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From the Transmitter comes a block of size N+L (where N is the number of subcarriers and L is the cyclic prefix length). Then the block goes through a Channel which adds delay and AWGN, so this process can be described as a convolution of a transmitted block with a channel (the channel length H).

The question: The output of the convolution increases the size of transmitted block (the output from a channel is of lenth [N+L+H]) so how can FFT be performed (of course after removing cyclic prefix)? (because the number of subcarriers must be the size of IFFT/FFT)

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You're doing the same length as in the transmitter.

You're ignoring the purpose of the cyclic prefix: it's both to allow the "echoes" from the previous symbol to die off (i.e. it contains H). That's why your CP is always a bit larger than the length of channel you're expecting.

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  • $\begingroup$ So if before transmitting the block an interpolation was made then in the receiver a downsample will be made....but again those things involve convolution thus increasing the length of the block before reaching the FFT. Does CP need to include those "echoes" too? $\endgroup$ – student Jan 29 at 12:21

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