278?88
Autonomous Master驭lave Frame Synchronization among
Microcellular Base Stations
Haruki Yahata
Information and Communications Systems Laboratory, Toshiba Corporation, Kawasaki, Japan 210-8501
SUMMARY
In the case of TDMA冯DD multiplexed transmission
systems such as the one used for PHS in the microcellular
mobile communication, the number of usable
channels decreases due to interference by signals from
nearby base stations, unless there is frame synchronization
of the signal transmitted from the base station. An autonomous
master駍lave synchronization system is proposed
which can easily cope with system modifications such as
addition of base stations. The timing difference of the
transmission and reception at the base station is evaluated.
The basic synchronization algorithm is as follows. (1) A
master station is placed at a rate of one out of several
hundred and the control signal of the master station is
generated with accurate timing. (2) The slave stations,
those not the master station, enter all-receive mode at the
synchronization control time and observe the timing of
the control signals received. (3) After observation for a
constant duration of time, the slave stations select the
earliest timing in terms of frame units from the timings
of the received control signals and transmit the synchronized
control signal. In most cases, the timing difference
of the transmission and reception obtained by this system
at each station is less than twice the propagation time
tW over the effective reachable distance of the base station
signal. ?1998 Scripta Technica, Electron Comm
Jpn Pt 1, 82(4): 1?3, 1999
Key words: Mobile communication; microcellular;
base station; frame synchronization; master駍lave synchronization;
autonomy.
1. Introduction
Mobile communication systems are spreading
widely as an information and communication infrastructure.
In order to cope with an explosive increase of subscribers,
it is important to study how effectively frequency is
used. The microcellular technique increases the frequency
reuse rate by reducing the region serviced by one base
station. The Personal Handy-phone System (PHS) uses this
technique. In PHS, the TDMA冯DD (Time Division Multiple
Access冯ime Division Duplex) system is used as its
multiplex transmission system. Unless there is frame synchronization
of radio channels transmitted from the base
stations in this system, the received signal from a hand set
is interfered with by the signal transmitted by a nearby base
station so that the conversation is disabled. For this reason,
methods have been studied to institute frame synchronization
among the radio channels transmitted by the base
stations. The simplest concept is the slave synchronization
of all base stations to a reference timing [1]. For instance,
it is possible to enact frame synchronization in reference to

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time information from the GPS (Global Positioning System).
However, it is uneconomical to install GPS receivers
at all base stations. Hence, a method has been studied for
frame synchronization by means of radio signals transmitted
by the base stations.
CCC8756-6621/99/040001-13
?1998 Scripta Technica 1
Akaiwa and colleagues have proposed a method in
which the timing of a particular station is generated by
taking the weighted sum of the timings of several received
frames from the nearby base stations [2]. This model is
identical to the mutual synchronization method studied for
the clock synchronization of a wired network. There are
many reports available on the mutual synchronization
method [3?]. The fundamental nature does not change
even if it is used for wireless. The mutual synchronization
method has the deficiency of change of clock frequency
unless the transmission delay is accurately compensated. It
is pointed out in Ref. 2 that this deficiency is unchanged
when the method is used for synchronization of the base
stations. Also, it is reported, when the base station clock is
switched after establishment of the synchronization from
the unified clock of the mutual synchronization network to
the clock of the external network (such as ISDN), the
switching time difference between base stations results in
time differences between the frames of base stations [6].
Kazama and colleagues have proposed a method in which
the distance between the base stations is computed from the
information on the transmitting base station number attached
to the received signal and the memorized position
coordinates of the nearby base stations, so that the propagation
delay can be compensated [7].
An alternative is the master駍lave synchronization
method. In this method, a master base station is installed at
a rate of one in about 100 stations. The master base station
receives accurate timing from the GPS to generate a reference
signal frame to which all slave stations are synchronized.
Chuang has proposed a method in which the base
station autonomously constructs a master駍lave synchronization
network. In this method, in master-slave synchronization
with several layers of hierarchy, the current hierarchy
numbers are transmitted to each other. While the timing is
adjusted to a signal with the hierarchy equal to or higher
than that of the station in question (by taking an average if
there are several), the hierarchy of such a station is modified
[8]. Since this method also uses the timing of the signal with
the same hierarchy as its own, there is an element of mutual
synchronization, and hence, strictly speaking, is a hybrid of
master駍lave and mutual synchronization.
In the above methods, autonomy is an important item.
Autonomy is the capability of constructing a new synchronization
network by the network itself at times of failure
and of system modification. Although there are several
advantages in operation, some inconveniences exist, such

