Chapter 4
4.1 : Digital Modulation
4.2 : Digital Transmission
4.3 : Multiple Access Methods
4.1 Digital Modulation
Outlines
a.
b.
c.
Introduction
Information capacity, Bits, Bit Rate, Baud,
M-ary Encoding
Digital Modulation Techniques
- ASK, FSK, PSK, QAM
Digital modulation
• Is the transmittal of digitally modulated analog signals
between two or more points in a communications system.
• Can be propagated through Earth’s atmosphere and
used in wireless communication system - digital radio.
• Offer several outstanding advantages over traditional
analog system.
• Ease of processing
• Ease of multiplexing
• Noise immunity
Cont’d...
• Applications:
•
•
•
•
Low speed voice band data comm. modems
High speed data transmission systems
Digital microwave & satellite comm. systems
PCS (personal communication systems) telephone
Why digital modulation?
• The modulation of digital signals with analogue carriers
allows an improvement in signal to noise ratio as
compared to analogue modulating schemes.
Important Criteria
1.
2.
3.
4.
5.
6.
High spectral efficiency
High power efficiency
Robust to multipath
Low cost and ease of implementation
Low carrier-to-co channel interference ratio
Low out-of-band radiation
Cont’d…
7.
8.
Constant or near constant envelop
Bandwidth Efficiency
• Ability to accommodate data within a limited
bandwidth
• Tradeoff between data rate and pulse width
9.
Power Efficiency
• To preserve the fidelity of the digital message at
low power levels.
• Can increase noise immunity by increasing signal
power
Forms of Digital Modulation
v(t )  V sin( 2ft   )
•If the amplitude, V of the carrier is varied proportional to
the information signal, a digital modulated signal is called
Amplitude Shift Keying (ASK)
•If the frequency, f of the carrier is varied proportional to
the information signal, a digital modulated signal is called
Frequency Shift Keying (FSK)
Cont’d…
• If the phase, θ of the carrier is varied proportional to the
information signal, a digital modulated signal is called
Phase Shift Keying (PSK)
• If both the amplitude and the phase, θ of the carrier are
varied proportional to the information signal, a digital
modulated signal is called Quadrature Amplitude
Modulation (QAM)
Cont’d...
Example 1
For the digital message 1101 1100 1010,
sketch the waveform for the following:
a. ASK
b. FSK
c. PSK
d. QAM
Block Diagram
Simplified block diagram of a digital modulation system
Cont’d…
• Precoder performs level conversion & encodes
incoming data into group of bits that modulate an
analog carrier.
• Modulated carrier filtered, amplified &
transmitted through transmission medium to Rx.
• In Rx, the incoming signals filtered, amplified &
applied to the demodulator and decoder circuits
which extracts the original source information
from modulated carrier.
• Information capacity, Bits & Bit Rate
– Information capacity is a measure of how much
information can be propagated through a
communication system and is a function of bandwidth
and transmission time.
– represents the number of independent symbols that
can be carried through a system in a given unit of
time.
– Basic digital symbol is the binary digit or bit.
– Express the information capacity as a bit rate.
Hartley’s Law
I  Bt
Where
I = information capacity (bps)
B = bandwidth (Hz)
t = transmission time (s)
From the equation, Information capacity is a linear
function of bandwidth and transmission time and
directly proportional to both.
Shannon’s Formula
I  B log 2 (1  NS )
or
I  3.32 B log 10 (1  NS )
Where
I = information capacity (bps)
B = bandwidth (Hz)
S
N
= signal to noise power ratio (unitless)
The higher S/N the better the performance and the
higher the information capacity
Example 2
By using the Shannon’s Formula, calculate
the information capacity if S/N = 30 dB and
B = 2.7 kHz.
Nyquist Sampling Rate
• fs is equal or greater than 2fm
fs >= 2fm
fs = minimum Nyquist sample rate (Hz)
fm = maximum analog input frequency (Hz)
Example 3
Determine the Nyquist sample rate for a
maximum analog input frequency 7.5 kHz.
M-ary Encoding
• It is often advantageous to encode at a level higher than
binary where there are more then two conditions
possible.
• The number of bits necessary to produce a given
number of conditions is expressed mathematically as
N  log 2 M
Where N = number of bits necessary
M = number of conditions, level or combinations
possible with N bits.
Cont’d…
• Each symbol represents n bits, and has M
signal states, where M = 2N.
Find the number of voltage levels which can
represent an analog signal with
a. 8 bits per sample
b. 12 bits per sample
Baud & Minimum BW
• Baud refers to the rate of change of a signal on the
transmission medium after encoding and modulation
have occurred.
1
baud 
ts
Where
baud = symbol rate (symbol per second)
ts
= time of one signaling element @ symbol
(seconds)
Cont’d…
• Minimum Bandwidth
– Using multilevel signaling, the Nyquist formulation for channel
capacity
f b  2 B log 2 M
Where fb= channel capacity (bps)
B = minimum Nyquist bandwidth (Hz)
M = number of discrete signal or voltage levels
Cont’d…
For B necessary to pass M-ary digitally modulated carriers

