Phase Shift Keying, Quadrature Amplitude Modulation, digital communication, digital modulation

1. Phase Shift Keying
■ We shift the phase of the carrier signal to represent
digital data.
■ How much shift is possible?
125

2. Binary Phase Shift Keying (BPSK)
© Dr. Aimal Khan 126

3. Binary Phase Shift Keying (BPSK)
■ How much shift is possible?
© Dr. Aimal Khan 127

4. Implementation of BPSK
V V
© Dr. Aimal Khan 128

5. BPSK
0 1
129

6. © Dr. Aimal Khan
M-ary Phase Shift Keying
)
2
2cos(
2
M
i
tf
T
ES csi




Mi
Tt
,...,2,1
,0


■ There can be multiple levels, generally they are equal to
2 power of number of bits.
■ When multiple levels than we must map the bits to
different levels
■ This can increase spectral efficiency
■ Cannot be implemented as BPSK given above, next
slides explain how to implement
)
2
2cos(
M
i
tfVS ci




130

7. © Dr. Aimal Khan
M-ary PSK implementation
)
2
2cos(
2
M
i
tf
T
ES csi




Mi
Tt
,...,2,1
,0


)2sin(
2
)
2
sin()2cos(
2
)
2
cos(
)2sin()
2
sin()2cos()
2
cos(
2
)(
tf
TM
i
Etf
TM
i
ES
tf
M
i
tf
M
i
T
ES
cscsi
ccsi
















)sin()sin()cos()cos()cos(  
131

8. © Dr. Aimal Khan
Conversion from M-levels (angle)
to constellation points
)
2
2cos(
2
M
i
tf
T
ES csi




Mi
Tt
,...,2,1
,0


)2sin(
2
)
2
sin()2cos(
2
)
2
cos(
)2sin()
2
sin()2cos()
2
cos(
2
)(
tf
TM
i
Etf
TM
i
ES
tf
M
i
tf
M
i
T
ES
cscsi
ccsi
















)sin()sin()cos()cos()cos(  
Inphase Component Quadrature Component
132

9. © Dr. Aimal Khan
Mapper
Pulse
Shaping
Multiplier
M-ary ASK
General Modulator Structure
000...00
000...01
.
.
.
111...11
Antenna
MV
V
V
.
.
.
2
1
133

10. © Dr. Aimal Khan
Mapper
Pulse
Shaping
M-ary PSK
General Modulator Structure
000...00
000...01
.
.
.
111...11
Antenna
XMXX VVV ..., 21
)2cos(
2
tf
T
c
Pulse
Shaping
)2sin(
2
tf
T
c
+
-
Inphase
Quadrature
X
X
QMQQ VVV ..., 21
134

11. © Dr. Aimal Khan
Two Dimensional Symbol similar to a
Point in Cartesian Coordinate System
),( QiXii VVV  Mi ,...,2,1
135

12. © Dr. Aimal Khan
Implementation of 4-PSK (QPSK)
■ Explained on the board
136

13. © Dr. Aimal Khan
Mapper for M=4 QPSK
00 )
12
cos(
M
E s

)
12
sin(
M
Es

Inphase Quadrature
i=1
sE
01 )
22
cos(
M
Es

)
22
sin(
M
Es
i=2
=0sE
0
2XV 2QV
1XV 1QV
137

14. © Dr. Aimal Khan
10 )
32
cos(
M
Es

)
32
sin(
M
Es

Inphase Quadrature
i=3
=0 sE
11 )
42
cos(
M
Es

)
42
sin(
M
Es
i=4
=0sE
Mapper for M=4 QPSK
3XV
4QV
3QV
138

15. 5.139
Constellation Diagrams
■ A constellation diagram helps us to define the
amplitude and phase of a signal when we are using
two carriers, one in quadrature of the other.
■ The X-axis represents the in-phase carrier and the Y-
axis represents quadrature carrier.

16. Conversion from M-levels (angle)
to constellation points Graphically
M
i2
)
2
2cos(
2
M
i
tf
T
ES csi




© Dr. Aimal Khan 140

17. M
i2
)
2
2cos(
2
M
i
tf
T
ES csi




)
2
cos(
M
i
Es

)
2
sin(
M
i
Es

Conversion from M-levels (angle)
to constellation points Graphically
© Dr. Aimal Khan 141

18. M
i2
),( QiXii VVV 
Mi ,...,2,1
XiV
QiV
)
2
2cos(
2
M
i
tf
T
ES csi




Conversion from M-levels (angle)
to constellation points Graphically
© Dr. Aimal Khan 142

19. © Dr. Aimal Khan
Relationship of Average Symbol
Energy and Pulses Amplitudes
),( QiXii VVV  Mi ,...,2,1
22
2
,
QiXi
isis
VV
VEE


