Synchronization

2
Synchronization is one of the most critical functions of a communication
system with coherent receiver. To some extent, it is the basis of a
synchronous communication system.
• Carrier synchronization
• Symbol/Bit synchronization
• Frame synchronization

3
Carrier synchronization
• Receiver needs estimate and compensate for frequency and phase differences
between a received signal’s carrier wave and the receiver’s local oscillator for the
purpose of coherent demodulation, no matter it is analog or digital communication
systems
Symbol/bit synchronization
• In digital systems, the output of the receiving filter (i.e. matched filter) must be
sampled at the symbol rate and at the precise sampling time instants. Hence, we
require a clock signal. The process of extracting such a clock signal at the receiver
is called symbol/bit synchronization.
Frame synchronization
• In frame-based digital systems, receiver also needs to estimate the starting /
stopping time of a data frame. The process of extracting such a clock signal is
called frame synchronization.

 PLL is often used in carrier syn. and symbol syn. It is a closed-loop control
system consisting of
 Phase detector (PD): generate the phase difference of vi(t) and vo(t).
 Voltage-controlled oscillator (VCO): adjust the oscillator frequency based on this
phase difference to eliminate the phase difference. At steady state, the output
frequency will be exactly the same with the input frequency.
 Loop filter (LF)
4

5
)](cos[)(
)](sin[)(
0
0
ttvtv
ttvtv
oo
ii





)(sinK)]()(sin[K)( ttttv eddd  

Loop filter is also a LPF.
A PD contains a multiplier and a lowpass filter. The output of PD is:
)()()( tvpFtv dc 
The output of the LF is (where F(p) is the transfer function)

)(K
)(
tv
dt
td
cv


6
The output of VCO can be a sinusoid or a periodic impulse train. The
differentiation of the output frequency are largely proportional to the input
voltage.
If F(p)=1，Then
)(sinK
)(
t
dt
td
e



This kind of loop is called the first-order loop

7
Digital
PD
Digital LP
Digital VCO
DPLL
Input
output

In a coherence system, a PLL is used for:
1. PLL can track the input frequency and generate the output signal with
small phase difference.
2. PLL has the character of narrowband filtering which can eliminate the
noise introduced by modulation and reduce the additive noise.
3. Memory PLL can sustain the coherence state for enough time.
CMOS-based integrated PLL has several advantages such as ease of
modification, reliable and low power consumption, therefore are widely
used in coherence system.
8

9
To extract the carrier：
1. Pilot-tone insertion method
Sending a carrier component at specific spectral-line along with the signal
component. Since the inserted carrier component has high frequency stability, it is
called pilot .
2. Direct extraction method
Directly extract the synchronization information from the received signal component.

   cos sinc cs t f t t a t  
10
Modulator Bandpass
filter
Add s(t)x(t)
/2phase
shift
-asin(ct)
cos(ct)
1. Pilot-tone insertion method
－insert pilot to the modulated signal
Thinking：
Why 900 shift？
The pilot signal is generated by shift the carrier by 900 and decrease by several dB,
then add to the modulated signal. Assume the modulated signal has 0 DC
component, then the pilot is

X(f)
fx0 f
S(f)
0
fcfc-fx fc+fx
11
The receiver uses a narrowband filter with central frequency fc to extract the
pilot and then the carrier can be generated by simply
shifting 900.
sin ca t cos ca t

     
   
   
2
1
0
cos cos sin cos
1 1 1
cos2 sin2
2 2 2
1
s
2
c c c c
c c
s t s t t f t t a t t
f t f t t a t
After the LPF t f t
   
 
   
  

12
DSB, SSB and PSK are all capable of pilot-tone insertion method. VSB can also apply
pilot-tone insertion method but with certain modification.

