By bilinearly transforming the rectangularly pulsed multicarrier basis signals, new basis sets containing full-response continuous basis signals are developed for constructing spectrally efficient orthogonal frequency-division multiplexing (OFDM) signals with or without cyclic prefix (CP) or zero padding (ZP). Both multiple-product and linear-combination formats are presented for these basis sets. In the multiple-product format, the developed full-response basis signals are shown to be zero-valued at interval edges, and thus can be used to construct continuous-phase OFDM signals. It is analytically shown that the constructed continuous-phase OFDM signals exhibit relatively small power spectral sidelobes which fall off as f 04 , and can thus provide much higher spectral efficiency than the traditional rectangularly pulsed OFDM signal. In the linear-combination format, the proposed basis signals are shown to be the linear combinations of rectangularly pulsed multicarrier basis signals, and thereby allow for the efficient realization of fast Fourier transform (FFT). Specifically, a spectrally precoded signaling structure is developed in conjunction with inverse FFT and guard insertion to construct continuous-phase OFDM signals with or without CP or ZP. The corresponding spectral decoders are also developed to enable zero-forcing (ZF) demodulation for spectrally precoded OFDM. With the zero-forcing demodulation, the spectrally precoded OFDM schemes are shown to outperform in average error-rate characteristics the conventional rectangularly pulsed and correlatively coded OFDM schemes on various delay-spread channels.

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.

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