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as the requirement for complex control.
In this paper, a method is introduced that can realize
autonomous master駍lave synchronization by a simple procedure,
using the characteristics of the signal from the
mobile communication base station. In addition, an evaluation
of the error of the synchronization timing and a
computer simulation are presented.
2. Prerequisites and Requirements for the
System
The base stations of the mobile communication are
connected to the trunk mobile communication network.
The trunk network may use an existing ground network. For
instance, the base stations of PHS are connected to the
ISDN lines. Since all base stations receive the clock at an
identical frequency from the ground network connected to
the trunk network or from the trunk network, clock synchronization
among the base stations is maintained. Hence, only
frame synchronization is required. Since the clock frequencies
are identical, frame synchronization is maintained even
after the frame synchronization function is disconnected,
once the frame phases are aligned for synchronization. The
effect of instantaneous disruption of the clock from the
ground network can be avoided by controlling the phase
locked loop (PLL) for clock extraction of the base station
with the phase difference of the frames. Since the base
stations can find out the time and align the clock timer
through the ground network, the time zone for frame synchronization
can be unified. It is sufficient to take the frame
synchronization intermittently, once a day, for instance. The
time zone can be selected at a time such as 2 AM when the
traffic volume is extremely light. Also, if the master stations
with a provision to receive precise timings from the GPS
are at a rate of one station in about 100 no significant effect
on system cost exists.
From the above findings, the following aspects are
useful.
(1) The clock frequencies of the base stations are
identical, since they are supplied by the ground network
(such as the ISDN network).
(2) Frame synchronization may be carried out intermittently,
such as once a day, at a time of low traffic (such
as 2 AM). Each station has a clock timer that can be adjusted
to the time of synchronization establishment (synchronization
establishment time).
(3) The master stations used for frame synchronization
reference can be placed at a rate of one per service
area. These master stations receive an accurate time reference
from the GPS and can form a signal frame.
Next, let us classify the methods of determining the
connection partners for synchronization. The fixed connection
method determines the partner base stations beforehand.
On the other hand, the autonomous connection
method changes the partner base stations in response to the
situation. In the fixed connection method, the date indicating
the partner connections needs to be modified when the
configuration is modified, such as by the addition of the
stations, and needs to load connection data different for

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each station. Although autonomy is not indispensable, it is
desirable.
2
3. Comparison of Methods
For configuration of the synchronization network,
mutual synchronization, master駍lave synchronization,
and a hybrid of the two are considered. Since the timing of
the received signals from several surrounding base stations
is used as the reference and no connection partner need to
be decided beforehand, the mutual synchronization method
can easily form a synchronization network autonomously,
depending on the variations of the base station placement.
However, there is a problem of variation of the unified clock
frequency of the system described above. On the other
hand, in master駍lave synchronization, a synchronization
network can be extremely simply constructed by fixed
connections, and the propagation delays among the stations
can be precomputed and easily compensated. However,
complex operations, such as that in Chuang韘 system for the
autonomous determination of the slave base stations, are
required.
It has been reported that a sufficient condition for
perpetual existence of a steady stable state in the hybrid
synchronization is that the gain for one input at each PLL
be larger than the sum of the gains for all other inputs [9].
In a synchronization network determining the connection
partner autonomously, it is extremely difficult and unrealistic
to maintain this gain relationship.
Let us compute the volumes of operations in the
mutual synchronization method, the fixed master駍lave
synchronization method, and the autonomous master駍lave
synchronization method (represented by the method of
Chuang).
First, in the mutual synchronization method and
Chuang韘 method, it is necessary to obtain convergence to
the phase value of the final frame by repetitive calculations.
The number of repeated operations for convergence is
related to the control gain. In the case of Chuang韘 method,
the number is 60 to 200 in the case of 289 base stations [8].
In the case of the mutual synchronization method, the
number of repeated operations reaches 2000 for 81 base
stations [2]. In order to carry out repeated calculations, the
control signal used as the reference for synchronization
needs to be received from other stations. Therefore, the time
for convergence is the product of the internal of the control
signal and the number of repeated operations and becomes
very long. On the other hand, in the fixed master駍lave
synchronization method, each base station needs only one
operation for synchronization, because the own frame
phase can be synchronized when the control signal of the
partner base station is received once. For the group of all
base stations, synchronization is successively handed over
from the master station. Hence, the entire synchronization
is established by as many control signal intervals as the
hierarchical stages of master駍lave synchronization. If the
master station is placed at the center, the number of hierarchical

