Transcript Lecture 4a
Digital Communications I:
Modulation and Coding Course
Spring - 2013
Jeffrey N. Denenberg
Lecture 4: BandPass Modulation/Demodulation
Last time we talked about:
Another source of error due to filtering
effect of the system:
Inter-symbol interference (ISI)
The techniques to reduce ISI
Pulse shaping to achieve zero ISI at the
sampling time
Equalization to combat the filtering effect of
the channel
Lecture 7
2
Today, we are going to talk about:
Some bandpass modulation schemes used
in DCS for transmitting information over
channel
M-PAM, M-PSK, M-FSK, M-QAM
How to detect the transmitted information
at the receiver
Coherent detection
Non-coherent detection
Lecture 7
3
Block diagram of a DCS
Format
Source
encode
Channel
encode
Pulse
modulate
Bandpass
modulate
Digital demodulation
Format
Source
decode
Channel
decode
Lecture 7
Demod.
Sample
Detect
4
Channel
Digital modulation
Bandpass modulation
Bandpass modulation:
The process of converting
a data signal to a sinusoidal waveform where its
amplitude, phase or frequency, or a combination of
them, are varied in accordance with the transmitting
data.
Bandpass signal:
2
E
s
(
t
)
g
(
t
)i
cos
t
(
i
1
)
t
(
t
)
0
t
T
i
T
c
i
T
where
gT (t ) is the baseband pulse shape with energy E g .
We assume here (otherwise will be stated):
g T (t ) is a rectangular pulse shape with unit energy.
Gray coding is used for mapping bits to symbols. 1
Es denotes average
symbol
Lecture
7 energy given by E
5s
E
M
M
i
1 i
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 the ML detection rule.
1 (t )
T
z1
0
r (t )
N (t )
T
0
zN
z1
z N
Lecture 7
z
z
Decision
circuits
(ML detector)
6
mˆ
Coherent detection
Coherent detection
requires carrier phase recovery at the
receiver and hence, circuits to perform
phase estimation.
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.
Lecture 7
7
Coherent detection ..
Circuits such as Phase-Locked-Loop (PLL) are
implemented at the receiver for carrier phase
estimation ( ˆ ).
I branch
2
E
r
(
t
)
g
(
t
) icos
t
(
t
)
n
(
t
)
T
i
i
T
Oscillator
PLL
2
ˆ
cos
ct
T
Used by
correlators
90 deg.
2
ˆ
sin
ct
T
Lecture 7
8
Q branch
Bandpass Modulation Schemes
One dimensional waveforms
Two dimensional waveforms
Amplitude Shift Keying (ASK)
M-ary Pulse Amplitude Modulation (M-PAM)
M-ary Phase Shift Keying (M-PSK)
M-ary Quadrature Amplitude Modulation
(M-QAM)
Multidimensional waveforms
M-ary Frequency Shift Keying (M-FSK)
Lecture 7
9
One dimensional modulation,
demodulation and detection
Amplitude Shift Keying (ASK) modulation:
2
E
i
s
(
t
)
cos
t
i
c
T
si(t)ai1(t) i 1,
,M
2
ct
1(t) cos
T
On-off keying (M=2):
“0”
“1”
s2
s1
0
E1
ai Ei
Lecture 7
10
1 (t )
One dimensional mod.,…
M-ary Pulse Amplitude modulation (M-PAM)
s
t)
a
i(
i
2
cos
t
c
T
4-PAM:
si (t ) ai 1 (t ) i 1, , M
“00”
s1
2
1 (t )
cosc t
T
3 Eg
“01”
“11”
s3
s2
Eg
0
2
E g 2i 1 M
2
( M 2 1)
Es
Eg
3
Lecture 7
s4
3 Eg
Eg
ai ( 2i 1 M ) E g
Ei s i
“10”
11
1 (t )
Example of bandpass modulation:
Binary PAM
Lecture 7
12
One dimensional mod.,...–cont’d
Coherent detection of M-PAM
1 (t )
r (t )
T
0
z1
ML detector
(Compare with M-1 thresholds)
Lecture 7
13
mˆ
Two dimensional modulation,
demodulation and detection (M-PSK)
M-ary Phase Shift Keying (M-PSK)
2
E
i
2
s
s
(
t
)
cos
t
c
i
T
M
si(t)ai1
t)ai2
t) i1
,
,M
1(
2(
2
2
ct 2(t) sin
ct
1(t) cos
T
T
i
i
2
2
ai1 E
ai2 E
s cos
s sin
M
M
E
s E
i s
i
2
Lecture 7
14
Two dimensional mod.,… (MPSK)
BPSK (M=2)
2 (t )
“0”
“1”
s1
s2
Eb
Eb
8PSK (M=8)
1 (t )
“010”
s3
