# doesn't OFDM inherently deals with ISI? why cyclic prefix is needed?

As far as I can understand, the motivation to OFDM and multi carrier communication in general was alot due to the ISI caused by multi-path which is equivalent to frequency selective channel. Now, by using OFDM, we send our symbols over sub-carriers, thus each symbol in the frequency domain is affected by approximately a constant channel response. Then, why is there an aditional need for cyclic prefix? doesn't using sub-carriers enough for dealing with the ISI?

The samples in one OFDM symbol are also scrambled due to the channel delay spread or subcarriers in the frequency domain are faded differently. So, we still need to equalize this effect. Here the function of CP comes! One OFDM symbol is convolved with the channel impulse response "linearly". If somehow this linear convolution can be converted to a circular convolution, the equalization of the channel is quite easy. We just need to take the FFT of our received OFDM symbol and channel, and make a simple point-to-point division as FFT(OFDM)./FFT(CHANNEL)(Channel should be zero padded to have the same size with the OFDM symbol) . So, what did CP do here? CP converts that linear convolution to a circular convolution by inserting the last samples of the OFDM symbol to the first samples.