Modulation, Demodulation and Coding Course - U

Comunicaciones Digitales Avanzadas
EL7041
EL7041 Comunicaciones Digitales
Avanzadas
César Azurdia Meza, Ph.D
Block diagram of a DCS
…1110011…
Format
Source
encode
Channel
encode
Digital
Modulation
Bandpass
modulate
Digital demodulation
…1110011…
Format
Source
decode
Channel
decode
Detect
Demod.
Sample
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

Eg .
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
s
Es denotes average symbol energy given by E
E

M
M
i
1 i
Gray Coding
Gray Coding
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 
z
z
Decision
circuits
(ML detector)
m̂
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.

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
90 deg.
Used by
correlators
2
ˆ

sin

ct
T
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)
One dimensional modulation,
demodulation and detection

Amplitude Shift Keying (ASK) modulation:
2
E
i


s
(
t
)

cos

t

i
c
T
si(t)ai1(t) i 1,
,M
2
ct
1(t) cos
T
ai  Ei
On-off keying (M=2):
“0”
“1”
s2
s1
0
E1
 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 ) 
cosc t 
T
 3 Eg
ai  ( 2i  1  M ) E g
Ei  s i
2
 E g 2i  1  M 
( M 2  1)
Es 
Eg
3
2
“01”
“11”
s3
s2
 Eg
0
Eg
“10”
s4
3 Eg
 1 (t )
Example of bandpass modulation:
Binary PAM
One dimensional mod.,...–cont’d

Coherent detection of M-PAM
 1 (t )
r (t )

T
0
z1
ML detector
(Compare with M-1 thresholds)
m̂
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) i1
,
,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
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”
s1
“10”
s5
“111”
“100”
s6
 1 (t )
“11”
“000”
s1
“110”
Es
s3
“001”
s4
s8
“101”
s7
 1 (t )
Two dimensional mod.,…(MPSK)

Coherent detection of MPSK
 1 (t )

T
0
r (t )
 2 (t )

z1
z1 ˆ
arctan
z2
T
0
z2
Compute
| i  ˆ |
Choose
smallest
m̂
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
)




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”
3
s3
s4
“1011” “1010”
1
s7
s8
1
3
s
s
s
s
12
11
-1
“1111” “1110”
16
15
-3
“0111” “0110”
 1 (t )
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
m̂
ML detector
(Compare
with
M

1
threshold
s)
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)
aijj(t) i1
,
,M
s3
j
1
2
it
i(t) cos
T
E
s E
i s
i
E
ij
aij  s
0 ij
Es
s2
Es
2
s1
 1 (t )
Es
 2 (t )
Multi-dimensional mod.,…(M-FSK)
 1 (t )

T
z1
0
r (t )
 M (t )

T
0
zM
 z1
 

 z M




ML detector:
z
z
Choose
the largest element
in the observed vector
m̂
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.
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
i
s2
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 )
i
(a1 , b1 )
 1 (t )
Non-coherent detection …

Optimum differentially coherent detector
 1 (t )

r (t )
T
m̂
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
m̂
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.
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 )
-
0
2/Tsin(

t)
2
z21  z22
2

T
0
z 22
 2
2
Decision stage:
ˆ
ifz(T
)
0
,m
1
ˆ
ifz(T
)
0
,m
0
m̂

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