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stages is less than 10 for 300 base stations. Hence,
the time required for establishing synchronization is much
shorter than those of other methods.
One repetition in the mutual synchronization and
Chuang韘 method consists of slightly shifting the frame
phase of the own station by deriving the weighted average
of the phase differences between the frame phase of the own
station and several of the frame phases of the received
control signals, and multiplying it by the control gain. This
operation is fundamentally identical to that of the PLL. For
stabilizing this control, a filter is often installed within the
control loop. Several add/subtract operations and several
multiplications are needed in one repetitive calculation. On
the other hand, in the fixed master駍lave synchronization
method, the reception timings of several received control
signals are memorized and, in addition, the base station
number information contained in the received control signal
is compared with the base station number to which the
own station must be subordinate. If agreement exists, the
frame timing of the own station is determined based on the
timing of the received control signal. This can be realized
by several comparison operations. If the propagation delays
among the base stations are memorized beforehand, compensation
of the propagation delay is possible even with one
add/subtract operation. This operation does not require
multiplication and hence is much simpler than other methods.
The above can be summarized as follows.
Master駍lave
synchronization
Fixed Autonomous
Mutual
synchronization
! ?!
$ ! $
! ??
Autonomy
Synchronization
error
Synchronization
establishing
time and
amount of operation
4. Summary of Operations of Autonomous
Master驭lave Synchronization Method
Here, a simple method is proposed that can autonomously
construct a master駍lave synchronization network
with simple control. To simplify the explanation, PHS is
used as an example. In PHS, the frame period of TDMA?
TDD is 5 ms, and the control signal is sent once every 20
3
frames and hence at 100-ms intervals. This control signal
is used as the reference for the timing of frame synchronization.
In the following, the operations of the autonomous
master駍lave synchronization method are explained.
(1) At the synchronization control period, the master
base station creates a signal frame in reference to GPS
and transmits the control signal.
(2) At the synchronization control period, the slave
base stations, the base stations other than the master, except
busy stations, enter the all-receive mode when no transmission
takes place and watch the received control signal.
(3) When a slave station receives a control signal
with a level above a specific value from a base station that
is not busy, it makes the observation period a certain time
length (more than 100 ms). The station memorizes the
received timings of control signals above a specific level.
(4) The received timings of the control signal at a

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frame unit of 5 ms are observed. The earliest is chosen as
the reference timing of synchronization. After the observation
period is completed, the control signal frame synchronized
with the reference timing is generated and the control
signal is sent out.
(5) Busy base stations start the synchronization
control period after completion of the busy state and enter
all-receive mode. By operations similar to the above, they
generate control signals in synchronization.
By the above procedure, the master駍lave synchronization
connection spreads in time with the master station as
the center. By choosing the earliest timing, the path with
the least propagation delay is chosen as the path for master駍lave
synchronization. Hence, the timings of the frames
of the slave stations located at equal distances from the
master station almost coincide, even without compensation
for delay. If about 200 ms is considered as the observation
period, about 200 ms is needed per hierarchical stage of
master駍lave connections. The time needed to establish the
frame synchronization from the master station to the 10th
stage slave connection is about 2 s.
The time chart of the synchronization process for the
base station orientation in Fig. 1 is shown in Fig. 2. The
timings shown here are those seen at the antenna end for
both transmission and reception.
Once a day, when the synchronization control period
(SCP) arrives, the master station BS0 receives accurate
reference STS (System Timing Standard) time information
from the GPS and uses it to generate the signal frame (SF)
and transmit the control signal (TCS). [See Fig. 2(d).]
Except for those that are busy, all slave stations enter
all-receive mode and wait for the reception of the control
signal. Although the busy base stations transmit the control
signal also, they ignore this control signal by consulting the
bit that indicates busy state in it. Slave station BS1 receives
Fig. 1. Location of base stations and propagation delay
between them.
Fig. 2. Time chart of synchronization process.
4
the transmitted control signal from the master station [in
Fig. 2(d)] after a transmission delay of t0-1 and memorizes
this timing as the frame timing MFT [in Fig. 2(f)]. In
addition, it starts the observation period (OP) [Fig. 2(e)] and
waits for the reception of other control signals. Since there
is no other control signal to be received by BS1, the signal
frame SF of the own station is corrected in accordance with
the memorized frame timing after the observation period
[Fig. 2(g)], and the synchronized control signal is transmitted
out [Fig. 2(h)]. The slave station BS2 also transmits the
control signal in a similar operation [Fig. 2(l)].
The slave station BS3 also is waiting for the reception
of the control signals from other stations at the synchronization
control period. The control signal [Fig. 2(l)] from
BS2 is received after a transmission delay of t2-3 and its
timing is stored in memory as the frame timing [Fig. 2(n)].

