M-ary Modulation, noise modelling, bandwidth, Bandpass Modulation BE Computer Engineering, NUST, Pakistan

1. M-ary Pulse-Modulation
 Multilevel signaling - a group of k-bit is transmitted by M=2k level
pulse.
71

2. M-ary Baseband Modulation
■ Explained on the Board
72

3. Noise in communication systems
• Thermal noise is described by a zero-mean white Gaussian random
process, n(t).
• Its PSD is flat, hence, it is called white noise.
Autocorrelation function
Probability density function
Power spectral density
73

4. Signal transmission through linear systems
Input Output
Linear system
–Deterministic signals:
–Random signals:
74

5. Signal transmission … - cont’d
• Ideal filters:
• Realizable filters:
RC filters Butterworth filter
High-pass
Low-pass
Band-pass
Non-causal!
© Dr. Aimal Khan 75

6. Bandwidth of signal
• Baseband versus bandpass:
• Bandwidth dilemma:
• Bandlimited signals are not realizable!
• Realizable signals have infinite bandwidth!
Baseband
signal
Bandpass
signal
Local oscillator
76

7. Bits per PCM Word
 PCM word size
 How many bits shall we assign to each analog sample?












p
l
p
p
L
pV
L
V
L
Vq
e
pVe
l
pp
pp
pp
pp
2
1
log
2
1
2
2
1
2
22
2
max
e: quantization error,
Vpp peak-to-peak voltage
q: quantization level
77

8. Bits Per Symbol
78

9. Bandwidth of signal …
• Different definition of bandwidth:
a)
b)
c)
Half-power bandwidth
Noise equivalent bandwidth
Null-to-null bandwidth
d) Fractional power containment bandwidth
e) Bounded power spectral density
f) Absolute bandwidth
(a)
(b)
(c)
(d)
(e)50dB
79

10. Spectral Efficiency
■ We can say that the Null-to-Null bandwidth is equal to 2/T. Where, T is
the width of the pulse.
■ In case of binary pulse we can only Transmit 1 bit per symbol (pulse).
In case of M-ary we can transmit log2(M).
■ Spectral efficiency is the number of bits transmitted per bandwidth
used. Thus, in case of binary pulses it is 1/(2/T). In case of M-ary it is
log2(M) /(2/T). We consider here NtoN Bandwidth
■ Binary pulses have less spectral efficiency as compared to M-ary.
However, the transmission of more bits per pulse will increase the
error probability. More bits per pulse means more erroneus bits.
80

11. DIGITAL BANDPASS
MODULATION TECHNIQUES
© Dr. Aimal Khan 81

12. 82

13. Baseband Transmission
■ We have discussed, How it works?
83

14. What is modulation ?
■ Modulation = Adding information to a carrier signal
■ Digital to Analog Modulation
– process of changing one of the characteristic of an
analog signal (typically a cosine wave) based on the
information in a digital signal
■ The cosine wave on which the characteristics of the
information signal are modulated is called a carrier
signal
84

15. 5.85
Figure 5.1 Digital-to-analog conversion
© Dr. Aimal Khan

16. Signal characteristics that can
be modified
signal x(t) = A cos(2πft + Φ)
• A – amplitude
• f – frequency
• Φ – phase
• A- amplitude and phase together
86

17. 5.87
Amplitude Shift Keying (ASK)
■ ASK is implemented by changing the
amplitude of a carrier signal to reflect
amplitude levels in the digital signal.
■ For example: a digital “1” could not affect the
signal, whereas a digital “0” would, by making
it zero.
■ The line encoding will determine the values of
the analog waveform to reflect the digital data
being carried.

18. Binary Vs M-ary Modulation
■ Binary: Only two modulation levels
■ M-ary: Two or more than Two modulation
levels
88

19. Binary Amplitude Shift Keying
On/Off Keying
s1 t  
2Eb
Tb
cos 2fct 
s2 t   
2Eb
Tb
cos 2fct 0 x
V x
© Dr. Aimal Khan 89

20. Implementation of binary ASK
On/Off Keying
s1 t  
2Eb
Tb
cos 2fct 
s2 t   
2Eb
Tb
cos 2fct 0 x
V x
V
© Dr. Aimal Khan 90

21. © Dr. Aimal Khan
Implementation of binary ASK
Bipolar Binary ASK
A
-A
V
-V
91

22. © Dr. Aimal Khan
Mapper
Pulse
Shaping
Multiplier
Bipolar Binary ASK
General Modulator Structure
V
-V0
1
Antenna
92

23. © Dr. Aimal Khan
M-ary Amplitude Shift Keying
■ 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
■ Implemented in a similar way as Binary ASK
)2cos(
2
tf
T
VS cii  ii EV
Mi
Tt



,...,2,1
,0)2cos( tfAS cii 
93

24. © 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
94

25. 5.95
Frequency Shift Keying
■ The digital data stream changes the frequency of the carrier signal,
fc.
■ For example, a “1” could be represented by f1=fc +f, and a “0”
could be represented by f2=fc-f.

26. Binary Frequency Shift Keying
© Dr. Aimal Khan 96

27. Implementation of BFSK
V
© Dr. Aimal Khan 97

28. © Dr. Aimal Khan
Mapper
Pulse
Shaping
VCO
Binary FSK
General Modulator Structure
V
-V0
1
Antenna
98

29. © Dr. Aimal Khan
M-ary Frequency Shift Keying
■ 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
■ Implemented in a similar way as Binary FSK
)2cos(
2
tf
T
E
S ii 
Mi
Tt
,...,2,1
,0

)2cos( tfAS ii 
99

30. © Dr. Aimal Khan
Mapper
Pulse
Shaping
VCO
M-ary FSK
General Modulator Structure
000...00
000...01
.
.
.
111...11
Antenna
MV
V
V
.
.
.
2
1
100

31. Binary Amplitude Shift Keying
On/Off Keying
s1 t  
2Eb
Tb
cos 2fct 
s2 t   
2Eb
Tb
cos 2fct 0 x
V x
© Dr. Aimal Khan 101

32. Implementation of binary ASK
On/Off Keying
s1 t  
2Eb
Tb
cos 2fct 
s2 t   
2Eb
Tb
cos 2fct 0 x
V x
V
© Dr. Aimal Khan 102

33. © Dr. Aimal Khan
Bipolar Binary ASK
General Modulator Structure
Mapper
Pulse
Shaping
Multiplier
V
-V0
1
Antenna
103

34. © Dr. Aimal Khan
Transmit Energy and Constellation
Diagram
Mapper
Pulse
Shaping
Multiplier
V
-V0
1
Antenna
104

35. © Dr. Aimal Khan
M-ary Amplitude Shift Keying
■ 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
■ Implemented in a similar way as Binary ASK
)2cos(
2
tf
T
VS cii  ii EV
Mi
Tt



,...,2,1
,0)2cos( tfAS cii 
105

36. Implementation of binary ASK
On/Off Keying
s1 t  
2Eb
Tb
cos 2fct 
s2 t   
2Eb
Tb
cos 2fct 0 x
V x
V
© Dr. Aimal Khan 106

37. © 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
107

38. Symbol Energy
Smaller value, this term
can be negletected.
108

39. Average Symbol Energy
109

40. Average Energy per bit Vs
Average Energy per Symbol
■ Normally for a communication System Energy per bit is given
■ Difference between Bit duration and Symbol Duration
■ For Binary M-ary Schemes
110