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# ofdm cyclic prefix doubt?

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#### gurpreet

##### Newbie level 4
Hello all,
in ofdm (orthogonal frequency division multiplexing), we compromise some data rate and introduce what is known as guard interval between two symbols. This guard interval can be anything, it doesn't matter because the reciever is finally going to ignore this interval. Now, my doubt is why they use "Cyclic Prefix" for it?
~gurpreet

cyclic prefix is used to maintain orthogonality between sub carriers.. One of the condition for orthogonality is to have integer number of cycles in the FFT sampling window. this is possible only if we use CP..

Points: 2

### ahmeddeia

Points: 2
remember that in ofdm we use orthogonal signals to transmitt data(cosines and sines that are orthogonal) , now if one of the of the sine or cosines got delayed by some amount, it will no longer be orthogonal to other carriers...so we need to ensure the whatever happens the carriers will always stay orthogonal
there is a book on the board that talks about multicarrier technology that can help alot

OFDM for wireless multimedia communications
by R.van nee this book

hi gurpreet,
you might be thinking that as the CP is discarded at the receiver, the CP can be anything. yes, the cyclic prefix can be anything. But, it is more advantageous to have it as a repeated version of the starting portion of the same OFDM symbol, this will help in maintaining the cyclic property of DFT so even if there is a slight error in detecting the start of OFDM symbol, this CP preserves the cyclic property of DFT.
If you remember, DFT assumes that the input is periodic when it is not the case. This has a direct link to the concept why CP is what it is..

Cyclic Prefix will ensure that your overall system can be described as a circulant matrix operation, which makes IDFT/DFT pair work.

CP, must be the last part of the symbol. because when the symbol(or carrier) is delayed in time domain, it may lose orthogonality b/c there might no more integer number of cycles of the sub-carriers within the symbol(or ifft) interval.. some one mentioned a book in this Question reply...its good..read it..
CP time might be blank, or may be any signal..but most advantageous is to use last part of the symbol as CP.

All the above opinions about CP's supporting 'orthogonality' is correct, but I would like to add some other advantages.

Since CP is the replica of the end of OFDM symbol, it would be effectively to utilize this property and do time/frequency synchronization. Please refer to the earlier publications in this area.

but they usually use the a part of preamble to make CP, i think so

CP is the last potion of the OFDM symbol..its the right concept...

CP is mainly added to the begining of the OFDM symbol to elliminate the effect of the multi-version arrival of the symbol due to multipath with causes delay.
It has a specific value that is calculated from a certain relation-in brief it is about 20% of the frame length-to maintain orthogonality between sub-carriers for proper detection

Nice Question !

Heres the Answer -->

Its all about making the receiver design simplER.
OFDMsymbol is usually transmitted in either of two forms viz. ZP(zero padded) or CP (cyclic prefixed).
While both provide similar immunity towards frequency selective (ie multitap) channel, the catch is that while using ZP-OFDM equalization at receiver requires a complicated design; while CP-ofdm consrves frequency orthogonality & thus enables the use of SINGLE-TAP equalizer in freq domain at receiver - thus easing out the receiver design & resource consumption by bounds !

Hope that answers ur question. Any other doubts r welcome

Hi gurpreet,
there are a lot of issues for using cyclic prefix in ofdm
1. It prevents contamination of a block by intersymbol interference from the previous block.
2. it makes the received block appear to be periodic with period M. This produces the appearance of circular convolution, which is essential to the proper functioning of the FFT operation.
3. cyclic prefix is used to maintain orthogonality between sub carriers. One of the
condition for orthogonality is to have integer number of cycles in the FFT sampling
window.
4.The length of the cyclic prefix is the maximum expected length of the channel impulse response. It may be larger tan that too.
5. Overlap-save or overlap-add signal processing techniques could also be used to avoid the extra overhead of the cyclic prefix.

saurav Dutt

CP is also used to avoid ISI.

wel i think this material will solve your problem

The math foundation of OFDM is that sinsoid is the eigenfunction of linear time invariant (LTI) channel. This means if one transmit a sinsoid signal to LTI system, the output is just a scaled version of the transmit signal. OFDM generalizes this idea by transmitting multiple signal over multiple frequencies.

However, sinsoid signal has infinite duration in time, which is not the case for practical communication system. In this case, inter-carrier interference occurs. CP is used to get around of this.

From singal processing perspective, CP leads to circular matrix, which make IDFT/DFT meaningful.

1-CP maintains orthogonality of subcarriers.
2-Using CP results in a smooth waveform (compared to a gap interval) and is better for High Power Amplifier and ADC in the receiver.
3-CP can be used in timing and frequency synchronization (in non-pilot based algorithms).

cyclic prefix is used for synchronisation.
some calculations are performed on cyclic prefix to check the starting point of frame.

Hello all! I know that there is a cyclic prefix and zero-prefix(0). And bts_dev writes about ZP(zero padded) ana CP (cyclic prefixed).

I have questions:
1)What advantages and disadvantages at cyclic prefix(CP)?
3)Why cyclic prefix used widely?
4)How process a signal with cyclic prefix(CP)? How works reciever? Who can present a code in MathLab?
5)How process a signal with zero-prefix(ZP)? How works reciever? Who can present a code in MathLab?

Thanks for help. Sorry for bad English.:|

Hi

If you left the guard period without any signaling there will be a discontinuity in phase which results in sharp edges in time domain and high frequency components in frequency domain.

A CP is added to avoid this phase discontinuity so the received signal will be band limited.
also the CP with maltipath channel will result of receiving a signal which is the original signal multiplide by several phase shifts. which results in simplifying the channel effect estimation and compensation

Salam
Hossam Alzomor
www(.)i-g(.)org

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