# 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.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Difference between extinct and extici spicies
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
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