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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 η ( k T s ) 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

δ ( t ) + 0 . 6 δ ( t - Δ ) ,

where Δ is some fraction of T s . For each transmitted symbol, the received signal will containtwo copies of the pulse shape p ( t ) , the first undelayed and the second delayed by Δ and attenuated by a factor of 0 . 6 . Thus, the receiver sees

c ( t ) = p ( t ) + 0 . 6 p ( t - Δ ) .

This is shown in [link] for Δ = 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 ( t ) . This is depicted in [link] by the small circles that occur at T s spaced intervals.

The optimum sampling times (as found by the energy maximization algorithm) differ when there is ISI in the transmission path, and change the effective digital model of the channel.
The optimum sampling times (as found by the energy maximization algorithm) differ when there is ISIin the transmission path, and change the effective digital model of the channel.

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 ( t ) 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.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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