# 0.11 Timing recovery  (Page 10/11)

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Consider a resampler with input $x\left(k{T}_{s}\right)$ and output $x\left(k{T}_{s}+\tau \right)$ . Use the approximation in [link] (b) to derive an approximate gradient descent algorithm that minimizesthe fourth power performance function

${J}_{FP}\left(\tau \right)=\frac{1}{N}\sum _{k={k}_{0}+1}^{{k}_{0}+N}{x}^{4}\left(k{T}_{s}+\tau \right)$

for a suitably large $N$ .

Implement the algorithm from [link] using clockrecOP.m as a basis and compare the behavior with the output power maximization. Consider

1. Convergence speed
2. Resilience to noise
3. Misadjustment when ISI is present

Now answer the same questions for the fourth power algorithm of [link] .

This problem explores a receiver that requires carrier recovery, timing recovery, and automatic gain correctionin order to function properly.

1. Write a carrier-recovery routine for the signal generated by BigEx1.m . You may want to use the receiver in BigIdeal.m for inspiration. Pay particular attention to the given parameters (Hint: the sampling rate isbelow the IF frequency, so the receiver front-end effectively employs subsampling). Describe the carrier recovery method used and plot the tracking of $\Phi$ . If the receiver employs preprocessing, take care to design the BPF appropriately.
2. Add a timing recovery algorithm to the receiver so that the receiver samples at the appropriate time. State the timing recovery method usedand plot the tracking of $\tau$ .
3. Add an AGC to the code and decode the message. Does the code recover the message appropriately?Calculate the error rate of the receiver.

## Two examples

This section presents two examples in which timing recovery plays a significant role.The first looks at the behavior of the algorithms in the nonideal setting. When there is channel ISI, theanswer to which the algorithms converge is not the same as in the ISI-free setting. This happens because the ISIof the channel causes an effective delay in the energy that the algorithm measures.The second example shows how the timing recovery algorithms can be used to estimate (slow) changes in theoptimal sampling time. When these changes occur linearly, they are effectively a change in the underlying period,and the timing recovery algorithms can be used to estimate the offset of the period in the same way that thephase estimates of the PLL in [link] can be used to find a (small) frequency offset in the carrier.

Modify the simulation in clockrecDD.m by changing the channel:

% T/m channel chan=[1 0.7 0 0 .5];

With an oversampling of m=2 , 2-PAM constellation, and beta=0.5 , the output of the output power maximization algorithm clockrecOP.m is shown in [link] . With these parameters, the iteration begins in a closed eye situation. Because of the channel, nosingle timing parameter can hope to achieve a perfect $±1$ outcome. Nonetheless, by finding a good compromise position (in this case, converging to anoffset of about 0.6), the hard decisions are correct once the eye has opened (which first occurs around iteration500).

Example  [link] shows that the presence of ISI changes the convergent valueof the timing recovery algorithm. Why is this?

#### Questions & Answers

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
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
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
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