■ From the previous constellation diagram it can be show
that
143

20. QPSK Constellation Diagram
Inphase axis
Quadrature axis
)0,(),(
),0(),(
)0,(),(
),0(),(
444
333
222
111
sQX
sQX
sQX
sQX
EVVV
EVVV
EVVV
EVVV




144

21. QPSK Constellation Diagram
Inphase axis
Quadrature axis
)0,(),(
),0(),(
)0,(),(
),0(),(
444
333
222
111
sQX
sQX
sQX
sQX
EVVV
EVVV
EVVV
EVVV




00
01
10
11
145

22. Average Energy of a PSK symbol
M
i2
© Dr. Aimal Khan 146

23. © Dr. Aimal Khan
Example of 8-PSK
■ Explained on the board
147

24. 8-PSK Constellation Diagram
Inphase axis
Quadrature axis
■ Further completed and explained on the board
148

25. Quadrature Amplitude Modulation
(QAM)/
Amplitude Phase Shift Keying
■ We shift the phase of the carrier signal as well as the
amplitude to represent digital data.
■ How many dimensions we have to modulate?
■ Thus it is the combination of ASK and PSK
149

26. Some Applications of QAM
■ 3G and 4G uses 16-QAM and 64-QAM
■ 64-QAM and 256-QAM are often used in digital
cable television
■ 16-QAM and 64-QAM are currently used for DVB
150

27. M-ary QAM or M-QAM
Mi
Tt
,...,2,1
,0

)2cos( icii tfVS  
Inphase axis
Quadrature axis
Example of non-square 4 QAM 151

28. Non Square 4-QAM
Example
00
01
10
11
152

29. © Dr. Aimal Khan
Mapper
Pulse
Shaping
M- QAM
General Modulator Structure
000...00
000...01
.
.
.
111...11
Antenna
XMXX VVV ..., 21
)2cos(
2
tf
T
c
Pulse
Shaping
)2sin(
2
tf
T
c
+
-
Inphase
Quadrature
X
X
QMQQ VVV ..., 21
153

30. Constellation Diagram for
Square 4-QAM
Inphase axis
Quadrature axis
d
d
154

31. Mapper for Square 4-QAM
Inphase axis
Quadrature axis
d
d
is mapped to
is mapped to
is mapped to
is mapped to
155

32. Constellation Diagram for
Square 8-QAM
Inphase axis
Quadrature axis
156

33. Constellation Diagram for Some
8-QAM
Inphase axis
Quadrature axis
d
d
157

34. Constellation Diagram for
Square 16-QAM
Inphase axis
Quadrature axis
2d
2d
2d
2d 2d 2d
158

35. Constellation Diagram for
Square 32-QAM
Inphase axis
Quadrature axis
2d
2d
2d 2d
2d
2d
2d
2d 2d2d
159

36. Constellation Diagram for Square 64-QAM
Inphase axis
Quadrature axis
2d
2d
2d 2d
2d
2d
2d
2d 2d2d
2d
2d
2d2d
160

37. How to calculate the average
Symbol Energy of QAM?
Inphase axis
Quadrature axis
2d
2d
2d
2d 2d 2d
161

38. How to calculate the average
Symbol Energy of QAM?
Inphase axis
Quadrature axis
2d
2d
2d
2d 2d 2d
22
,
QiXi
iis
VV
VE




M
i
iss E
M
E
1
,
1
2
2
10
160
16
1
d
dEs


Example of 16 QAM with energy of each symbol on its top
For Square 16-QAM
ith symbol energy
Average Symbol Energy
162

39. Finding d from Average Symbol Energy
 If the average symbol energy is given and we need to find
d for any Square M-QAM from that average energy
 Calculate the average symbol energy in terms of d as
 given on the previous slides
 Equate d from the resulting solution e.g.
For Square 16-QAM
2
2
10
160
16
1
d
dEs


10
sE
d 
163

40. Natural Mapping Vs Gray Mapping
■ So far discussed that we can map them anywhere we desire, now
■ Natural Mapping: Just enumerates the symbols in binary form starting
normally from the lowest value or phase
■ In Gray mapping: maximum 1 bit difference between Neighour symbols
000 001 010 011 100 101 110 111
000 001 010011 110 111 101 100
8-ASK in Natural Mapping
8-ASK in Gray Mapping
164

41. Inphase axis
Quadrature axis
000
001
010
011
100
101
110
111
000
001010
011
110
111
101
100
Inphase axis
Quadrature axis
8-PSK in Natural Mapping 8-PSK in Gray Mapping
Natural Mapping Vs Gray Mapping
165

42. Natural Mapping for Square 16-
QAM
Inphase axis
Quadrature axis
2d
2d
2d
2d 2d 2d
0000 0001 0010 0011
0100 0101 0110 0111
1000 1001 1010 1011
1100 1101 1110 1111
166