13
The drawback of narrowband filter:
• The pass band is not narrow enough
• fc is fixed, cannot tolerate any frequency drift with respect to the central
frequency
• Can be replaced by PLL Pilot-tone insertion method is suitable for DSB,
SSB, VS and 2PSK

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2. Direct extraction method
1. If the spectrum of the received signal already contains carrier
component, then the carrier component can be extracted simply by a
narrowband filter or a PLL.
2. If the modulated signal suppresses the carrier component, then the
carrier component may be extracted by performing nonlinear
transformation or using a PLL with specific design.

1. Square transformation
   
   
     
     
 
2 2 2
2 2
2
Example a DSB signal cos
1 1
s cos2
2 2
1 1
2
c
c
m
s t f t t
If f t s t does not have carrier component
t f t f t t
now f t f t f t
then s t


 


 
 
 
：
has 0 DC component，then
square transformation:
contains DC component,let it be ，so：
 
1 1
cos2 ( )cos2
2 2 2
m c m cf t t f t t   
15

    ttfttfts cmcm  2cos)(
2
1
2cos
2
1
2
1
2
12

2
2
c
c


The first term is the DC component. The second term is the low
frequency component. The third term is the component. The
4th term is the frequency component symmetrical distributed of
—modulation noise. After narrowband filtering, only the 3rd
term and a small fraction of 4th term left, then the carrier
component can be extracted by frequency division.
Since the carrier is extracted by freq
o
uency division, its phase
may shift by 180 . Besides, modulation noise may cause random
phase jitter.
16

18
2. In-phase orthogonal loop —Costas Loop
Contains in-phase branch and orthogonal branch. All parts except LF and VCO are
similar with a “phase detector”.

19
   
         
   
   
1
1
Let s cos
1
1 1
cos sin sin sin 2
2 2
1
After LPF sin
2
1
2
(
c
c c e e c e
e
e
e e
t f t t
f t t t f t f t t
r t f t
When r t f t

     


 

    


（）upper branch
is the phase difference between generated carrier and the original carrier
is small，
     
     
2
2
2
2)
1 1
cos
2 2
1
(3) ( )
4
e
1 e d
r t f t f t
r t r t f t v t


 
  
lower branch

   
c
2
1.Costas loop works on instead of 2 so when f is large
Costas loop is easier to realize
2.The output of in-phase loop r is the signal f
c cf f
t t
Advantages of Costas loop：
，，
20

21
3. Performance of carrier synchronization technique
1) Phase error: steady-state phase error, random phase error
2) Synchronization build time and hold time

 In a digital communication system, the output of the receiving filter must be
sampled periodically at the symbol rate and at the precise sampling time
instance.
 To perform this periodic sampling, we need a clock signal at the receiver
 The process of extracting such a clock signal is called symbol
synchronization or timing recovery
 One method is for the transmitter to simultaneously transmit the clock
frequency along with the information signal. The receive can simply employ
a narrowband filter or PLL to extract it. This method requires extra power
and bandwidth and hence, but frequently used in telephone transmission
systems.
 Another method is to extract the clock signal from the received data signal
by using some kind of non-linear transformation.
22

 Due to the symmetry, the values of the correlation
function at
 the early samples and
 the late samples are equal.
 Thus, the proper sampling time is the midpoint
between and
 Basic Idea: exploit the symmetry properties of the output signal of matched
filter or correlator
23

25
1. Nonlinear-transformation-based method
Some transformations can add synchronous signal with f = 1/T to the original
signal. For example, we can transform the signal to return-to-zero waveform.
After narrowband filtering and phase shifting, we can generate the clock signal
used for synchronization.

28
3. Performance of symbol synchronization system
D-PLL
1. Phase error
2. Synchronization build time
3. Synchronization hold time
4. Synchronous bandwidth

29
 Recall that carrier and symbol synchronization needs to estimate the phase
of synchronous signal which can be realized by using a PLL.
 Frame synchronization is to insert frame alignment signal (distinctive bit
sequence) and then detect the alignment symbol.
 Besides adding frame alignment bits, some code such as self-synchronizing
code can be synchronized without adding extra bits.
 Here, we only focus on the first method inserting frame alignment signal.

