In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP).
My question is related to that step of adding a CP. As I know, adding the CP is My question, if $H$ is the vector of $y$ in frequency domain, "$H = Fy$", so Can we diagonalize $H$ by left-right multiplying by proper DFT? Which mean $A = F \, H \, F^H$ and $A$ is a diagonal matrix of $N \times N$ ?? Does that right in OFDM? And what's about after removing the CP when performing DFT operating in receiver side, will this propriety of circular convolution will be kept?