<< Chapter < Page Chapter >> Page >

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

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
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 .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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 .?
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Discrete multi-tone communication over acoustic channel' conversation and receive update notifications?