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In addition, the observation period is initiated [Fig. 2(m)]
and the reception of other control signals is awaited. Next,
the control signal [Fig. 2(h)] transmitted from BS1 is received
after t1-3 and its timing is stored in memory [Fig.
2(o)]. During the observation period of BS3, these two
control signals are received. Of these two timings, the
earlier one in terms of frame units is selected. The difference
between the two timings is a unit of less than 1 ms. In
comparison with the frame period of 5 ms, these two are
very closely spaced. The term 靍arly?with respect to frame
units applies to the earlier one in these collections. In this
example, the smaller of t0-2 + t2-3 and t0-1 + t1-3 is selected.
Here, the latter is selected, a the frame synchronized
to this timing is generated, and the control signal is transmitted.
[See Figs. 2(p) and 2(q).] The selection of the one
earlier in terms of frame units corresponds to the selection
of the shortest of several paths via several base stations.
Even if multiple paths exist, the one arriving earliest is
selected, and hence the process is almost equivalent to the
selection of the shortest distance between stations.
If the above operations continue, timing synchronization
spreads concentrically from the master station. BS1
and BS2 are the first stage of the master駍lave synchronization,
while BS3 is in the second stage. Each base station
does not need to know the stage. This stage is called the
synchronization sequence.
Let us express the synchronization algorithm in equations.
The basic algorithm to select one path from several
to the slave station A with the synchronization sequence n
is as follows, after the path from the master station M to the
synchronization sequence (n - 1) is determined.
Let us denote the base station with the synchronization
sequence j-th stage in the i-th path as Si; j. Here, Si;0 is
M while Si;n is A. Also, the propagation delay from Si; j to
Si; j+1 is written as ti; j. The timing tRAi of the signal received
by A through the i-th path is the total of the propagation
delays from M to A through path i:
tRAi = ti;M瓵 = ti;0 + ti;1 + 鬃 + ti;(n-1)
The base station A is selected with the transmission timing
tTA:
(2)
In this method, there is no need for repetitive calculations.
Each base station can determine the frame phase of
the own station by one operation. The time for establishing
synchronization is considered almost identical to that for
the fixed master駍lave synchronization method described
above. The content of the operation is to memorize several
receiving control timings and to select the earliest one.
Hence, several comparison operations take place. The number
of operations is similar to that in the fixed master駍lave
connection method. Hence, the present method attains
autonomy with an amount of operations and a synchronization
establishment time similar to those in the fixed
master駍lave synchronization method.
5. Evaluation of the Frame