43. Gray Mapping for Square 16-
QAM
Inphase axis
Quadrature axis
2d
2d
2d
2d 2d 2d
0000 0001 00100011
0100 0101 01100111
1000 1001 10101011
1100 1101 11101111
167

44. 168

45. Mapper
Pulse
Shaping
)2cos(
2
tf
T
c
X
)2cos(
2
tf
T
c
169

46. © Dr. Aimal Khan
Bandpass
Demodulate
Detector
Pulse to
Samples
Receive
Filter
Sampler
)2cos(
2
tf
T
c
170

47. © Dr. Aimal Khan
Bandpass Demodulation/ASK
Mapper
Pulse
Shaping
LPF
X
X
Channel
Bandpass Modulator
Bandpass Demodulator
)2cos(
2
tf
T
c
)2cos(
2
tf
T
c
)2cos(
2
tf
T
c
)2cos(
2
tf
T
c
171

48. )2cos(
2
)()( tf
T
tvts c
T
tv
tr
tf
T
tv
T
tv
tf
T
tv
tf
T
tvtr
tftf
T
tv
tf
T
tf
T
tvtr
c
c
c
cc
cc
)(
)(
))22cos(
)()(
))22cos(1(
2
12
)(
))22cos()0(cos(
2
12
)()(
2
)cos()cos(
)cos()cos(thatknowwe
)2cos()2cos(
2
)(
)2cos(
2
)2cos(
2
)()(















This Signal is at double
the carrier frequency so
will be filtered out by the
low pass filter (LPF)
)2cos(
2
)()( tf
T
tvtr c
We assume no channel
effects here for simplicity,
therefore, transmitted
signal s(t) is equal to the
received signal r(t)
© Dr. Aimal Khan 172

49. X+9p
© Dr. Aimal Khan
Bandpass Demodulation of PSK, QAM
Mapper
Pulse
Shaping
LPF
X
X
Channel
Inphase Bandpass
Modulator
)2cos(
2
tf
T
c
)2cos(
2
)( tf
T
tv cX 
Pulse
Shaping X
Quadrature
Bandpass Modulator
)2sin(
2
tf
T
c
)2sin(
2
)( tf
T
tv cQ 
+
X
Inphase Bandpass
Demodulator
)2cos(
2
tf
T
c
X
Quadrature
Bandpass Demodulator
)2sin(
2
tf
T
c
LPF


)2cos(
2
)(
)(
tf
T
tv
tr
cX 
)2sin(
2
)( tf
T
tv cQ 
)2cos(
2
)()( tf
T
tvts cX  )2sin(
2
)( tf
T
tv cQ 
If noise is considered then
we get
and
173

50.  
T
tv
tr
tf
tv
tftvtv
T
tr
tf
tv
tf
tv
T
tr
tftftvtftftv
T
tr
tf
T
tf
T
tvtf
T
tvtr
X
X
c
Q
cXX
X
c
Q
c
XX
ccQccXX
ccQcXX
)(
)(
)
2
)22sin(
)(()
2
)22cos()(
(
2
)(2
)(
)
2
)22sin(
)(()
2
)22cos(1
)((
2
)(
)2cos()2sin()()2cos()2cos()(
2
)(
)2cos(
2
)2sin(
2
)()2cos(
2
)()(






 








 


















These Signals are at double
the carrier frequency so will
be filtered out by the low
pass filter (LPF)
We assume no channel
effects here for
simplicity, therefore,
transmitted signal s(t)
is equal to the received
signal r(t)
)2cos(
2
)()( tf
T
tvts cX  )2sin(
2
)( tf
T
tv cQ 
)2cos(
2
)()( tf
T
tvtr cX  )2sin(
2
)( tf
T
tv cQ 
Inphase Demodulation of PSK, QAM
© Dr. Aimal Khan 174

51.  
T
tv
tr
tf
tv
tvtftv
T
tr
tf
tv
tf
tv
T
tr
tftftvtftftv
T
tr
tf
T
tf
T
tvtf
T
tvtr
Q
Q
c
Q
QcX
Q
c
Q
c
XQ
ccQccXQ
ccQcXQ
)(
)(
)
2
)22cos(
)((
2
)(
)´
2
)22cos()(
(
2
)(
)
2
)22cos(1
)(()
2
0)22sin(
)((
2
)(
)2sin()2sin()()2sin()2cos()(
2
)(
)2sin(
2
)2sin(
2
)()2cos(
2
)()(






 








 


















These Signals are at double
the carrier frequency so will
be filtered out by the low
pass filter (LPF)
We assume no channel
effects here for
simplicity, therefore,
transmitted signal s(t)
is equal to the received
signal r(t)
)2cos(
2
)()( tf
T
tvts cX  )2sin(
2
)( tf
T
tv cQ 
)2cos(
2
)()( tf
T
tvtr cX  )2sin(
2
)( tf
T
tv cQ 
Quadrature Demodulation of PSK, QAM
© Dr. Aimal Khan 175