# 0.12 Linear equalization  (Page 3/17)

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The design objective of the equalizer is to undo the effects of the channel and to remove theinterference. Conceptually, the equalizer attempts to build a system that isa “delayed inverse” of [link] , removing the intersymbol interference while simultaneouslyrejecting additive interferers uncorrelated with the source. If the interference $\eta \left(k{T}_{s}\right)$ is unstructured (for instance white noise) then there is little that alinear equalizer can do to remove it. But when the interference is highly structured (such as narrowband interference from anotheruser), then the linear filter can often notch out the offending frequencies.

As shown in Example  [link] of [link] , the solution for the optimal sampling times found bythe clock recovery algorithms depend on the ISI in the channel. Consequently, the digital model (such as [link] ) formed by sampling an analog transmission path (such as [link] ) depends on when the samples are taken within each period ${T}_{s}$ . To see how this can happen in a simple case, consider a two-path transmissionchannel

$\delta \left(t\right)+0.6\delta \left(t-\Delta \right),$

where $\Delta$ is some fraction of ${T}_{s}$ . For each transmitted symbol, the received signal will containtwo copies of the pulse shape $p\left(t\right)$ , the first undelayed and the second delayed by $\Delta$ and attenuated by a factor of $0.6$ . Thus, the receiver sees

$c\left(t\right)=p\left(t\right)+0.6p\left(t-\Delta \right).$

This is shown in [link] for $\Delta =0.7{T}_{s}$ . The clock recovery algorithms cannot separate the individualcopies of the pulse shapes. Rather, they react to the complete received shape, which is their sum. The power maximizationwill locate the sampling times at the peak of this curve, and the lattice of sampling times will be different fromwhat would be expected without ISI. The effective (digital) channel model is thus a sampled versionof $c\left(t\right)$ . This is depicted in [link] by the small circles that occur at ${T}_{s}$ spaced intervals.

In general, an accurate digital model for a channel depends on many things: the underlying analog channel,the pulse shaping used, and the timing of the sampling process.At first glance, this seems like it might make designing an equalizer for such achannel almost impossible. But there is good news. No matter what timing instants are chosen, no matterwhat pulse shape is used, and no matter what the underlying analog channel may be(as long as it is linear), there is a FIR linearrepresentation of the form [link] that closely models its behavior. The details may change, but it is always a sampling of the smooth curve (like $c\left(t\right)$ in [link] ) that defines the digital model of the channel.As long as the digital model of this channel does not have deep nulls(i.e., a frequency response that practically zeroes out some important band of frequencies), there is a good chance that theequalizer can undo the effects of the channel.

## Trained least-squares linear equalization

When there is a training sequence available (for instance, in the known frame information that is used insynchronization), this can also be used to help build or “train” an equalizer.The basic strategy is to find a suitable function of the unknown equalizer parameters that can be used to definean optimization problem. Then, applying the techniques of Chapters [link] , [link] , and [link] , the optimization problem can be solved in a variety of ways.

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
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