In communication system, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. In communication system, the Nyquist ISI criterion describes the conditions which when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference(ISI). It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference.

1. PONDICHERRY UNIVERSITY
( Pondicherry University,Chinna Kalapet,Kalapet,Puducherry -605014)
PRESENTATION
ON
“NYQUIST CRITERION FOR ZERO ISI”
Submitted in the partial fulfillment of the requirement for the Award of Degree of
M-TECH ELECTRONICS AND COMMUNICATION
ENGINEERING
SUBMITTED BY
FAIZAN SHAFI [21304012]
Under the Guidance of
Dr. R.Nakkeeran
ASSOCIATE PROFESSOR
DEPARTMENT OF ELECTRONICS ENGINEERING
SCHOOL OF ENGINEERING AND TECHNOLOGY
PONDICHERRY UNIVERSITY,KALAPET,
PUDUCHERRY-605014

2. Intersymbol interference (ISI)
In communication system, intersymbol interference (ISI) is a form of distortion of a signal in
which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as
the previous symbols have similar effect as noise, thus making the communication less
reliable. The spreading of the pulse beyond its allotted time interval causes it to interfere with
neighbouring pulses. ISI is usually caused by multipath propagation or the inherent linear or
non-linear frequency response of a communication channel causing successive symbols to
blur together.
The presence of ISI in the system introduces errors in the decision device at the
receiver output. Therefore, in the design of the transmitting and receiving filters, the
objective is to minimize the effects of ISI, and thereby deliver the digital data to its destination
with the smallest error rate possible. Ways to alleviate(remove or correct) inter symbol
interference include adaptive equalization and error correcting codes.
Causes
Multipath Propagation
One of the causes of inter symbol interference is multipath propagation in which a
wireless signal from a transmitter reaches the receiver via multiple paths. The causes of this
include reflection (for instance, the signal may bounce off buildings), refraction (such as
through the foliage of a tree) and atmospheric effects such as atmospheric
ducting and ionospheric reflection. Since the various paths can be of different lengths, this
results in the different versions of the signal arriving at the receiver at different times. These
delays mean that part or all of a given symbol will be spread into the subsequent symbols,
thereby interfering with the correct detection of those symbols. Additionally, the various
paths often distort the amplitude and/or phase of the signal, thereby causing further
interference with the received signal.
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3. Bandlimited channels
Another cause of intersymbol interference is the transmission of a signal through
a bandlimited channel, i.e., one where the frequency response is zero above a certain
frequency (the cutoff frequency). Passing a signal through such a channel results in the
removal of frequency components above this cutoff frequency. In addition, components of
the frequency below the cutoff frequency may also be attenuated by the channel.
This filtering of the transmitted signal affects the shape of the pulse that arrives at the
receiver. The effects of filtering a rectangular pulse not only change the shape of the pulse
within the first symbol period, but it is also spread out over the subsequent symbol periods.
When a message is transmitted through such a channel, the spread pulse of each individual
symbol will interfere with following symbols. The bandlimiting can also be due to the physical
properties of the medium for instance, the cable being used in a wired system may have a
cutoff frequency above which practically none of the transmitted signal will propagate.
Communication systems that transmit data over bandlimited channels usually
implement pulse shaping to avoid interference caused by the bandwidth limitation. If the
channel frequency response is flat and the shaping filter has a finite bandwidth, it is possible
to communicate with no ISI at all. Often the channel response is not known beforehand, and
an adaptive equalizer is used to compensate the frequency response.
Countering ISI
There are several techniques in communication system and data storage that try to work
around the problem of intersymbol interference.
 Design systems such that the impulse response is short enough that very little energy
from one symbol smears (spreads over) into the next symbol.
 Separate symbols in time with guard periods.
 Apply an equalizer at the receiver that, broadly speaking attempts to undo the effect
of the channel by applying an inverse filter.
 Apply a sequence detector at the receiver, that attempts to estimate the sequence of
transmitted symbols using the Viterbi algorithm.
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4. Nyquist criteria (Sampling Theorem)
For any signal to have efficient reconstruction, the rate of sampling should be greater than or
equal to twice the highest frequency component present in the input signal.
fs ≥ 2fmax
ts = 1/fs
where, fs = sampling frequency
ts = sampling time
fmax = highest frequency component
Nyquist criterion for zero ISI
In communication system, the Nyquist ISI criterion describes the conditions which when
satisfied by a communication channel (including responses of transmit and receive filters),
result in no intersymbol interference(ISI). It provides a method for constructing band-limited
functions to overcome the effects of intersymbol interference.
When consecutive symbols are transmitted over a channel by a linear modulation (such
as ASK, QAM, etc.), the impulse response (or equivalently the frequency response) of the
channel causes a transmitted symbol to be spread in the time domain. This causes
intersymbol interference because the previously transmitted symbols affect the currently
received symbol, thus reducing tolerance for noise. The Nyquist theorem relates this time-
domain condition to an equivalent frequency-domain condition.
The Nyquist criterion is closely related to the Nyquist-Shannon-sampling theorem, with
only a differing point of view.
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5. Nyquist criterion
If we denote the channel impulse response as h(t),then the condition for an ISI free response
can be expressed as:
For all integers n, where Ts is the symbol period. The Nyquist theorem says that this is
equivalent to:
Where H(f) is the fourier transform of h(t). This is the Nyquist ISI Criterion.
This criterion can be understood in the following way: frequency-shifted replicas of H(f) must
add up to a constant value. This condition is satisfied when H(f) spectrum has even symmetry,
has bandwidth less than or equal to 2/Ts, and its single-sideband has odd symmetry at the
cutoff frequency ±1/2Ts.
In practice this criterion is applied to baseband filtering by regarding the symbol sequence as
weighted impulses (Dirac delta function). When the baseband filters in the communication
system satisfy the Nyquist criterion, symbols can be transmitted over a channel with flat
response within a limited frequency band, without ISI. Examples of such baseband filters are
the raised-cosine filter, or the sinc filter as the ideal case.
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6. Derivation
To derive the criterion, we first express the received signal in terms of the transmitted symbol
and the channel response. Let the function h(t) be the channel impulse response, x[n] the
symbols to be sent, with a symbol period of Ts; the received signal y(t) will be in the form
(where noise has been ignored for simplicity):
Sampling this signal at intervals of Ts, we can express y(t) as a discrete-time equation:
If we write the h[0] term of the sum separately, we can express this as:
and from this we can conclude that if a response h[n] satisfies
only one transmitted symbol has an effect on the received y[k] at sampling instants, thus
removing any ISI. This is the time-domain condition for an ISI-free channel. Now we find
a frequency-domain equivalent for it. We start by expressing this condition in continuous
time:
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7. for all integer n. We multiply such a h(t) by a sum of Dirac delta function (impulses) 𝜹(𝒕)
separated by intervals Ts . This is equivalent of sampling the response as above but using a
continuous time expression. The right side of the condition can then be expressed as one
impulse in the origin:
Fourier transforming both members of this relationship we obtain:
and
This is the Nyquist ISI criterion and, if a channel response satisfies it, then there is no ISI
between the different samples.
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8. THANK YOU
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