isi & pulse shaping_good
DESCRIPTION
ISITRANSCRIPT
-
5/25/2018 ISI & Pulse Shaping_good
1/20
Eeng 360 1
Chapter 3
INTERSYMBOL INTERFERENCE (ISI)
Intersymbol Interference
ISI on Eye Patterns
Combatting ISI
Nyquists First Method for zero ISI
Raised Cosine-Rolloff Pulse Shape
Nyquist Filter
Huseyin Bilgekul
Eeng360 Communication Systems IDepartment of Electrical and Electronic Engineering
Eastern Mediterranean University
-
5/25/2018 ISI & Pulse Shaping_good
2/20
Eeng 360 2
Intersymbol Interference
Intersymbol interference (ISI)occurs when a pulse spreads out in such a way thatit interferes with adjacent pulses at thesample instant.
Example: assume polar NRZ line code. The channel outputs are shown as spreaded(width Tbbecomes 2Tb) pulses shown (Spreading due to bandlimited channelcharacteristics).
Data 1
bT 0 bT0bT bT
Data 0
bT 0 bT0bT bT
Channel Input
Pulse width Tb
Channel Output
Pulse width Tb
-
5/25/2018 ISI & Pulse Shaping_good
3/20
Eeng 360 3
Intersymbol Interference
For the input data stream:
The channel output is the superposition of each bits output:
1 11100
bT bT2 bT3 bT40 bT5
A
bT bT2 bT3 bT40 bT5
1 1110 0
bT bT2 bT3 bT40 bT5
Resultant
Channel OutputWaveform
-
5/25/2018 ISI & Pulse Shaping_good
4/20
Eeng 360 4
ISI on Eye Patterns
The amount of ISI can be seen on an oscilloscope using an EyeDiagramor Eyepattern.
Time (Tb)
Amplitude
NoiseMargin
Distortion
bT Extension
Beyond TbisISI
-
5/25/2018 ISI & Pulse Shaping_good
5/20
Eeng 360 5
Intersymbol Interference If the rectangular multilevel pulses are filtered improperly as they pass through a
communications system, they will spread in time, and the pulse for each symbol may be
smeared into adjacent time slots and cause Intersymbol Interference.
How can we restrict BW and at the same time not introduce ISI? 3 Techniques.
-
5/25/2018 ISI & Pulse Shaping_good
6/20
Eeng 360 6
Flat-topped multilevel input signal having pulse shape h(t) and values ak:
Intersymbol Interference
in
out
w ( )* *
1 Where Where pulses/s
*
n s n s n s
n n
s
n e
s
n s e
n
s
n
t a h t nT a h t t nT a t nT h t
th t
a h t
DT
nT
T
w t a t nT h t
Equivalent impulse response: * * *h t h t h t h t h t e T C R
he(t) is the pulse shape that will appear at the output of the receiver filter.
-
5/25/2018 ISI & Pulse Shaping_good
7/20Eeng 360 7
out n e sn
w t a h t nT
Equivalent transfer function:
Receiving filter can be designed to produce a neededHe(f)in terms ofHT(f)andHC(f):
Output signal can be rewritten as:
Intersymbol Interference
He(f), chosen such to minimize ISI is called EQUALIZING FILTER)
H
e
R
T C
H ff
H f H f H f
* * *h t h t h t h t h t e T C R
sin
H Where H se T C R ss s
T ftf H f H f H f H f f F T
T T f
Equivalent Impulse Response he(t) :
-
5/25/2018 ISI & Pulse Shaping_good
8/20Eeng 360 8
Combating ISI Three strategies for eliminating ISI:
Use a line code that is absolutely bandlimited.
Would require Sinc pulse shape.
Cant actually do this (but can approximate).
Use a line code that is zero during adjacent sample instants.
Its okay for pulses to overlap somewhat, as long as there is no overlap atthe sample instants.
Can come up with pulse shapes that dont overlap during adjacent sampleinstants.
Raised-Cosine Rolloff pulse shaping
Use a filter at the receiver to undo the distortion introduced bythe channel.
Equalizer.
-
5/25/2018 ISI & Pulse Shaping_good
9/20Eeng 360 9
Nyquists First Method for Zero ISIISI can be eliminated by using an equivalent transfer function,He(f), such that the impulse
response satisfies the condition:
, 00, 0
e sC kh kT
k
k is an integer, is the symbol (sample) period
is the offset in the receiver sampling clock times
C is a nonzero constantsin
Now choose the function for ( )
s
e
T
xh t
x
Sampling Instants
ISI occurs but,
NO ISI is present at thesampling instants
is a Sa function
sin (
)
out n e s
n
e
se
s
w t a h t nT
h
f th t
f t
-
5/25/2018 ISI & Pulse Shaping_good
10/20Eeng 360 10
There will be NO ISI and the bandwidth requirement will be minimum (Optimum
Filtering)if the transmit and receive filters are designed so that the overall transfer functionHe(f)
is:
This type of pulse will allow signalling at a baud rate ofD=1/Ts=2B(for BinaryR=1/Ts=2B)
whereBis the absolute bandwidth of the system.
