eee353 lec9 handouts
TRANSCRIPT
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Digital CommunicationSystems
Dr. Shurjeel Wyne
Lecture 9
CH 4 -Bandpass Modulation& Demodulation
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Today, we are going to talkabout:
Some bandpass modulation schemes used
in DCS for transmitting information over
channel
Passband M-ASK, M-PSK, M-QAM, M-FSK
How to detect the transmitted information at the
receiver
Coherent detection
Non-coherent detection
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Block diagram of a DCS
FormatSource
encode
FormatSource
decode
Channel
encode
Pulse
modulate
Bandpass
modulate
Channel
decode
Demod.
SampleDetect
Channel
Digital modulation
Digital demodulation
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Bandpass modulation
Bandpass modulation: The process of converting datasignal to a sinusoidal waveform whose amplitude, phase,
frequency, ora combination of them, is varied in accordance
with the transmitted data.
General Bandpass signal:
where is the baseband pulse shape with energy .
We assume here (unless stated otherwise):
is a rectangular pulse shape with unit energy.
Gray coding is used for mapping bits to symbols.
denotes average symbol energy given by
)(tgT
)(tgT gE
sE M
i isE
ME
1
1
TtttfifT
Etgts ic
iTi 0,)()1(2cos
2)()(
1gE
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Demodulation and detection Demodulation: The receiver signal is converted to
baseband, filtered and sampled.
Detection: Sampled values are used for detection using a
decision rule such as ML detection rule.
Nz
z
1
z
T
0
)(1 t
T
0
)(tN
)(tr
1z
Nz
zDecision
circuits
(ML detector)m
6
Coherent and Non-coherentdetection
Coherent detection
requires carrier phase recovery at the receiver
and hence, circuits to estimate carrier phase
Possible sources of carrier-phase mismatch at
the receiver:
Propagation delay causes carrier-phase offset in
the received signal. The oscillators at the receiver which generate the
carrier signal, are not usually phased locked to the
transmitted carrier.
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Coherent and non-coherent
detection Circuits such as Phase-Locked-Loop (PLL) are
implemented at the receiver for carrier phaseoffset estimation ( ).
Non-coherent detection
does not require carrier phase recovery (useseither differentially encoded modulation or
energy detectors. It has lesser complexity thancoherent detection, but at the price of a highererror rate.
PLL
Oscillator 90 deg.
)()(cos2
)()( tnttT
Etgtr ii
iT cos
2t
Tc
sin2
tT
c
Used by
correlators
I branch
Q branch
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Bandpass Modulation Schemes
One dimensional waveforms
Amplitude Shift Keying (ASK)
On-Off Keying
M-ary Amplitude Shift Keying (M-ASK)
Two dimensional waveforms
M-ary Phase Shift Keying (M-PSK)
M-ary Quadrature Amplitude Modulation (M-QAM) Multidimensional waveforms
M-ary Frequency Shift Keying (M-FSK)
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One dimensional modulation
Amplitude Shift Keying (ASK) modulation:
tT
Ets cii cos2
)(
cos2)(
2,,1)()(
1
1
ii
c
ii
Ea
tT
t
Mitats
)(1 t1s2s
01E
0 1
Example:
On-off keying (M=2):
10
One dimensional modulation
M-ary Amplitude shift Keying (M-ASK)
tT
ats cii cos2
)(
gs
gii
gi
c
ii
EM
E
MiEE
EMia
t
T
t
Mitats
3
)1(
12
)12(
cos2
)(
,,1)()(
2
22
1
1
s
Example:
4-ASK
)(1 t2s1s
0gE3
00 01
4s3s11 10
gE gE gE3
...
M
i isE
ME
1
1
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Example of bandpass modulation:
Binary ASK (M=2)
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Coherent detection of M-ASK
T
0
)(1 t
ML detector(Compare with M-1 thresholds)
)(tr1z
m
One dimensional modulationdemodulation and detection
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Two dimensional modulation
M-ary Phase Shift Keying (M-PSK)
M
it
T
Ets c
si
2cos
2)(
2
21
21
2211
2sin
2cos
sin2
)(cos2
)(
,,1)()()(
iis
sisi
cc
iii
EE
M
iEa
M
iEa
tT
ttT
t
Mitatats
s
...
