Transcript Chapter3_Lect6.ppt

Chapter 3:
DIFFERENTIAL ENCODING
 Differential Encoding
 Eye Patterns
 Regenerative Receiver
 Bit Synchronizer
 Binary to Mary Conversion
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
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Differential Coding System
 Differential encoding removes the problem of Unintentional Signal Inversion.
 Polarity of the differentially encoded signal may be inverted without affecting the decoded
signal.
Modulo-2 addition
Exclusive OR
I1
I2
Out
0
0
0
0
1
1
1
0
1
1
1
0
en  d n  en 1
d n  en  en 1
 Represents Modulo-2 adder (XOR)
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Example of Differential Coding
Encoding
en  d n  en1
Input sequence
dn
Encoded sequence en
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
Reference digit
Decoding (with correct channel polarity)
Receiver sequence
en
1
~ ~ ~
d n  en  en1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
(Correct polarity)
Decoded sequence
dn
Decoding (with inverted channel polarity)
Received sequence
en
0
(Inverted polarity)
Decoded sequence
dn
 Decoded sequence is same whether there is inversion or not.
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Eye patterns
 The effects of channel filtering and channel noise can be seen by observing the received line
code on an oscilloscope.
Received Line
Code
Information from Eye Pattern
• Timing error  Eye opening
• Sensitivity  Slope of the
open eye
• Noise Margin  height of the
eye opening
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Regenerative Repeater
 Regenerate a noise-free digital signal. Amplify and clean-up the signal periodically
Increases the amplitude
Produces a sample value
Minimize the effect of
channel noise & ISI
Produces a high level o/p
if sample value>VT
Generates a clocking signal
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Synchronization
 Synchronization signals are clock-type signals necessary within a receiver for
detection of data from the corrupted input signal.
 Digital communications need at least 3 types of synchronization signals.
• Bit Synchronization (Bit Synch.): To distinguish bit intervals.
• Frame Synchronization (Frame Synch.): To distinguish groups of bits.
• Carrier Synchronization: For bandpass signals with coherent detection.
 Sync signals are derived from
• Corrupted input signal.
• From a separate channel that transmits sync signals.
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Bit Synchronizer for NRZ Signals
 Derive the synch signal from the corrupted received signal.
 Used for unipolar NRZ signals.
 Synchronizer complexity depends on the line code used.
 Synchronizarion of RZ signals is easier since PSD has delta at f=R=1/Tb.
 Bit synchronizer for NRZ signals is given below.
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Square-law Bit Synchronizer for NRZ Signals
• Square Law Device
converts polar NRZ
signal to unipolar RZ
format.
• Unipolar RZ signals
have delta in the PSD at
f=R=1/Tb.
• This frequency
component can be
obtained by filtering.
• Filtered sinusoidal is
converted to clock pulses
using a comparator.
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Binary-to-multilevel polar NRZ Signal Conversion
 Binary to multilevel conversion is used to reduce the bandwidth required by the binary
signaling.
• Multiple bits (l number of bits) are converted into words having SYMBOL durations
Ts=lTb where the Symbol Rate or the BAUD Rate D=1/Ts=1/lTb.
• The symbols are converted to a L level (L=2l ) multilevel signal using a l-bit DAC.
• Note that now the Baud rate is reduced by l times the Bit rate R (D=R/l).
• Thus the bandwidth required is reduced by l times.
Ts: Symbol Duration
L: Number of M ary levels
Tb: Bit Duration
l: Bits per Symbol
L=2l
D=1/Ts=1/lTb=R/l
Bnull=R/l
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Power Spectra for Multilevel Polar NRZ Signals
(c) L = 8 = 23 Level Polar NRZ Waveform Out
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Spectral Efficiency
 The Spectral efficiency of a digital signal is given by, where R is the data rate and
B is the bandwidth required.

R
B
 Bit s 
Hz
• If limited BW is desired, then use a signaling technique that has high spectral efficiency.
• Maximum spectral efficiency (which is limited by channel noise) is given by the
Shannon’s Channel Capacity formula:
max 
C
S

 log 2 1  
B
 N
Spectral efficiency for multilevel signaling is
 l
 bit s 
Hz
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PSD of a multilevel polar NRZ waveform
I
R (k )   (an an  k )i Pi
i 1
For k  0
8
R 0   a n i Pi  21
2
where Pi 
i 1
1
for all of the eight possible values.
8
For k  0, Rk   0.
Then the PSD for 2 t  is
Pw2  f  
F f 
Ts
2
21  0 where the pulse width is Ts  3Tb .
For the rectangula r pulse width 3Tb :
PSD for a multilevel polar NRZ signal:
 sin lfTb
Pmultilevel NRZ  f   K 
 lfTb



Ps(f) 
F(f)
Ts
2

 R ( k )e
 j 2kfTs
k 
2
where k is a constant
R
l
 Multilevel signaling is used to reduce the BW of a digital signal
The null bandwidth is
Bnull 
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