Chapter 5 – Signal Encoding and
Modulation Techniques
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Encoding and Modulation Techniques
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Digital Signaling Versus Analog Signaling
 Digital signaling
 Digital or analog data is encoded into a digital signal
 Encoding may be chosen to conserve bandwidth or to
minimize error
 Analog Signaling
 Digital or analog data modulates analog carrier signal
 The frequency of the carrier fc is chosen to be compatible
with the transmission medium used
 Modulation: the amplitude, frequency or phase of the carrier
signal is varied in accordance with the modulating data
signal
 by using different carrier frequencies, multiple data signals
(users) can share the same transmission medium
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Digital Signaling
 Digital data, digital signal
 Simplest encoding scheme: assign one voltage level to
binary one and another voltage level to binary zero
 More complex encoding schemes: are used to improve
performance (reduce transmission bandwidth and minimize
errors).
 Examples are NRZ-L, NRZI, Manchester, etc.
Analog data, Digital signal
 Analog data, such as voice and video
 Often digitized to be able to use digital transmission facility
 Example: Pulse Code Modulation (PCM), which involves
sampling the analog data periodically and quantizing the
samples
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Analog Signaling
 Digital data, Analog Signal
 A modem converts digital data to an analog signal so that it
can be transmitted over an analog line
 The digital data modulates the amplitude, frequency, or
phase of a carrier analog signal
 Examples: Amplitude Shift Keying (ASK), Frequency Shift
Keying (FSK), Phase Shift Keying (PSK)
Analog data, Analog Signal
 Analog data, such as voice and video modulate the
amplitude, frequency, or phase of a carrier signal to produce
an analog signal in a different frequency band
 Examples: Amplitude Modulation (AM), Frequency
Modulation (FM), Phase Modulation (PM)
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Digital Data, Digital Signal
 Digital signal
discrete, discontinuous voltage pulses
each pulse is a signal element
binary data encoded into signal elements
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Periodic signals




