lecture 7 appendix a: pulse shapesfaculty.weber.edu/snaik/ece4900_ece6420/07lec07_appa.pdf · 1)...

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EE4900/EE6720 Digital Communications Suketu Naik

EE4900/EE6720: Digital Communications

Lecture 7

Appendix A:

Pulse Shapes

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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

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Full Response Pulse Shapes:

NRZ, RZ, MAN, HS

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Pulse Shapes: Time Domain

Non-Return-to-Zero (NRZ)

Return-to-Zero (RZ)

Manchester (MAN)

Half-Sine (HS)

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Pulse Shapes: Time Domain

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Pulse Shapes: Frequency Domain

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Pulse Shapes: Frequency Domain

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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

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Partial Response Pulse Shapes:

Square Root Raised Cosine

(SRRC)

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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

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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

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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

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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

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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

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2) Design HS (Half-Sine) pulse

Half Sine pulse:


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

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3) Design SRRC(squar-root-raised-cosine) pulse

SRRC pulse:


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

lecture 7 appendix a: pulse shapesfaculty.weber.edu/snaik/ece4900_ece6420/07lec07_appa.pdf · 1)...

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