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Synchronization Error
t
Let Lw be the effective wave propagation distance and
W the propagation time over this distance. After the syn-
W.
chronization path is established by the algorithm explained
in section 4, we investigate the difference between the
receiving timing of the signal transmitted from base station
B within a distance of Lw from base station A and the
transmission timing of A. The difference between the synchronization
sequence of A and that of B is 0 or ?. This is
because the synchronization path is established between the
two stations and the difference of the synchronization sequences
becomes ? before the difference of the synchronization
sequences becomes ? due to the fact that distance
between A and B is within L
In reference to the frame timing of the master station,
the transmission timings for A and B are denoted t
tTB. Also, the propagation times from B to A and from A to
TA and
B are tB-A and tA-B. The base station disposition is to a
certain extent planned. If the minimum distance between
the adjacent stations is LDmin and the propagation delay
is tDmin
, then
(3)
(1) Basic algorithm case
(i) When synchronization sequence of A = synchronization
sequence of B + 1
From Eq. (2), tTA is selected as the smallest of the
receiving timings tRAi. Hence, other receiving timings are
larger than this value (and hence slower).
5
The timing difference tEA,B of transmission and reception
at A is
(4)
Since B is considered to be at a position closer to the
master station than A,
(5)
From Eqs. (3) to (5), the range of tEA,B is
(6)
(ii) When synchronization sequence of A = synchronization
sequence of B ?1
If B is subordinate to A,
(7)
If B is not subordinate to A,
(8)
Combining Eqs. (7) and (8) with Eq. (3),
(9)
Also, since B is located farther away from the master station
than A,
(10)
From Eqs. (3), (9), and (10), the range of tEA,B is
(11)
(iii) When synchronization sequence of A = synchronization
sequence of B
The two base stations with the same synchronization
sequence have their observation period almost at the same
time instance and determine the frame timing. Therefore,
the control signal of the partner cannot be referenced. For
example, even if an earlier timing can be obtained by being
subordinate to B with an increased stage of synchronization
sequence of A, the synchronization sequences may be set
the same. If the base station disposition is completely free
and if the two synchronization paths separated from a
station (which need not be the master station) arrive at the
two base stations with identical synchronization sequences
with a distance of less than Lw through certain synchronization
stages, while one of the paths is straight and another
is indirect, then it is easy to imagine that the difference of
the two synchronization path lengths has the potential to
increase as the number of intermediate synchronization
stages is increased. Then, it easily occurs that tEA,B can be

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outside the range combining Eqs. (6) and (11):
(12)
However, in general, the base stations are not randomly
located. If the base station placement is under a plan
and the maximum value LDmax of the distance between the
adjacent base stations (with a propagation time of tDmax) is
set at a value smaller than LW, then the synchronization path
can be established without significant detour. This can be
understood from Fig. 3. Then, it can be expected that the
difference of the two synchronization paths separated from
a certain station does not increase significantly even if the
number of synchronization stages is increased.
Let us consider base stations A and B with their
synchronization sequences larger by one than that of base
station M. If the distance among the three base stations is
within LW and more than the minimum distance LDmin
between the base stations, then the transmission and reception
timing difference at A, tEA,B = tM-B + tB-A - tM-A, can
be derived from the difference between the total of two sides
and one side of the triangle formed by M, B, and A. If the
range of the length of each side is fixed, the range taken by
tEA,B in consideration of a possible case of M, A, and B on
a straight line is
(13a)
(13b)
This range is the one which can be taken by the
transmission and reception timing difference of the signals
from two base stations subordinate to an identical base
station and is narrower than the range in Eq. (12). The range
taken by the transmission and reception timing difference
by the signals from two base stations with an increase of n
stages of synchronization sequence, passing through separate
synchronization paths from the identical base station,
is wider than the one in Eq. (13). This is called the extended
range of Eq. (13). Whether this range exceeds the one in Eq.
(12) is examined by simulation. The approximate range
taken by tEA,B is Eq. (12). It is not necessary to worry about
a negative value when the maximum absolute value of
tEA,B is considered.
(2) Case of fixed correction to the transmission
timing
6
Fig. 3. Synchronization paths autonomously selected on given disposition of base stations and effective wave propagation
distance.
The transmission timing of each base station is delayed
as the synchronization sequence is increased. In order
to reduce this increase, a fixed correction (-tHR) is inserted
in the transmission timing of each base station. The operation
is simple since the correction is fixed. The operation of
the transmission timing is derived by
(14)
in place of (2). Since each stage of the synchronization
sequence receives a correction of -tHR, the base station at
the n-th stage receives a total correction of -ntHR. If A is at
the n-th stage, its transmission timing is
(15)
Since min(ti;M瓵) is unchanged from the case of (2), the
synchronization path is identical to the one without correction.
Here, the timing difference is evaluated.
(i) When the synchronization sequence of A = synchronization

