Cyclic Prefix in OFDM

cyclic prefix ofdm

Hai,
I am new to OFDM...was reading up a few articles on OFDM and came across cyclic prefix quite frequently..Can someone please explain what this is and why it is used..?? Or can someone provide me some material which explain the same...

thanks in advance

- matt

ofdm cyclic prefix

chek out:
h**p://

or go here directly--> h**p://xdsl.ftw.at/docs/papers/2002_IZS_CPanalysisSlides.pdf

or if u still wanna get deeper to know exact diff btwn use of IDFT n cyclic prefix in ofdm.. chek this--> h**p://users.rsise.anu.edu.au/~jmanton/Manton_Dissect_OFDM.pdf

cyclic prefix in ofdm

In OFDM we work on frequency domain.

When the transmitted signal frequency response is X and the channel response is H

it is allways desireble to get received signal frequency reponse as,

Y=H*X, then you can recover X simply as X=Y/H;

but according to DFT theory multiplication of two DFTS H*X, is allways time domain circular convolution . Than is circ(h,x).......
( X is FFT of x)

But when you pass the signal x through the channel only liner convolution with h occurs. To mimic circ convolution we make x by a cyclic prefix.

cyclic prefix circular convolution

Cyclic prefix is used to avoid intersymbol interference(ISI) which is a common phenonmenon in frequency selective channel. Usually length of the CP is kept greater or atleast equal to the length of the channel impulse response.

circular convolution cyclic prefix

but according to DFT theory multiplication of two DFTS H*X, is allways time domain circular convolution . Than is circ(h,x).......
( X is FFT of x)

But when you pass the signal x through the channel only liner convolution with h occurs. To mimic circ convolution we make x by a cyclic prefix.

Click to expand...

thanx janath

How does adding a cyclic prefix convert the linear convolution between h and x into a circular convolution..?? Also what exactly should be the length of the CP, which is added at the end of x...Also, what effect does adding CP in the time domain have on the frequency domain representation...

Please forgive me if my doubts are too basic....

- matt

ofdm circular convolution

assume that the sequnce is,

x(0),x(1),x(2),x(3)

and the channel impulse response is h(0), h(1);

if we take DFT of x and h, h has to be extended upto N (4)points,

h(0), h(1), 0,0;

now if we multiply DFTs of x(that is X) and h(that is H), then coreespondingly there should be circular con in time domain;

for example for the first symbol;

x(0)*h(o) + x(1)*0 + x(2)*0+x(3)*h(1);------(A)

obviously just sending x through the channel you cannot get this;we do not get the last term

so what we do is
add taplength-1 (here it is 2-1=1)cyclic extension to x sequence as,

x(3) x(0) x(1) x(2) x(3), noW if we do the linear convolution

for the "second term" you get

x(3)*h(1)+x(0)*h(o) + x(1)*0 + x(2)*0

which exactly the cicular convolution in (A); similary you can get the other term....


so what you have to do is; add channel_tap_length -1 cyclic extension to x sequence and just pass through the channel;


and remove first channel_tap_length -1 symbols and take the rest N symbols(here is is 4), and take FFT
that will be H*X

Hope this will help

circular prefix

Thank you very much for your well explained answer..!