Cyclic Prefix and Its Significance in LTE


What is  cyclic prefix or why do we need the CP in LTE or for that matter in any wireless/OFDM system? The answer lies in the name itself. Cyclic indicates that, the CP maintains the cyclic nature of something and prefix says it is added at the beginning.
Basically, the CP is nothing but a portion of the signal itself, which is copied and added to the beginning of the signal. The below diagram should explain more about the same,



Cyclic Prefix for LTE
Why CP is added?
Now to understand why CP is added, you should know the basics of FFT/IFFT or the significance of doing a FFT/IFFT over any signal. In LTE, for downlink, an IFFT is performed to realize the OFDM concept. Now, first place what does FFT does?What does IFFT does to a signal? If you take a FFT of a signal, you are basically taking the signal from time domain to frequency domain and for IFFT, it is the vice versa, i.e from frequency domain to time domain.
Lets see what happens when we take a FFT of a simple sine wave, below illustration depicts the same,

FFT/IFFT Illustration
In the above figures, first let us consider,
Figure-B : In this figure you can see a time domain signal, which is a sine wave of frequency 1Hz and a FFT is performed over this sine wave and the result is on the right. You can see 2 spikes on either sides of the axis, lets neglect the spike on the negative side of the quadrant, so on the positive side, the spike is seen at 1Hz co-ordinate on the frequency axis. What does this indicate? Simple, the FFT of a time domain signal gives you the different frequencies within that signal, so we have a single spike which indicates the time domain signal is a sine wave of frequency 1Hz.
Now how can we relate this to CP? In case of LTE, the encoding is performed in frequency domain and then we perform an IFFT, which is exactly the reverse of the process, we are doing in above figure. We perform a 1024 point IFFT, which means, instead of single spike, we will have 1024 different spikes and we perform a IFFT over these tones and we get a time domain signal, to which we the CP and transmit over the air.
Now at the receiver side, he does an FFT to get back these 1024 tones back and start decoding. Since, we know that a wireless channel is more prone to different types of disturbances, such as multipath, AWGN, Doppler etc, the signal is more prone to corruption or a delay. So what happens when this delayed signal is received at the receiver? Will he be able to successfully perform a FFT to get back the 1024 tones? Lets see the effect in the Figure-A
Figure-A: Lets assume this is a receiver, where he has received a delayed version of the time domain signal. He was supposed to get start receiving the signal at time=A, but he got a signal starting from time=B. So now, if there was no CP added then he could have possibly lost the portion of signal between A & B, but because the transmitter added the CP, whose length is more than B-A, the lost signal can be found at the end of the signal (Indicated in red color, marked as CP). Because of the CP, the continuity of the sine wave is still maintained and when the receiver does an FFT of the same, he will still get a spike at 1Hz because of the continuity of the signal.
So, thats all about the CP. CP not only helps in the continuity, but also in avoiding the inter symbol interference. Which means, even when multiple reflected copies of signals get added at the receiver, he should still be able to distinguish between symbols and CP makes sure this is maintained.
CP Length
What should be the ideal CP length? Simple, the CP length should be the maximum possible delay, introduced due to the farthest supported radius in LTE. That means, if a eNodeB supports coverage of 10Kms, then the CP length should be more than the maximum time the signal can take to reach from a UE , which is 10Km away from the eNodeB. That, is why we have two different types of CP, normal and extended CP. So if a eNodeB needs to support a very large coverage area, then he should support extended CP to accomodate for the different multipath delays.

I hope this article helped you in understanding the CP.

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