Download Introduction to Digital Modulation

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
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• 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
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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)
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• 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)
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Block Diagram
Simplified block diagram of a digital modulation system
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• 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
– 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.
– It often convenient to express the information
capacity of a system as a bit rate.
– Bit rate is the number of bits transmitted
during one second and is expresses in bits per
second (bps)
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 1
By using the Shannon’s Formula, calculate
the information capacity if S/N = 30 dB and
B = 2.7 kHz.
M-ary Encoding
• It is often advantageous to encode at a level higher than
binary where there are more than 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.
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• Each symbol represents n bits, and has M
signal states, where M = 2N.
Example 2
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.
• Hence, baud is a unit of transmission rate, modulation
rate or symbol rate and therefore, the terms symbols per
second and baud are often used interchangeably.
1
baud 
ts
Where
baud = symbol rate (symbol per second)
ts
= time of one signaling element @ symbol
(seconds)
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• 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
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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)
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Digital Amplitude Modulation
 A cos(c t ) for logic '1' , vm (t )  1
vask (t )  
for logic '0' , vm (t )  1
 0
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• For every change in the input binary data stream,
there is one change in ASK waveform, and the
time of one bit (tb) equals the time of one analog
signaling element (ts).
• When the binary input is high, the output is a
constant-amplitude, constant-frequency signal
and when the binary input is low, the carrier is
off.
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)
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• The carrier frequency (fc) is shifted (deviated) up
and down in the frequency domain by the binary
input signal.
• As the binary input signals changes from a logic
0 to a logic 1 and vice versa, the output
frequency shifts between two frequencies: a
mark, or logic 1 frequency (fm) and a space, or
logic 0 frequency (fs).
B  ( f s  fb )  ( f m  fb )  f s  f m  2 fb  2(f  fb )
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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°
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a) Truth Table
b) Phasor Diagram
c) Constellation Diagram
Continue…
Continue…
• Logic 1 input produces an analog output
signal with 00 phase angle, and a logic 0
input produces an analog output signal
with a 1800 phase angle.
• As the binary input shifts between a logic 1
and a logic 0 condition and vice versa, the
phase of the BPSK waveform shifts
between 00 and 1800, respectively.
Bandwidth Efficiency
– Used to compare the performance of one digital
modulation technique to another.
Bη = Transmission bit rate (bps)
Minimum bandwidth (Hz)
Example 3
For 8-PSK system, operating with an
information bit rate of 24 kbps, determine:
a. Baud
b. Minimum bandwidth
c. Bandwidth efficiency
END OF PART 1