<< Chapter < Page Chapter >> Page >
Describes the role of cyclic prefixing.

Why the prefix?

In an ideal world, we wouldn't have to worry about cyclic prefixes; the channel would be a wire and everything we send would be received in exactly the same form. However, implementing our DMT system in an ideal world would be pretty useless, as all the cool benefits from DMT would go to waste. Thus, we implemented a channel with an ugly (but not too ugly) frequency response, which added two forms of interference: inter-symbol-interference (ISI) and inter-channel-interference (ICI), which we will discuss next.

Inter-symbol-interference (isi)

ISI arises from the fact that the channel performs a linear convolution of its impulse response with the time-domain waveform. By this time, the blocks (now known as symbols ) have been mirrored, IFFT'd and concatenated. At the intersection of adjacent symbols, the linear convolution of the signal with the impulse response (whose support is assumed to be less than the symbol length but greater than unity) overlaps parts of both symbols. This means that independent symbols affect each other; one symbol"bleeds"into another. The addition of a prefix provides a buffer between symbols that prevends this.

Isi

Inter-symbol-interference (ISI): This indicates the linear convolution of the channel impulse response h with the time-domain input to the channel x . Notice the overlap at the intersection of the two symbols.

Inter-channel-interference (ici)

ICI comes from the fact that the carrier frequencies for DMT lose their orthogonality due to the frequency response of the channel. If we looked at the FFT of a block at the input to the channel, we'd see a sinc function at each carrier frequency since the IFFT modulates each carrier with a rectangular pulse. The DFT basis is orthonormal, so each of the basis vectors (sinusoids) are orthogonal to all the rest; this means each of the sincs are orthogonal (zero inner product) as well. The frequency response of the channel has the effect of attenuating certain frequencies more than others, so each of the sincs is changed by a different amount. Since the inner product is a measure of the similarity of two vectors, two previously"completely dissimilar"sinc functions now have at least some degree of similarity; i.e they are no longer orthogonal. Without orthogonal carriers, the FFT cannot exactly recover the correctspectral coefficients. Cyclic padding solves this problem by turning the linear convolution of the channel inpulse response with the signal into a cyclic convolution.

Ici

Inter-channel-interference (ICI): This represents two carrier frequencies as sincs in the frequency-domain. The frequency response of the channel causes the carrier frequencies for the transmitted signal to lose orthogonality.

Cyclic prefix

The addition of a cyclic prefix to each symbol solves both ISI and ICI. In our system, we assume the channel impulse response has a known length L . The prefix consists simply of copying the last L -1 values from each symbol and appending them in the same order to the front of the symbol. By having this buffer of essentially junk data in the front, the convolution of the impulse response with the signal at the end of a symbol does not affect any of the actual data at the beginning of the next symbol. In addition, by repeating the last elements at the beginning, the first real"data"elements of each symbol experience overlap with the"end"of the symbol, just as in cyclic convolution. This means the linear convolution of the channel impulse response with the concatenated symbols becomes concatenated cyclic convolutions of the impulse response with the individual symbols. Since cyclic convolution directly corresponds to multiplication in the frequency domain, this has great import with respect to equalization, as we will see later. After the time-domain signal passes through the channel, it is broken back into the parallel symbols and the prefix is simply discarded.

Cyclic prefix

This is one time-domain symbol with the cyclic prefix and last L elements shown in red (This is a slightly exaggerated pad length).

Our related MATLAB functions: cyclicpad.m , decyclicpad.m

Home | Previous: Implementation | Next: The Channel

Questions & Answers

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Ece 301 projects fall 2003. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10223/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Ece 301 projects fall 2003' conversation and receive update notifications?

Ask