This topic will cover the listed topics below regarding linear equalization and its variations: Fundamental of equalization Equalizer Categories of equalization Depending on the time nature Structure of adaptive equalization Classification of equalizer Linear equalizer Transversal equalizer Lattice equalizer Advantage and disadvantages of lattice Disadvantages of linear equalizer Equalization, diversity, and channel coding are three techniques which can be used independently or in tandem to improve received signal quality. Equalization compensates for intersymbol interference (ISI) created by multipath within time dispersive channels. If the modulation bandwidth exceeds the coherence bandwidth of the radio channel, ISI occurs and modulation pulses are spread in time. An equalizer within a receiver compensates for the average range of expected channel amplitude and delay characteristics. Equalizers must be adaptive since the channel is generally unknown and time varying.

1. PRESENTED BY
VAISHALI.K
M.Tech (ECE) - Ist yr
21304023
DEPARTMENT OF ELECTRONICS & COMMUNICATION
ENGINEERING
PONDICHERRY UNIVERSITY
SUBMITTED TO
Dr.R.NAKKERAN,
Head of the department,
Dept.Of Electronics Engineering

2.  Introduction
 Fundamental of equalization
 Equalizer
 Categories of equalization
 Depending on the time nature
 Structure of adaptive equalization
 Classification of equalizer
 Linear equalizer
 Transversal equalizer
 Lattice equalizer
 Advantage and disadvantages of lattice
 Disadvantages of linear equalizer
 References 2

3.  Equalization, diversity, and channel coding are three techniques which
can be used independently or in tandem to improve received signal
quality.
 Equalization compensates for intersymbol interference (ISI) created by
multipath within time dispersive channels.
 If the modulation bandwidth exceeds the coherence bandwidth of the
radio channel, ISI occurs and modulation pulses are spread in time.
 An equalizer within a receiver compensates for the average range of
expected channel amplitude and delay characteristics.
 Equalizers must be adaptive since the channel is generally unknown
and time varying.
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4.  Intersymbol interference (1S1) caused by multipath in band limited
(frequency selective) time dispersive channels distorts the transmitted
signal, causing bit errors at the receiver.
 1S1 has been recognized as the major obstacle to high speed data
transmission over mobile radio channels. Equalization is a technique
used to combat intersymbol interference.
 In a broad sense, the term equalization can be used to describe any
signal processing operation that minimizes 1S1.
 In radio channels, a variety of adaptive equalizers can be used to cancel
interference while providing diversity.
 Since the mobile fading channel is random and time varying, equalizers
must track the time varying characteristics of the mobile channel, and
thus are called adaptive equalizers.
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5.  The goal of equalizers is to eliminate intersymbol interference (ISI)
and the additive noise as much as possible.
 Intersymbol interference(ISI) arises because of the spreading of a
transmitted pulse due to the dispersive nature of the channel, which
results in overlap of adjacent pulses.
 In Fig there is a four‐level pulse amplitude modulated signal (PAM),
x(t). This signal is transmitted through the channel with impulse
response h(t). Then noise n(t) is added. The received signal r(t) is a
distorted signal.
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6.  Equalizers are used to overcome the negative effects of the channel.
In general, equalization is partitioned into two broad categories;
 Maximum likelihood sequence estimation (MLSE) which entails
making measurement of channel impulse response and then
providing a means for adjusting the receiver to the transmission
environment.
 Equalization with filters, uses filters to compensate the distorted
pulses. The general channel and equalizer pair is shown in Figure..
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7.  These type of equalizers can be grouped as preset or
adaptive equalizers.
 Preset equalizers assume that the channel is time invariant and try to
find H(f) and design equalizer depending on H(f). The examples of
these equalizers are zero forcing equalizer, minimum mean square
error equalizer, and decision feedback equalizer.
 Adaptive equalizers assume that the channel is time varying channel
and try to design equalizer filter whose filter coefficients are varying in
time according to the change of channel, and try to eliminate ISI and
additive noise at each time.
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11.  Equalization techniques can be subdivided into two general
categories — linear and nonlinear equalization.
 These categories are determined from how the output of an adaptive
equalizer is used for subsequent control (feedback) of the equalizer.
 In general, the analog signal d^(t) is processed by the decision making
device in the receiver. The decision maker determines the value of the
digital data bit being received and applies a slicing or thresholding
operation (a nonlinear operation) in order to determine the value of d(t).
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12.  If d(t) is not used in the feedback path to adapt the equalizer, the
equalization is linear.
 On the other hand, if d(t) is fed back to change the subsequent
outputs of the equalizer, the equalization is nonlinear.
 Many filter structures are used to implement linear and nonlinear
equalizers. Further, for each structure, there are numerous
algorithms used to adapt the equalizer.
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13.  The most common equalizer structure is a linear transversal equalizer
(LTE). A linear transversal filter is made up of tapped delay lines, with
the taps spaced a symbol period (Ts)
 The simplest LTE uses only feed forward taps, and the transfer function
of the equalizer filter is a polynomial in z^-1. This filter has many zeroes
but poles only at z = 0, and is called a finite impulse response (FIR)
filter, or simply a transversal filter.
 If the equalizer has both feedforward and feedback taps, its transfer
function is a rational function of z^-1 , and is called an infinite
impulse response (IIR) filter with poles and zeros.
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17.  The current and past values of the received signal are linearly weighted
by the filter coefficient and summed to produce the output.
 If the delays and the tap gains are analog, the continuous output of the
equalizer is sampled at the symbol rate and the samples are applied to
the decision device.
 The output of this transversal filter before decision making (threshold
detection) is
 The minimum mean squared error that a linear transversal equalizer can
achieve is
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20.  Two main advantages of the lattice equalizer is its numerical stability
and faster convergence time.
 Also, the unique structure of the lattice filter allows the dynamic
assignment of the most effective length of the lattice equalizer.
 Hence, if the channel is not very time dispersive, only a fraction of the
stages are used.
 When the channel becomes more time dispersive, the length of the
equalizer can be increased by the algorithm without stopping the
operation of the equalizer.
 The structure of a lattice equalizer, however, is more complicated than a
linear transversal equalizer. 20

21.  Linear equalizers do not perform well on channels which have deep
spectral nulls in pass band.
 To compensate for distortions, linear equalizers places too much gain in
vicinity of special nulls, and thus enhances noise present in those
frequencies
 So, non linear equalizers are used where channel distortion are too
severe for a linear equalizers to handle.
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22.  Theodore S. Rappaport, “Wireless Communication Principles
&Practice”, PHI, 2007.
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