Data element: a single binary 1 or 0
Signal element: a voltage pulse of constant amplitude
Unipolar: All signal elements have the same sign
Polar: One logic state represented by positive voltage the other
by negative voltage
 Data rate: Rate of data (R) transmission in bits per second
 Duration or length of a bit: Time taken for transmitter to emit
the bit (Tb=1/R)
 Modulation rate: Rate at which the signal level changes,
measured in baud = signal elements per second. Depends on
type of digital encoding used.
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Interpreting Signals
Need to know
 timing of bits: when they start and end
 signal levels: high or low
factors affecting signal interpretation
 Data rate: increase data rate increases Bit Error Rate (BER)
 Signal to Noise Ratio (SNR): increase SNR decrease BER
 Bandwidth: increase bandwidth increase data rate
 encoding scheme: mapping from data bits to signal elements
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Comparison of Encoding Schemes
signal spectrum
 Lack of high frequencies reduces required bandwidth,
 lack of dc component allows ac coupling via transformer,
providing isolation,
 should concentrate power in the middle of the bandwidth
Clocking
 synchronizing transmitter and receiver with a sync
mechanism based on suitable encoding
error detection
 useful if can be built in to signal encoding
signal interference and noise immunity
cost and complexity: increases when increases data rate
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Encoding Schemes
Positive level (+5V)
Negative level (-5V)
Positive level (+5V)
No line signal (0V)
Negative level (-5V)
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Encoding Schemes
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NonReturn to Zero-Level (NRZ-L)
Two different voltages for 0 and 1 bits
Voltage constant during bit interval
no transition, i.e. no return to zero voltage
more often, negative voltage for binary one
and positive voltage for binary zero
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NonReturn to Zero INVERTED (NRZI)
Nonreturn to zero inverted on ones
Constant voltage pulse for duration of bit
Data encoded as presence or absence of signal
transition at beginning of bit time
 transition (low to high or high to low) denotes binary 1
 no transition denotes binary 0
Example of differential encoding since have
– data represented by changes rather than levels
– more reliable detection of transition rather than level
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Advantages and disadvantages of
NRZ-L, NRZI
Advantages
 easy to engineer
 good use of
bandwidth
Disadvantages
 dc component
 lack of synchronization
capability
Unattractive for signal transmission applications
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Multilevel Binary
Bipolar Alternate Mark Inversion (AMI)
Use more than two levels (three levels,
positive, negative and no line signal)
Bipolar-AMI
zero represented by no line signal
one represented by positive or negative pulse
one pulses alternate in polarity
no loss of sync if a long string of ones
long runs of zeros still a problem
no net dc component
lower bandwidth
easy error detection
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Multilevel Binary
Pseudoternary
Binary one represented by absence of line
signal
Binary zero represented by alternating
positive and negative pulses
No advantage or disadvantage over
bipolar-AMI
Each used in some applications
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Multilevel Binary Issues
Advantages:
No loss of synchronization if a long string of 1’s occurs, each
introduce a transition, and the receiver can resynchronize on
that transition
No net dc component, as the 1 signal alternate in voltage
from negative to positive
Less bandwidth than NRZ
Pulse alternating provides a simple mean for error detection
Disadvantages
receiver distinguishes between three levels: +A, -A, 0
a 3 level system could represent log23 = 1.58 bits
requires approx. 3dB more signal power for same probability
of bit error
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Theoretical Bit Error Rate (BER) For
Various Encoding Schemes
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Manchester Encoding
has transition in middle of each bit period
low to high represents binary one
transition serves as clock and data
high to low represents binary zero
used by IEEE 802.3 (Ethernet) LAN standard
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Differential Manchester Encoding
midbit transition is clocking only
transition at start of bit period representing binary 0
no transition at start of bit period representing binary 1
used by IEEE 802.5 token ring LAN
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Advantages and disadvantages of
Manchester Encoding
Disadvantages
 at least one transition per bit time and possibly two
 maximum modulation rate is twice NRZ
R
L
D : Modulation rate, [baud ]
D
R : Data Rate, [bps ]
L : number of bits per signal elements
 requires more bandwidth
Advantages
 synchronization on mid bit transition (self clocking codes)
 has no dc component
 has error detection capability (the absence of an expected
transition can be used to detect errors)
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Modulation Rate versus Data Rate
Data rate (expressed in bps)
 Data rate or bit rate R=1/Tb=1/1μs=1Mbps
Modulation Rate (expressed in baud) is the rate at
which signal elements are generated
 Maximum modulation rate
for Manchester is
D=1/(0.5Tb)=2/1μs=2Mbaud
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Scrambling
Use scrambling to replace sequences that would
produce constant voltage
These filling sequences must
 produce enough transitions to maintain synchronization
 be recognized by receiver & replaced with original
 be same length as original
Design goals
 have no dc component
 have no long sequences of zero level line signal
 have no reduction in data rate
 give error detection capability
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B8ZS and HDB3
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Bipolar with 8-Zero Substitution (B8ZS)
To overcome the drawback of the AMI code that a
long string of zeros may result in loss of
synchronization, the encoding is amended with the
following rules:
 If 8 zeros occurs and the last voltage pulse was positive,
then the 8 zeros are encoded as 000+–0–+
 If zeros occurs and the last voltage pulse was negative,
then the 8 zeros are encoded as 000–+0+–
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High Density Bipolar-3 zeros (HDB3)
The scheme replaces strings with 4 zeros by sequences
containing one or two pulses
In each case, the fourth zero is replaced with a code
violation (V)
 successive violations are of alternate polarity
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Digital Data, Analog Signal
Main use is public telephone system
has freq range of 300Hz to 3400Hz
use modem (modulator-demodulator)
The digital data modulates the amplitude A,
frequency fc , or phase θ of a carrier signal
A cos( 2f ct   )
Modulation techniques
Amplitude Shift Keying (ASK)
Frequency Shift Keying (FSK)
Phase Shift Keying (PSK)
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Modulation Techniques
Amplitude Shift Keying
(ASK)
Binary Frequency Shift
Keying (BFSK)
Binary Phase Shift Keying
(BPSK)
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Amplitude Shift Keying (ASK)
In ASK, the two binary values are represented by to
different amplitudes of the carrier frequency
The resulting modulated signal for one bit time is
 A cos( 2f ct ), binary 1
s(t )  
binary 0
0,
Susceptible to noise
Inefficient modulation technique
used for
 up to 1200bps on voice grade lines
 very high speeds over optical fiber
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Binary Frequency Shift Keying (BFSK)
The most common form of FSK is Binary FSK (BFSK)
Two binary values represented by two different
frequencies ( f1 and f2 )
 A cos( 2f1t ), binary 1
s(t )  
 A cos( 2f 2t ), binary 0
0
0
1
1
0
1
0
0
0
1
0
f2
f2
f1
f1
f2
f1
f2
f2
f2
f1
f2
less susceptible to noise than ASK
used for
 up to 1200bps on voice grade lines
 high frequency radio (3 to 30MHz)
 even higher frequency on LANs using coaxial cable
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Full-Duplex BFSK Transmission on
a Voice-Grade line
 Voice grade lines will pass voice frequencies in the range 300
to 3400Hz
 Full duplex means that signals are transmitted in both directions
at the same time
f1
f2
f3
f4
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Multiple FSK (MFSK)
More than two frequencies (M frequencies) are used
More bandwidth efficient compared to BFSK
More susceptible to noise compared to BFSK
MFSK signal:
si (t )  A cos( 2f i t ),
1 i  M
where
f i  f c  (2i  1  M ) f d
f c  the carrier frequency
f d  the difference frequency
M  number of different signal elements  2 L
L  number of bits per signal element
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Multiple FSK (MFSK)
 MFSK signal:
si (t )  A cos( 2f i t ),
1 i  M
where
f i  f c  ( 2i  1  M ) f d
M  number of different signal elements  2 L
L  number of bits per signal element
 Period of signal element
Ts  LTb ,
Ts : signal element period
Tb :bit period
 Minimum frequency separation
1 / Ts  2 f d