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Two dimensional mod, (MPSK)
)(1 t
2s1s
bE
0 1
bE
)(2 t
3s
7s
110
)(1 t
4s 2ssE
000
)(2 t
6s 8s
1s
5s
001011
010
101
111 100
)(1 t
2
s1
s
sE
00
11
)(2 t
3s 4s10
01
QPSK (M=4)
BPSK (M=2)
8PSK (M=8)
Exceptional case: can be represented by single dimension
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Two dimensional mod,(MPSK)
demodulation and detection
Coherent detection of MPSK
Compute Choose
smallest2
1arctanz
z
|| i
T
0
)(1 t
T
0
)(2 t
)(tr
1z
2z
m21
16
Two dimensional modulation M-ary Quadrature Amplitude Mod. (M-QAM)
ici
i tT
Ets cos
2)(
3
)1(2andsymbolsPAMareandwhere
sin2
)(cos2
)(
,,1)()()(
21
21
2211
MEaa
tT
ttT
t
Mitatats
sii
cc
iii
...
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Two dimensional mod, (M-QAM)
)(1 t
)(2 t
2s1s 3s 4s0000 0001 0011 0010
6s5s 7s 8s
10s9s 11s 12s
14s13s 15s 16s
1 3-1-3
1000 1001 1011 1010
1100 1101 1111 1110
0100 0101 0111 0110
1
3
-1
-3
16-QAM
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Two dimensional mod, (M-QAM)demodulation and detection
Coherent detection of M-QAM
T
0
)(1 t
ML detector1z
T
0
)(2 t
ML detector
)(tr
2z
mParallel-to-serialconverter
s)threshold1with(Compare M
s)threshold1with(Compare M
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Example of two dim. modulation
)(1 t
2s 1s
sE
00
11
)(2 t
3s 4s10
01QPSK
3
s
7s
110
)(1 t
4s 2ssE
000
)(2 t
6s 8s
1s
5s
001011
010
101
111 100
8PSK
)(1 t
)(2 t
2s1s 3s 4s0000 0001 0011 0010
6s5s 7s 8s
10s9s 11s 12s
14s13s 15s 16s
1 3-1-3
1000 1001 1011 1010
1100 1101 1111 1110
0100 0101 0111 0110
1
3
-1
-3
16QAM
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Multi-dimensional modulation M-ary Frequency Shift keying (M-FSK)
detectioncoherent-non,1
detectioncoherent,2
1
)1(2cos2
cos2
)(
HzT
f
HzT
f
tfifT
Et
T
Ets c
si
si
2
1
0cos
2)(
,,1)()(
iis
sijii
M
jjiji
EE
ji
jiEat
Tt
Mitats
s
)(1 t
2s
1s
3s
)(3 t
)(2 t
sE
sE
sE,...,
frequency spacing required
to guarantee orthogonal
FSK waveforms
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Multi-dimensional mod,(M-FSK)
demodulation & detection
Coherent detection of M-FSK
Mz
z
1
z
T
0
)(1 t
T
0
)(tM
)(tr
1z
Mz
z
ML detector:Choose waveform
corresponding to
the largest element
in the observed vector
m
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Non-coherent detection Non-coherent detection:
No need for a reference in-phase with the
received carrier
Less complexity as compared to coherent
detection at the price of higher error rate.
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Types of non-coherent detection
1. Differentially coherentdetection Example: Differential PSK (DPSK)
The term differentially coherentdetection ofdifferentially encoded PSK (which is the usualmeaning of DPSK) refers to a detection schemeoften classified as non-coherent because it does notrequire a reference in-phase with the receivedcarrier.
At the transmitter, the current information bits and
previous symbol, determine the phase of the currentsymbol (called differential encoding).
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Non-coherent detection (DPSK)
Differential encoding of the DPSK message The symbol phase, , changes if data bits in
current symbol interval differ from data bits in
previous symbol interval.
,...,MiTtttT
Ets i
si 1,0,)(cos
2)( 0
)(1 t1s2s 0
0 1 2 3 4 5 6 7
1 1 0 1 0 1 1
1 1 1 0 0 1 1 1
0 0
Symbol index:
Data bits:
Diff. encoded bits:
Symbol phase: k
kmk
ki
Binary (M=2) DPSK encoding example
Note: The first bit of the encoded bit sequence, c(k), is chosen arbitrarily, here taken to be binary 1.
kc
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Consider the received signal with phase shift
sequence entering the correlator, in the
absence of noise:
0 0 k
Non-coherent detection (DPSK)
k 0 1 2 3 4 5 6 7
Detection for the Binary (M=2) DPSK encoding example
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2. Energy detection
Example: energy detection for orthogonal
signals such as M-FSK.
The received energy corresponding to each
candidate signal is used for detection.
Types of non-coherent detection
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