Widely-Linear Nyquist Criteria for DFT-Spread OFDM of Constellation-Rotated PAM Symbols

In this paper, the Nyquist criteria for ordinary linear modulation are generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM) of constellation-rotated PAM symbols. Unlike the conventional Nyquist criteria with a linear receiver, the new criteria are to remove intersymbol interference in the output of a widely-linear (WL) receiver. It is shown that not only the folded spectrum, but also the shifted and reverse-folded spectrum is crucial in the criteria, where the shift offset is determined by the rotation angle. As a design example, combinations of a constellation rotation angle and a square-root raised cosine pulse are proposed. It is shown that the proposed design can achieve better performance both in spectral efficiency and in peak-to-average power ratio than the conventional DFT-spread OFDM of π/2-BPSK symbols. The optimal one-tap frequency-domain equalizer is also derived under the WL zero-forcing (ZF) constraint. It is shown that, when the rotation angle is properly chosen, the proposed one-tap WL-ZF equalizer significantly outperforms the one-tap linear ZF equalizer in output signal-to-noise ratio. The proposed equalizer also outperforms the conventional equalizer in error vector magnitude measured at the output of a nonlinear power amplifier.