# 0.11 Timing recovery  (Page 10/11)

 Page 10 / 11

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?

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
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!