Spectrally Precoded DFT-Based OFDM and OFDMA With Oversampling

Spectrally precoded orthogonal frequency-division multiplexing (SP-OFDM) and SP-OFDM multiple access (SP-OFDMA) are bandwidth-efficient rectangularly pulsed multicarrier signaling formats that can provide power spectral sidelobes decaying asymptotically as f^-2L-2, with L being a preassigned positive-integer design parameter, which results in a compact spectrum. The existing spectral precoders for SP-OFDM and SP-OFDMA are designed based on the rectangularly pulsed analog multicarrier waveform representation that has an unlimited power spectrum; thus, the corresponding waveforms cannot be exactly synthesized in a discrete Fourier transform (DFT) structure. Consequently, these spectral precoders are subject to modification in DFT-based OFDMA and OFDM systems in which signaling waveforms are digitally synthesized with the use of DFT and provide discrete approximation embodiments to analog multicarrier waveform counterparts. In this paper, a general constraint on spectral precoding and the corresponding spectral precoders are developed for DFT-based OFDMA and OFDM with oversampling to ensure the desirable spectral property that the resultant spectrally precoded DFT-based waveforms provide powerspectral-sidelobe envelope bounds decaying asymptotically as f^-2L-2. It is analytically shown that the precoders suitable to DFT-based waveforms can be simply obtained by properly transforming the previously designed precoders suitable to corresponding analog multicarrier waveforms with an appropriate diagonal phase-rotation matrix, while yielding similar spectral performance and peak-to-average power ratio (PAPR) characteristics.