Nyquists First Method for Zero ISI
sin1 1
Wherese e ss s s s
f tfH f h t f
f f f t T
s
MINIMUM BANDAbsolute bandwidth is:
2Signalling Rate is: =1 2 Pulses/se
ID
c
W THsf
B
D T B
0f
He(f)1/fs
fs/2
-fs/2
-
5/25/2018 ISI & Pulse Shaping_good
11/20Eeng 360 11
Nyquists First Method for Zero ISI
-
5/25/2018 ISI & Pulse Shaping_good
12/20Eeng 360 12
Nyquists First Method for Zero ISI
he(t)
0f
He(f)
1/fs
fs/2-fs/2
Since pulses are not possible to create due to: Infinite time duration.
Sharp transition band in the frequency domain.
The Sinc pulse shape can cause significant ISI in the presence of timing errors. If the received signal is not sampled at exactlythe bit instant (Synchronization
Errors), then ISI will occur.
We seek a pulse shape that: Has a more gradual transition in the frequency domain.
Is more robust to timing errors.
Yet still satisfies Nyquists first method for zero ISI.
Zero crossings at non-zero integer multiples of the bit period
-
5/25/2018 ISI & Pulse Shaping_good
13/20Eeng 360 13
Raised Cosine-Rolloff Nyquist Filtering
1
1
1
0 1 0
1,
1
1 cos , B is the Absolute Bandwidth2 2
0,
e
f f
f f
H f f f Bf
f B
f B f f f f
0
1 00 2
0
Where is the 6-dB bandwidth of the filter
Rolloff factor: Bandwidth: B (1 )2
sin2 cos22
2 1 4
o
b
e e
f
Rf
r rf
f t f th t F H f f
f t f t
Because of the difficulties caused by the Sa type pulse shape, consider otherpulse shapes which require more bandwidthsuch as the Raised Cosine-rolloff
Nyquist filter but they are less affected by synchrfonization errors.
The Raised Cosine Nyquist filter is defined by its rollof factor number r=f/fo.
0
Rolloff factor: Bandwidth: B (1 )2
bRfr rf
-
5/25/2018 ISI & Pulse Shaping_good
14/20Eeng 360 14
Raised Cosine-Rolloff Nyquist Filtering
0Rolloff factor: Bandwidth: B (1 ) (1 )2 2
f R Dr r rf
11
12
c so2
e
f f
fH f
Now filtering requirements are relaxed because absolute bandwidth isincreased.
Clock timing requirements are also relaxed.
The r=0 case corresponds to the previous Minimum bandwidth case.
oB f f
-
5/25/2018 ISI & Pulse Shaping_good
15/20Eeng 360 15
Raised Cosine-Rolloff Nyquist Filtering
Impulse response is given by:
1 00 2
0
sin2 cos2 2
2 1 4e e
f t f th t F H f f
f t f t
The tails of he(t) are now
decreasing much faster than the Sa
function (As a function of t2).
ISI due to synchronization errorswill be much lower.
-
5/25/2018 ISI & Pulse Shaping_good
16/20Eeng 360 16
Raised Cosine-Rolloff Nyquist Filtering
Frequency response and impulse
responses of Raised Cosine pulses for
various values of the roll off parameter.
r B
r ISI
d ll ff l
-
5/25/2018 ISI & Pulse Shaping_good
17/20Eeng 360 17
Raised Cosine-Rolloff Nyquist FilteringIllustrating the received bit stream of Raised Cosine pulse shapedtransmission corresponding to the binary stream of 1 0 0 1 0 for 3 different
values of r=0, 0.5, 1.
1 0 0 1 0 1 0 0 1 0
B d d h f R d N F l
-
5/25/2018 ISI & Pulse Shaping_good
18/20Eeng 360 18
The bandwidth of a Raised-cosine (RC) rolloff pulse shape is a function of the
bit rate and the rolloff factor:
Or solving for bit rate yields the expression:
This is the maximum transmitted bit rate when a RC-rolloff pulse shape with
Rolloff factor ris transmitted over a baseband channel with bandwidthB.
2
1
BR
r
Bandwidth for Raised Cosine Nyquist Filtering
1 1
12
1 Multilevel Signalling
2
o o o
o
fB f f f f rf
RB r
DB r
N F l
-
5/25/2018 ISI & Pulse Shaping_good
19/20Eeng 360 19
Nyquist Filter
00
,
20, Elsewhere
e
fY f f f
H f ff
0
0
0 0 0
( ) is a real function and even symmetric about = 0:
( ), 2
Y is odd symmetric about :
( ),
Y f f
Y f Y f f f
f f
Y f f Y f f f f
02sD f f
Theorem: A filter is said to be aNyquist filterif the effective transfer function is :
There will be no intersymbol interference at the system output if the symbol rate is
Raised Cosine Filter is also called a NYQUIST FILTER.
NYQUIST FILTERS refer to a general class of filters that satisfy theNYQUISTs First Criterion.
N F l Ch
-
5/25/2018 ISI & Pulse Shaping_good
20/20Eeng 360 20
00,
2
0, Elsewhere
e
fY f f f
H f f
f
Nyquist Filter Characteristics
0
0
0 0 0
( ) is a real function and even symmetric about = 0:
( ), 2
Y is odd symmetric about :
( ),
Y f f
Y f Y f f f
f f
Y f f Y f f f f