2 (t )
“011”
s4
s2
QPSK (M=4)
Es
2 (t )
“01”
s2
“00”
s5
s1
“111”
“10”
“100”
s6
1 (t )
“11”
“000”
s1
“110”
Es
s3
“001”
s8
“101”
s7
s4
Lecture 7
15
1 (t )
Two dimensional mod.,…(MPSK)
Coherent detection of MPSK
1 (t )
T
z1 ˆ
arctan
z2
0
r (t )
2 (t )
z1
Compute
Choose
smallest
| i ˆ |
T
0
z2
Lecture 7
16
mˆ
Two dimensional mod.,… (M-QAM)
M-ary Quadrature Amplitude Mod. (M-QAM)
2
E
i
s
(
t
)
cos
t
i
c
i
T
s
t
)
a
(
t
)
a
(
t
) i
1
,
,M
i(
i
1
1
i2
2
2
2
(
t
)
cos
t
(
t
)
sin
t
1
c
2
c
T
T
2
(
M
1
)
where
a
and
a
are
PAM
symbols
and
E
i
1
i2
s
3
(
M
1
,M
1
)(
M
3
,M
1
)
(
M
1
,M
1
)
(
M
1
,
M
3
)
(
M
3
,
M
3
)
(
M
1
,
M
3
)
a
,
a
i
1
i
2
(
M
1
,
M
1
)(
M
3
,
M
1
)
(
M
1
,
M
1
)
Lecture 7
17
Two dimensional mod.,… (M-QAM)
16-QAM
“0000”
s1
“1000”
s5
2 (t )
“0001” “0011” “0010”
s2
“1001”
s6
-3
-1
s9
s10
“1100”
“1101”
s13
s14
“0100”
“0101”
Lecture 7
3
s3
s4
“1011” “1010”
1
s7
s8
1
3
s
s
s
s
1 (t )
12
11
-1
“1111” “1110”
16
15
-3
“0111” “0110”
18
Two dimensional mod.,… (M-QAM)
Coherent detection of M-QAM
1 (t )
T
z1
ML detector
(Compare
with
M
1
threshold
s)
0
r (t )
Parallel-to-serial
converter
2 (t )
T
0
z2
mˆ
ML detector
(Compare
with
M
1
threshold
s)
Lecture 7
19
Multi-dimensional modulation, demodulation &
detection
M-ary Frequency Shift keying (M-FSK)
2
E
2
E
s
s
s
(
t
)
cos
t
cos
t
(
i
1
)
t
i
i
c
T
T
1
f
2
2
T
3 (t )
M
si(t)
aijj(t) i1
,
,M
s3
j
1
2
it
i(t) cos
T
E
s E
i s
i
Es
E
ij
aij s
0 ij
s2
Es
2
s1
Lecture 7
1 (t )
Es
20
2 (t )
Multi-dimensional mod.,…(M-FSK)
1 (t )
T
z1
0
r (t )
M (t )
T
0
zM
z1
z M
Lecture 7
ML detector:
z
z
Choose
the largest element
in the observed vector
21
mˆ
Non-coherent detection
Non-coherent detection:
No need for a reference in phase with the
received carrier
Less complexity compared to coherent
detection at the price of higher error rate.
Lecture 7
22
Non-coherent detection …
Differential coherent detection
Differential encoding of the message
The symbol phase changes if the current bit is
different from the previous bit.
2
E
s
(
t
)
cos
t
(
t
)
,
0
t
T
,
i
1
,...,M
i
0
i
T
(
nT
)
((
n
1
)
T
)
(
nT
)
k
k
i
Symbol index: k 0 1 2 3 4 5 6 7
1 1 0 1 0 1 1
Data bits: mk
Diff. encoded bits 1 1 1 0 0 1 1 1
0 0
Symbol phase: k
Lecture 7
i
s2
23
0
s1
1 (t )
Non-coherent detection …
Coherent detection for diff encoded mod.
assumes slow variation in carrier-phase mismatch during
two symbol intervals.
correlates the received signal with basis functions
uses the phase difference between the current received
vector and previously estimated symbol
2
E
r
(
t
)
cos
t
(
t
)
n
(
t
),
0
t
T
0
i
T
(
nT
)
((
n
1
)
T
)
(
nT
)
((
n
1
)
T
)
(
nT
)
i
j
i
j
i
2 (t )
(a2 , b2 )
Lecture 7
i
(a1 , b1 )
24
1 (t )
Non-coherent detection …
Optimum differentially coherent detector
1 (t )
r (t )
T
mˆ
Decision
0
Delay
T
Sub-optimum differentially coherent detector
r (t )
T
0
Decision
Delay
T
Performance degradation about 3 dB by using suboptimal detector
Lecture 7
25
mˆ
Non-coherent detection …
Energy detection
Non-coherent detection for orthogonal signals
(e.g. M-FSK)
Carrier-phase offset causes partial correlation between
I and Q branches for each candidate signal.
The received energy corresponding to each candidate
signal is used for detection.
Lecture 7
26
Non-coherent detection …
Non-coherent detection of BFSK
2/Tcos(
t)
1
T
T
T
z11
2
0
z11 z12
2
2/Tsin(
t)
1
r (t )
z12
0
2/Tcos(
t)
2
z 21
2
2
+
2
z (T )
-
Decision stage:
ˆ
ifz(T
)
0
,m
1
ˆ
ifz(T
)
0
,m
0
0
2/Tsin(
t)
2
z21 z22
2
T
0
z 22
2
2
Lecture 7
27
ˆ
m