In ofdm systems after applying IDFT we take the last N/x samples and place them before these N samples. This is called cyclic prefix(CP).So why to use a cyclic prefix?
Why is the CP known to combat the inter symbol interference.Why can't we use some junk data or zeros over there? Can't this junk data combat the ISI ?.
Regards, Phani Tej
Answer
The cyclic prefix is to make sure that any multi-path interference (or other process similar to a linear time-invariant filter in the transmission channel) acts as a circular convolution on the FFT data frame, thus not affecting the orthogonality of the data channels within the FFT bins. It also allow some slop in the receiver's symbol clock.
Thus the cyclic prefix has to be a circular repetition of the IFFT data, either before or after the IFFT block, and long enough to be as long or longer than the maximum expected multi-path delay time differential in the channel, plus the maximum of any timing error between the received data block and the receiver symbol clock. The N/4 is just a default estimate of this time for some common channels, but longer may be required.
Anything other that a circular repetition can cause multi-path delays to act as a non-linear spectral spreading function (relative to the FFT frame) which will affect channel orthogonality, and thus S/N related reliability.
Repetition (circular or otherwise) also helps to statistically even out the PAP (peak to average power) ratio over the extended frame. And prefix repetition may help push any transmitter anomalies due to sudden changes in this ratio forward of the FFT frame.
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