inter symbol intereference

8/6/2019 Inter Symbol Intereference

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Baseband PAMNyquist criterion

Inter-symbol Interference (ISI)

Pulse shaping (raised cosine baseband filtering)

Eye diagrams

Interpolation filter bank

Symbol clock recovery

Before you start with the experiment, it is necessary that you have anunderstanding (at some level) of the following concepts:

PAMTuesday, June 07, 2011

1:03 PM

experiments Page 1


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Modulated Impulse Train

Time (seconds)

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-0.5

0

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Modulated Pulse Train

Time (seconds)

Random binary PAM representation

Interpolating function is a rectangular pulse,of duration

T,hence no overlap is observed between adjacent pulses

ISITuesday, June 07, 2011

2:15 PM

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Modulated Impulse Train

Time (seconds)

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Time (seconds)

20% overlap between adjacent pulses

The interpolating function is again a rectangular function with

duration T+(0.2T)

If we consider any random pulse of duration greater than thesample duration

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2Modulated Impulse Train

Time (seconds)

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-1

0

1

2Modulated Pulse Train

Time (seconds)

Thus waveform appears distorted

And if we sample the waveform at the sampling

instants,incorrect value of the samples is obtained

experiments Page 4


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The total waveform has folded spectrum in frequency domain

And sampling will lead to periodicity of the folded spectrum

If we want the sample values to be detected properly

We can design the pulse shaping filter at the receiver suchthat the spectrum of sampled signal is 1 in the entire

frequency domain,indicating a impulse in the time domain

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1

We employ a half sine pulsehspulse = sin(pi*[0:0.01:2]/2)

We analyze the spectrum of half sine pulse

It is of duration twice that of the samping interval

experiments Page 5


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-1

0

1


Time (seconds)

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-1

0

1


Time (seconds)

Sine the pulse has zero crossings at samping instants

When we sample the signal at the ampling instants ,it gives us

the correct sample values,it is not affected by the ISI at

sampling instants

However the half since pulse has sharp transitions at sampling

instants we would line smoother transitions for better

detection

experiments Page 6


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-6 -4 -2 0 2 4 6-0.2

0

0.2

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1

1.2

Consider raise cosine pulse

The duration of the pulse is 12 ie it 6 samples duration to left

and right of the current samples

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0

1

2 Modulated Impulse Train

Time (seconds)

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-1

0

1


Time (seconds)

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Again we see that at sampling instants proper values are

detected

Hence if we take a pulse that has zero crossings at sampling

instants we are able to detect the proper samples values at

sampling instant

This pulse is better than half sine pulse as at the sampling

instants we have gradual change

No sharp transition are seen at sampling instants

Thus it is more resistant to timing error in sampling

you see that effective detection with the sampling receiver is possible, even with overlapping pulses,

provided the pulses satisfy Nyquist's criterion.We can reduce the bandwidth requirement by using gradually varying pulsesAnd also detect the values at sampling instants correctly is impulse response of the transmit filtersatisfies nyquist criterion

experiments Page 8


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Received waveform in the presence of noise and ISI after

equalization to remove channel distortion

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Additive Noise Channel

Tuesday, June 07, 2011

2:41 PM

experiments Page 9


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Increasing noise variance increases the noise

More variance,more badly are the samples affected by the

noise

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6 7 8 9 10 11 12 13 14 15-2

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Also a time delay introducted by the channel will lead to more

serious errors as the desired values at sampling instants are

time shifted

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At the receiver we need to synchronize with the incoming

pulse ,performed proceeding to sample the signal to obtain the

proper sample values of input binary sequence

We pass this waveform through a matched filter

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10

Sine we have not used the time shifted version of the

transmit filter we have distorted output

We can not extract the sample values

We use the rc pulse in the receiver filter also

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We normalize the RC pulse to have unit energy

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1


Time (seconds)

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0

1


Time (seconds)

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1.5

Noise variance of 0.01

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We can see that with increase noise variance

At some of the sample values the variance between actual

values and obtained values in larger

Hence quantization levels must be increased so that in spiteof noise the correct sample values can be detected.

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Sinc pulse transmit filter

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Time (seconds)

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Time (seconds)

If the length of filter is 24 samplesWe need to shift the received samples by 24/2 to get the

proper timing

Wednesday, June 08, 2011

11:53 AM

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The threshould is 0 thus if the samples values us less than 0

we say it is symbol 1 that is transmitted and if the sampled

values is greater than 1 it is symbol 0 that has been

transmitter

Before the matched filter the output looks likes

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-0.8

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0

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It is corrupted by noise of vaiance 0.05

By introduction of matched filter noise only along the

components of signal vectors are condidered

Other noise components are filtered out by use of matched

filter

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Time (seconds)

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Time (seconds)

The above is pulse produced by raised cosine tranmit filter

The signal after passing through channel

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0

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Time (seconds)

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-1

0

1

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The signal after matched filtering operation

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Time (seconds)

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-50

0

50

Thus if we set the threshold as 0,we can detect the symbols

without error,

We sample at the time instants T to obtain the correct values

of the samples

These samples are passed to a decision device ,

The decision device has knowledge of symbols being

transmiited,it has map of signal space

The output of matched filter is the observation vectorThis vector is mapped into signal space

Distance is calculated between the signal vector's and

observation vector

1.rule in the decision of minimum distance

2.calulcate the likelyhood function for the signal vectors and

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given observation vector and decide in the favor of symbol

correspondin to maximum likelyhood

Values

3.

inter symbol intereference

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