Spectral precoding for rectangularly pulsed OFDM

Spectrally precoded orthogonal frequency-division multiplexing (OFDM) is a promising rectangularly pulsed OFDM signaling format which can provide very small power spectral sidelobes, while allowing for efficient implementation by fast Fourier transform and guard interval insertion. In this paper, general constraints on spectral precoding are developed for OFDM signals with zero padding (ZP-OFDM) or cyclic prefix (CP-OFDM) to warrant the desirable spectral property that the power spectral sidelobes decay asymptotically as f^-2K-2, where K is a preassigned positive integer. In accordance with the constraints, block partitioning is adopted to construct a general signaling format to facilitate the precoder design of the spectrally precoded CP-OFDM that can provide fast decaying sidelobes. New correlative and orthogonal precoders are also devised so that the desirable spectral property of fast sidelobe decaying is achieved with spectrally precoded ZP-OFDM and CP-OFDM signals.