1 /( LTb )  2 f d  1 / Tb  2 Lf d (bit rate)
 MFSK signal bandwidth:
Wd  M (2 f d )  2Mf d
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Example
 With fc=250KHz, fd=25KHz, and M=8 (L=3 bits), we have the
following frequency assignment for each of the 8 possible 3-bit
f i  f c  (2i  1  M ) f d
data combinations:
000

001

010

011

100

101

110

111

f1  75 KHz 
f 2  125 KHz 

f 3  175 KHz 

f 4  225 KHz 
 bandwidth  Ws  2 Mf d  400 KHz
f 5  275 KHz 
f 6  325 KHz 

f 7  375 KHz 
f 8  425 KHz 

 This scheme can support a data rate of:
1 / Tb  2 Lf d  2(3bits)( 25Hz )  150 Kbps
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Example
 The following figure shows an example of MFSK with M=4. An
input bit stream of 20 bits is encoded 2bits at a time, with each
of the possible 2-bit combinations transmitted as a different
frequency.
f i  f c  (2i  1  M ) f d
00

i 1
 f1  f c  3 f d
01

i2
 f2  fc  fd
10

i3
 f3  fc  f d
11

i4
 f4  fc  3 fd
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Phase Shift Keying (PSK)
Phase of carrier signal is shifted to represent data
Binary PSK (BPSK): two phases represent two
binary digits
binary 1
 A cos( 2f c t ),
s (t )  
 A cos( 2f c t   ), binary 0
binary 1
 A cos( 2f c t ),

  A cos( 2f c t ), binary 0
 Ad (t ) cos( 2f c t ),
d (t )  1
0
0
1
1
0
1
0
0
0
1
0
π
π
0
0
π
0
π
π
π
0
π
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Differential PSK (DPSK)
 In DPSK, the phase shift is with reference to the previous bit
transmitted rather than to some constant reference signal
 Binary 0:signal burst with the same phase as the previous one
 Binary 1:signal burst of opposite phase to the preceding one
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Four-level PSK: Quadrature PSK (QPSK)
 More efficient use of bandwidth if each signal element
represents more than one bit
 eg. shifts of /2 (90o)
 each signal element represents two bits
 split input data stream in two & modulate onto the phase of the carrier


A
cos(
2

f
t

)
c

4

3
 A cos( 2f c t 
)

4
s (t )  
3
 A cos( 2f c t 
)
4



A cos( 2f c t  )

4

 11

01

00
 10
 can use 8 phase angles & more than one amplitude
 9600bps modem uses 12 phase angles, four of which have two
amplitudes: this gives a total of 16 different signal elements
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QPSK and Offset QPSK (OQPSK)
Modulators
QPSK :
OQPSK :
1
1
I (t ) cos( 2f c t ) 
Q(t ) sin( 2f c t )
2
2
1
1
s (t ) 
I (t ) cos( 2f c t ) 
Q(t  Tb ) sin( 2f c t )
2
2
s (t ) 
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Example of QPSK and OQPSK Waveforms
for QPSK :
1 11 1

4
3
4
 3
0 0  1  1 
4

1 0  1 1 
4
0 1  1 1 
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Performance of ASK, FSK, MFSK, PSK and
MPSK
Bandwidth Efficiency
 ASK/PSK:
 MPSK:
data rate
R
1


,
transmissi on bandwidth BT 1  r
R log 2 M

,
BT
1 r
0  r 1
M : number of different signal elements
R
log 2 M

 MFSK:
BT (1  r ) M
Bit Error Rate (BER)
 bit error rate of PSK and QPSK are about 3dB superior to
ASK and FSK (see Fig. 5.4)
 for MFSK & MPSK have tradeoff between bandwidth
efficiency and error performance
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Performance of MFSK and MPSK
 MFSK: increasing M decreases BER and decreases bandwidth Efficiency
 MPSK: Increasing M increases BER and increases bandwidth efficiency
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Quadrature Amplitude Modulation (QAM)
QAM used on asymmetric digital subscriber line
(ADSL) and some wireless standards
combination of ASK and PSK
logical extension of QPSK
send two different signals simultaneously on
same carrier frequency
 use two copies of carrier, one shifted by 90°
 each carrier is ASK modulated
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QAM modulator
QAM :
s(t )  d1 (t ) cos( 2f c t )  d 2 (t ) sin( 2f c t )

 

ASK
ASK
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QAM Variants
Two level ASK (two different amplitude levels)
each of two streams in one of two states
four state system
essentially QPSK
Four level ASK (four different amplitude levels)
combined stream in one of 16 states
Have 64 and 256 state systems
Improved data rate for given bandwidth
but increased potential error rate
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