Transcript Digital Modulation

DIGITAL TRANSMISSION
PART 4
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.High spectral efficiency
2.High power efficiency
3.Robust to multipath
4.Low cost and ease of implementation
5.Low carrier-to-co channel interference ratio
6.Low out-of-band radiation
7.Constant or near constant envelop
8.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
Digital Modulation
• The transmittal of digitally modulated
analog signals (carriers) between two
or more points in a communication
system.
• Can be propagated through Earth’s
atmosphere and used in wireless
communication system.
Cont’d
• Digital modulation systems use analog
carrier to transport the information
through the system.
• The information signal is digital which
could be digitally encoded analog
signal.
Carrier Signal
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)
•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,V and the phase, θ of the carrier are
varied proportional to the information signal, a digital
modulated signal is called Quadrature Amplitude
Modulation (QAM)
Information Capacity @ Bit rate
• A measure of how much information can
be propagated through a communication
system.
• A function of bandwidth and transmission
time.
• represented by the binary digit @ bit
Hartley’s Law
I  Bt
Where
I = information capacity (bps)
B = bandwidth (Hz)
t = transmission time (s)
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  3.32B log 10 (1  NS )
Where
I = information capacity (bps)
B = bandwidth (Hz)
S
N
= signal to noise power ratio
The higher S/N the better the performance and the higher the
information capacity
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.
Baud
• 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)
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
For B necessary to pass M-ary digitally modulated carriers
 fb  fb
 
B  
 baud
 log 2 M  N
Amplitude Shift Keying (ASK)
• A binary information signal directly modulates the
amplitude of an analog carrier.
vask (t )  [1  vm (t )] A2 cos(ct )
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)
 A cos(ct ) for logic '1' , vm (t )  1
vask (t )  
for logic '0' , vm (t )  1
 0
Frequency Shift Keying (FSK)
• Called as 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)
FSK Bandwidth
B  ( f s  fb )  ( f m  fb )  f s  f m  2 fb  2(f  fb )
Phase Shift Keying (PSK)
BPSK Transmitter
BPSK Receiver
BPSK
BPSK
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•
•
•
•
Bit value 0 – sine wave
Bit value 1 – inverted sine wave
Very simple PSK
Low spectral efficiency
Robust , used in satellite system
QPSK
QPSK
•
•
•
•
2 bits coded as one symbol
Symbol determines shift of sine wave
Needs less bandwidth compared to BPSK
More complex
CONSTELLATION DIAGRAM
• Graphical representation of the complex envelope of
each possible symbol state
 ..The x-axis represents the in-phasecomponent
and the y-axisthe quadraturecomponent 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.
QAM
• Combine amplitude and phase modulation
• It is possible to code n bits using one
symbol
• 2n discrete levels, n = 2 identical to QPSK
• BER increase with n, but less compared to
PSK scheme.
• Amplitude and phase shift keying can be combined to transmit
several bits per symbol.
 ..Often referred to as linearas 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-array schemes (such as 64-QAM) are very
bandwidth-efficient but more susceptible to noise and require
linear amplification
CONCLUSION
• To decide which modulation method should be
used , we need to make considerations of :
a)..Bandwidth
b)..Speed of Modulation
c)..Complexity of Hardware
Frequency-Division Multiplexing (FDM)
(a) Individual signals occupy H Hz
A
f
H
0
B
0
f
H
C
f
0
H
(b) Combined signal fits into channel bandwidth
A
B
C
f
Time-Division Multiplexing (TDM)
(a) Each signal transmits 1 unit every 3T seconds
A1
A2
0T
6T
3T
B1
t
B2
6T
3T
0T
C1
t
C2
0T
t
6T
3T
(b) Combined signal transmits 1 unit every T seconds
A1 B1
0T 1T 2T
C1
A2
3T 4T
B2
5T
C2
6T
t