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Text to binary conversion

The first step is to convert our information into binary. We used the sentence “hello, this is our test message,” repeated four times, as our text message. To get it into binary, we used standard ASCII text mapping.

hello = 01101000 01100101 01101100 01101100 01101111

Series to parallel

The next step is converting this vector of zeros and ones into a matrix. The vector is simply broken up into blocks of length L, and each block is used to form column of the matrix.

Constellation mapping

Now the fun begins. The primary method of modulation in DMT is by inverse Fourier Transform. Although it may seem counterintuitive to do so, by taking the inverse Fourier Transform of a vector or a matrix of vectors, it effectively treats each value as the Fourier coefficient of a sinusoid. Then, one could transmit this sum of sinusoids to a receiver that would in turn take the Fourier Transform (the inverse transform of the inverse transform, of course) and retrieve the original vectors.

But instead of taking the transform of our vectors of zeros and ones, we first convert bit streams of length B to specific complex numbers. We draw these complex numbers from a constellation map (a table of values spread out along the complex plane). See the figure below for an example of a 4 bit mapping.

Constellation mapping table

const map
This table shows which bit stream is mapped to which complex value.

Signal mirroring and inverse fourier transform

Why would we do that, you might ask. Doesn’t converting binary numbers to complex ones just make things more complicated? Well, DMT utilizes the inverse Fourier Transform in order to attain its modulation. So taking the IFFT of a vector of complex numbers will result in a sum of sinusoids, which are great signals to be sending over any channel (they are the eigenfunctions of linear, time-invariant systems).

But before taking the inverse transform, the vectors/columns of the matrix must be mirrored and complex conjugated. The Inverse Fourier Transform of a conjugate symmetric signal results in a real signal. And since we can only transmit real signals in the real world, this is what we want.

Cyclic prefix

If we were transmitting over an ideal wire system, we would be done at this point. We could simply send it over the line and start demodulating. But with most channels, especially our acoustic one, this is not the case. The channel’s impulse response has non-zero duration, and will therefore cause inter-symbol interference in our output.

Intersymbol interference occurs during the convolution of the input and impulse response. Since the impulse response has more than a single value length, it will thus cause one block’s information to bleed into the next one.

To prevent this, we added what is called a cyclic prefix to each block. As long as the length of the cyclic prefix is at least as long as the impulse response, it should prevent ISI. However, it has a secondary effect as well. We created the prefix by adding the last N values of each block (where N is the length of the response) to the beginning, preserving the order. Doing this effectively converts the linear convolution of the impulse response with the block sequence to circular convolution with each block separately, since there will now be the “wrap-around” effect. This will be handy later when we start characterizing the channel, since circular convolution in time is equivalent to multiplication of DFT’s in frequency.

00010110011010001 =>01000100010110011010001

The first six bits in the second bit stream, 010001, is the cylcic prefix. Note that although these values are binary, they could essentially range from -1 to 1 since they sample the sinusoid sum that was formed after inverse Fourier Transforming.

Please see the block diagram below. It summarizes the entire transmission process covered above.

Transmission block diagram

Transmission block diagram.
This diagram shows the all of the components and flow of our transmission system.

Questions & Answers

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.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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Source:  OpenStax, Discrete multi-tone communication over acoustic channel. OpenStax CNX. Dec 16, 2009 Download for free at http://cnx.org/content/col11146/1.1
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