lecture 7 appendix a: pulse shapes...3) design srrc(squar-root-raised-cosine) pulse srrc pulse: use...
TRANSCRIPT
-
1
EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Lecture 7
Appendix A:
Pulse Shapes
-
2
EE4900/EE6720 Digital Communications Suketu Naik
Modulator based on Synthesis Equation
Data/Audio/Video
[101 100 001 000 010 011 110 111]
Serial to Parallel
Group of
3 bits
One look-up table
per symbol
Constructing one
symbol so(t)
signal s(t) is created
from K-symbols
Example
Same group of bits
go to each path
1) Group of bits (e.g. 101)= the
decimal index (e.g. 5)
2) Now the coefficient with that
index is selected
Pulse-shaping filter
can be used here
-
3
EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Full Response Pulse Shapes:
NRZ, RZ, MAN, HS
-
4
EE4900/EE6720 Digital Communications Suketu Naik
Pulse Shapes: Time Domain
Non-Return-to-Zero (NRZ)
Return-to-Zero (RZ)
Manchester (MAN)
Half-Sine (HS)
-
5
EE4900/EE6720 Digital Communications Suketu Naik
Pulse Shapes: Time Domain
-
6
EE4900/EE6720 Digital Communications Suketu Naik
Pulse Shapes: Frequency Domain
-
7
EE4900/EE6720 Digital Communications Suketu Naik
Pulse Shapes: Frequency Domain
-
8
EE4900/EE6720 Digital Communications Suketu Naik
Pulse Shapes
Q: Which one is the best?
A: Trade-off between time-domain and freq. domain
NRZ and HS are better for timing synchronization (Ch8)
MAN and RZ are better for bandwidth efficiency
NRZ
HS
MAN
RZ
-
9
EE4900/EE6720 Digital Communications Suketu Naik
EE4900/EE6720: Digital Communications
Partial Response Pulse Shapes:
Square Root Raised Cosine
(SRRC)
-
10
EE4900/EE6720 Digital Communications Suketu Naik
Inter Symbol Interference (ISI)
ISI: Inter Symbol Interference (similar to aliasing
covered in Lecture 3)
ISI happens when spectrum spreads and there is an
overlap of frequency components
The overlap
may result in
an error at
the receiver
Q: How to eliminate ISI? A: Reduce bandwidth
-
11
EE4900/EE6720 Digital Communications Suketu Naik
Nyquist no-ISI Criteria
Goals:
1) Reduce bandwidth
2) Acceptable ISI
Ts=Symbol Rate or Symbol Time
1/Ts=Symbol Frequency
B=Bandwidth
1) No ISI but excessive BW
2) Minimum ISI but excessive BW
3) Acceptable ISI and less BW
SRRC can meet these goals and is very popular pulse shape
Compromise
between ISI
and BW
-
12
EE4900/EE6720 Digital Communications Suketu Naik
SRRC Pulse: Continuous Time
α =Roll-off factor: indicates excess BWα = 0: 0% excess BW
α = 0.5: 50% excess BW
α = 1: 100% excess BW
t
-
13
EE4900/EE6720 Digital Communications Suketu Naik
SRRC Pulse: Discrete-time
Lp=3
Lp=6
Lp=12
Lp=# of Symbols
used to create the
SRRC pulse
Higher the LP, less
the ISI
-
14
EE4900/EE6720 Digital Communications Suketu Naik
Matlab/Simulink Exercise
1) Design NRZ (non-return-to-zero) pulse
NRZ pulse:
Use Ts (symbol time in Fig. A.1.1) to set the pulse width
and the amplitude.
Example:
Ts=1 s, simulation sampling rate R =16 samples/s,
Discrete NRZ pulse width= R*Ts=16 samples.
amp=sqrt(1/16);
NRZ=amp*ones(1,16);
Now hit enter and type the following:
fvtool(NRZ,'Analysis’,'impulse')
Also look a the magnitude response (freq. domain) in
fvtool
-
15
EE4900/EE6720 Digital Communications Suketu Naik
Matlab/Simulink Exercise
2) Design HS (Half-Sine) pulse
Half Sine pulse:
Use Ts (symbol time in Fig. A.1.1) to set the pulse width
and the amplitude.
Example:
Ts=1 s, simulation sampling rate R =16 samples/s,
Discrete HS pulse width= R*Ts=16 samples.
amp=sqrt(2/16);
HalfSine=amp*sin((2*pi*[0:15]/16)/2);
Now hit enter and type the following:
fvtool(HalfSine,'Analysis','impulse')
Also look a the magnitude response (freq. domain) in
fvtool
-
16
EE4900/EE6720 Digital Communications Suketu Naik
Matlab/Simulink Exercise
3) Design SRRC(squar-root-raised-cosine) pulse
SRRC pulse:
Use Ts (symbol time in Fig. A.2.4) to set the pulse width
and the amplitude.
Example:
Ts=1 s, simulation sampling rate R = 8 samples/s,
Discrete SRRC pulse width= RxTs=8 samples.
help rcosdesign
SRRC = rcosdesign(0.5,4,2);
This creates a filter with roll-off factor=0.5, Lp=4 symbols, Samples
per symbol=2. So the total pulse width=4x2=8 samples.
fvtool(SRRC,'Analysis','impulse')
Also look a the magnitude response (freq. domain) in fvtool