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sequence of B + 1
Since tTA is selected as min(tRAi) by (14),
(16)
Since B is considered to be closer to the master station
than A,
(17)
If Eq. (15) is used,
(18)
If Eqs. (16) and (18) are combined, the range of tEA,B is
(19)
(ii) When synchronization sequence of A = synchronization
sequence of B ?1
From the algorithm,
(20)
Hence,
(21)
7
Since it is considered that B is farther away from the
master station than A,
(22)
Hence,
(23)
If Eqs. (21) and (23) are combined, the range of tEA,B is
(24)
(iii) When synchronization sequence of A = synchronization
sequence of B
Since tTA and tTB receive the same amount of correction,
tEA,B is the same as the value without correction.
To what extent the region combining Eqs. (19) and
(24) is enlarged depends on the magnitude of the correction
tHR. The maximum limiting value becomes the minimum
if tHR = tW/ 2 is chosen. Both Eqs. (19) and (24) become
1.5 tW. The minimum limiting value is given by Eq. (24)
for tHR > tDmin /2. Further, the value becomes negative if
tHR > tDmin. If the correction value is chosen around
tHR = tW/ 2, then the absolute value of the minimum value
is substantially smaller than the maximum limiting value
even if the minimum limiting value is negative. For
tHR = tW/ 2, the range given by Eqs. (19) and (24) is
(25)
Insertion of an appropriate fixed correction value implies
the transformation of the region in Eq. (12) into that in Eq.
(25). On the other hand, the range of tEA,B by the base station
signal of the same synchronization sequence is the extended
range of Eq. (13) and is identical to the value without
correction.
In the absence of correction, the maximum limiting
value by Eq. (12) and the extended range of Eq. (13) is in
many cases determined by Eq. (12). If an appropriate fixed
correction value is inserted, the maximum limiting value by
Eq. (25) and the extended range of Eq. (13) is determined
by the extended range of (13). Hence, the maximum value
of tEA,B decreases. The fixed correction value is desired to
be near
(26)
(3) Case with timing determination error
At each base station, the transmission timing tTA is
determined by Eq. (2) or Eq. (14). Let us consider the case
where timing errors in +tER~-tER occur due to the difference
of the distance actually traveled by the radio wave
from the straight-line distance between the base stations, or
due to fluctuations of the delay in the internal circuits. If the
range of the errors is not symmetric in the positive and
negative directions, the shift of the center value is included
in the fixed correction tHR. Then, the center value can be
considered to be 0. If the total of the synchronization
sequences of A and B is N, there is a possibility of increasing
the absolute value of the timing difference by NtER in the
worst case. However, the probability of the worst case is
extremely small. The degree of influence on the timing
difference is examined by simulation.
(4) Near the boundary of the governing territories

