Spectral analysis of OFDM signals and its improvement by polynomial cancellation coding

In orthogonal frequency division multiplexing (OFDM) systems, the subcarriers are generated by an inverse discrete Fourier transform (DFT). OFDM has a relatively slow spectral rolloff. In the literature, the spectra of these subcarriers are often represented by a sequence of sinc functions with the same polarity. This does not explain the intercarrier interference (ICI) cancellation properties of polynomial cancellation coding (PCC) in OFDM. In this paper, the Fourier transform of the subcarriers are derived and the results show that spectra of these subcarriers are more accurately represented by a sequence of sinc functions with alternating polarity. The derived representation is consistent with the ICI cancellation properties of PCC. This paper also gives the derivation of spectral rolloff as a function of frequency and the number of subcarriers in OFDM and PCCOFDM. It is shown that the spectral rolloff of OFDM signals is improved by PCC and the resultant OOB power is much lower than in normal OFDM.