fb
B
 log M
2


fb

  N  baud

Where N is the number of bits encoded into each
signaling element.
•
•
•
•
Amplitude Shift Keying (ASK)
Frequency Shift Keying (FSK)
Phase Shift Keying (PSK)
Quadrature Amplitude Modulation (QAM)
Amplitude Shift Keying (ASK)
• A binary information signal directly modulates the amplitude of an
analog carrier.
• Sometimes called Digital Amplitude Modulation (DAM)
vask (t )  [1  vm (t )] cos(ct )
A
2
Where vask (t) = amplitude shift keying wave
vm(t) = digital information signal (volt)
A/2 = unmodulated carrier amplitude (volt)
ωc = analog carrier radian frequency (rad/s)
Cont’d...
Digital Amplitude Modulation
 A cos(c t ) for logic '1' , vm (t )  1
vask (t )  
for logic '0' , vm (t )  1
 0
Frequency Shift Keying (FSK)
• Called as Binary Frequency Shift Keying (BFSK)
• The phase shift in carrier frequency (∆f) is proportional to the
amplitude of the binary input signal (vm(t)) and the direction of
the shift is determined by the polarity
v fsk (t )  Vc cos2 [ f c  vm (t ) f ]t 
Where vfsk(t) = binary FSK waveform
Vc = peak anlog carrier amplitude (volt)
fc = analog carrier center frequency (Hz)
∆f = peak shift in analog carrier frequency (Hz)
vm(t) = binary input signal (volt)
Vc cos2 [ f c  f ]t for logic '1' , vm (t )  1
v fsk (t )  
Vc cos2 [ f c  f ]t for logic '0' , vm (t )  1
f 
fm  fs
2
,
where
f  frequency deviation (Hz)
f m  f s  absolute difference between mark & space frequency (Hz)
B  ( f s  fb )  ( f m  fb )  f s  f m  2 fb  2(f  fb )
Cont’d...
Binary Input
Frequency Output
0
Space (fs)
1
Mark (fm)
Phase Shift Keying (PSK)
• Another form of angle-modulated, constant amplitude
digital modulation.
• Binary digital signal input & limited number of output
phases possible.
• M-ary digital modulation scheme with the number of
output phases defined by M.
• The simplest PSK is Binary Phase-Shift Keying (BPSK)
– N= 1, M=2
– Two phases possible for carrier with one phase for logic 1 and
another phase for logic 0
– The output carrier shifts between two angles separated by 180°
Cont’d...
a) Truth Table
b) Phasor Diagram
c) Constellation Diagram
Cont’d...
BPSK Transmitter
Cont’d...
BPSK Receiver
CONSTELLATION DIAGRAM
Definition : A graphical representation of the complex
envelope of each possible symbol state.
 The x-axis represents the in-phase component
and the y-axis the quadrature component of the
complex envelope
 The distance between signals on a constellation
diagram relates to how different the modulation
waveforms are and how easily a receiver can
differentiate between them.
Cont’d...
Cont’d...
Quadrature Amplitude Modulation
(QAM)
• Combine amplitude and phase-shift
keying.
• Method of voice band data transmission.
• QAM = 4-PSK
Cont’d...
Cont’d...
Cont’d...
• Amplitude and phase shift keying can be combined to transmit
several bits per symbol.
– Often referred to as linear as they require linear
amplification.
– More bandwidth-efficient, but more susceptible to noise.
• For M = 4, 16QAM has the largest distance between points, but
requires very linear amplification. 16PSK has less stringent
linearity requirements, but has less spacing between
constellation points, and is therefore more affected by noise.
• High level M-ary schemes (such as 64-QAM) are very
bandwidth-efficient but more susceptible to noise and require
linear amplification
Bandwidth Efficiency
– Used to compare the performance of one digital
modulation technique to another.
Bη = Transmission bit rate (bps)
Minimum bandwidth (Hz)
Example 5
For 16-PSK system, operating with an
information bit rate of 32 kbps, determine:
a. Baud
b. Minimum bandwidth
c. Bandwidth efficiency
•
•
•
•
•
Solution:
16PSK= log2(M)
a) baud= 32000/4=8000
b) minimum bandwidth = 32000/4 =8000
c)Bandwidth efficiency =transmission bit
rate/minimum bandwidth= 32000/8000=4
bits per cycle
CONCLUSION
• To decide which modulation method should
be used , we need to make considerations of
a)
b)
c)
Bandwidth
Speed of Modulation
Complexity of Hardware