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sought. If Bq does not exist, station A cannot have synchroq
exists, then the distance metric nization sequence p. If B
LMBq of Bq is read and the distance LBq-A between A and
Bq is computed. Then, the receiving distance metric
(27)
is derived. If several Bq exist, the minimum value of the
receiving distance metric min(RLMA,Bq) is selected and the
distance metric LMA of base station A is computed by the
following equation and is memorized:
(28)
where LERA is the timing decision error of base station A.
After the paths of the master駍lave connections of all
EA,Br of base stations are determined, the timing difference t
all received signals and transmitted signals at base station
A is derived and evaluated. The distance metric LMBr of all
base stations Br located within a distance LW from the own
station A is read and the distance LBr-A between A and Br is
computed. According to Eq. (27), the receiving distance
metric RLMA,Br at A is computed. The timing difference
LEA,Br between the received signal from Br and the transmitted
signal of A is
(29)
The maximum and minimum values of the above are derived.
6.2. Simulation results
In the simulation, the base station dispositions by five
types of random sequence are used for one set of parameters.
Their statistics are obtained.
(1) Effects of the degree of fluctuations of the base
station dispositions and the effective wave propagation
distance
Two kinds of fluctuations of the base station dispositions
are chosen. Disposition 1 is for sB = 0.5 when the
locations of the base station are anywhere within ?.5 from
the lattice point along both the vertical and horizontal axes.
The minimum distance between the adjacent stations is 0
while the maximum is 2.24. Disposition 2 is for sB = 0.25
when the locations of the base station are closer to the lattice
point than in disposition 1. The minimum distance between
the adjacent stations is 0.5 while the maximum is 1.58. In
Fig. 3, the base station locations by dispositions 1 and 2 by
one of the five random sequences are shown (with omission
around the periphery of 13 ?13). The synchronization paths
for effective wave propagation distance LW = 1.5 are shown
with solid lines. For comparison, some of the synchronization
paths for LW = 2.5 are presented with dotted lines. The
master station index is [6, 6]. In disposition 1, the maximum
distance between the adjacent base stations for LW = 1.5 is
substantially larger than the effective wave propagation
distance. Therefore, there are some locations where the
synchronization path is detoured. In disposition 2, the distance
between the adjacent base stations is mostly within
LW = 1.5 and hence the synchronization paths are not
detoured.
EA,Br per
W
In Table 1, the number of base stations (Num.) and
the maximum (Max. LE) and minimum value (Min. LE) of
the transmission and reception timing difference L
synchronization sequence (Hier.) are shown. For disposition
1, Max. LE often exceeds 2LW substantially for LW =

12楼2005-04-16 14:56

202.109.83.*

1.5 and 2.0, while it exceeds 2LW only slightly with LW =
2.5. In disposition 2, Max. LE never exceeds 2LW. Also, in
both dispositions, Min. LE never becomes smaller than
-LW. If the effective wave propagation distance is chosen
larger than the maximum distance between the adjacent
base stations, the timing difference is mostly between 2L
and -LW.
The following simulation is carried out for disposition
2 in which the base stations are disposed rather regularly.
(2) Effect of timing correction and timing decision
error
In order to investigate the case with a large synchronization
sequence, the master station index is made [0, 6]
and the station is placed at the edge. The simulation is
carried out for LW = 2.5. The results are shown in Table 2.
9
Table 1. Timing difference between received signal and
transmitted signal on given base station disposition and
effective wave propagation distance
(a) Here, LHR = 0 and LER = 0 are the fundamental
algorithm. Even if the synchronization sequence is increased,
Max. LE never exceeds 2LW.
Table 2. Timing difference between received signal and transmitted signal in using fixed correcting value for transmission
timing with random error
10
(b) When a correction of LHR = 1.5 is carried out,
Max. LE becomes smaller than that in (a) for all synchronization
sequences except the maximum sequence of 7. This
is as discussed in section 5. The shortest distance between
the stations is 0.5 and the maximum limiting value by Eq.
(13) is 4.5. This value may be exceeded when the synchronization
sequence proceeds but never exceeds 2LW = 5.0.
The limit of Min. LE is given by Eq. (23) and is ?.0.
© In the case of a corrected value of LHR = 2.0,
Max. LE does not decrease from (b). Also, Min. LE has its
absolute value larger by 0.5 than (b). There is no effect of
the increased corrected value over (b) but the minimum
value is rather worse.
(d) In the case of the timing decision error width of
LER = 0.1 for LHR = 1.5, Max. LE increases with the synchronization
sequence but never exceeds 2LW. This level of
timing decision error does not have a significant influence.
(e) In the case of LHR = 1.5 and LER = 0.2, both Max.
LE and Min. LE have larger degradations than in (d). As the
number of slave stages is increased, the timing decision
error must be kept small.
(3) Boundary of master駍lave synchronization region
from two master stations
The results for the two master stations at [0, 6] and
[12, 6] are shown in Table 3. The section with large values
of synchronization sequence is near the boundary. In the
cases of LW = 1.5 and 2.5, the values are not worse than
those in Table 1. There is no problem with several scattered
master stations.
(4) Effect of busy base stations
The effects are studied in the case where busy base
stations are adjacent and the synchronization paths need to
be detoured. The master station is at [6, 6]. The indices for
the busy stations are [3, 6], [6, 3], [9, 6], [6, 9], [4, 6], [6,

13楼2005-04-16 14:56

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禁言 |16楼2005-04-16 18:46

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