 Start-stop method
 Bunched frame alignment signal
 Distributed frame alignment signal
30

start bit "0" width
stop bit: "1", width
System will keep sending stop bit when it is idle. When "1" "0", the receiver will
start to receive a data symbol.
b
b
T
T

：，：
31
1. Start-stop method
It is widely used in teleprinter. Each symbol contains 5-8 data bits, a start bit and
a stop bit.

Drawbacks:
1). Low transmission efficiency
2). Low timing accuracy
32

33
Bunched frame alignment signal
This method inserts synchronous code at a particular place in each
frame. The code should have a sharp self-correlation function. The detector
should be simple to implement.
Frame synchronization code:
 Barker code
 optimal synchronous code
 pseudo-random code.

 
 
 
1 2 3
1
1 Barker code
A n bits barker code , , , its self-correlation function
satisfies
0
0or 1 0
0
n i
n j
x i i j
i
x x x x x
n j
R j x x j n




    
：
=+1 or -1.
：
Barker code is not a periodic sequence. It is proved that when 12100, we can only
find barker code with 2,3,4,5,7,11,13.
j n
n
n



 


34

n barker code
2 + +
3 + + -
4 + + + - ，+ + - +
5 + + + - +
7 + + + - - + -
11 + + + - - - + - - + -
13 + + + + - - + + - + - +
35

 
 
1 1 2 2 7 7
1 2 2 3
Example A barker code with 7 find its self-correlation function
0: 0 7
1: 1 0
Similarly, we can determine .
The result is shown below, we can see it has a shar
x
x
x
n
j R x x x x x x
j R x x x x
R

     
    
：，
(j)
p peak when j 0.
36

(2) Barker code generator
—shift register
Example：when n=7, a 7 bits shift register. The initial state is a barker code.
37

1
:"1"
1
1
:"0"
1
If the output connection of the shift register is the same with a barker code then
input
input






The barker code detector follows:
output "1":?
output "0":?
output "1":?
output "0":?
，
when the input is a barker code, the output of the shift register is "1111111". The
detector will send a synchronous impulse.
39

40
 Distributed frame alignment signal
 The synchronous code is distributed in the data signal. That means between
each n bits, a synchronous bit is inserted.
 Design criteria of synchronous code:
 Easy to detect. For example: “11111111”or ”10101010”
 Easy to separate synchronous code from data code. For example: In some
digital telephone system，all ”0” stands for ring, so synchronous code can
only use “10101010”.

 
0
1 1
m
n xx x
L n e e
x
P C P P


  
41
Performance of frame synchronization system
—Bunched frame alignment signal
1. Probability of missing synchronization PL
• Affected by noise, the detector may not be able to detect the
synchronous code. The probability of this situation is called
probability of missing synchronization PL.
• Assume the length of synchronous code is n，bit error rate is Pe. The
detector will not be able to detect if more than m bit errors happen,
then:

2. Probability of false synchronization PF
 Since data code can be arbitrary, it may be the same with synchronous code. The
probability of this situation is called probability of false synchronization PF.
 PF equals to the probability of appearance of synchronous code in the data code.
 In a binary code, assume 0 and 1 appears with the same probability. There are 2n
combinations of a n bit code.
 Assume when there are more than m bit errors, the data code will also be
detected as synchronous code.
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L L F
P and P depends on the length of synchronous code n and the maximum bit error m.
When n , P P when m , P P
L F
F     ，；，
43

s
L
3. Average build time t
Assume both P and P will not happen the worst case is we need one frame to
build frame synchronization. Assume each frame contains N bits, each bit has a width
T , then one f
F
b
，
 
b
b
1
s
rame costs NT .
Now assume a missing synchronization or a flase synchronization also needs NT
to rebuild the synchronization, then:
1
Bisedes, the average build time of using the dis
b L Ft NT P P  
 2 2
1 2
s
tributed frame alignment signal is:
1
Apparently, , so the previous method is more widely used.
s b
s
t N T N
t t
 

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Synchronization

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