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

• Published in: IEEE transactions on communications 2021-05, Vol.69 (5), p.2909-2922
• Main Authors: Choi, Jeonghoon, Kim, Jubum, Cho, Joon Ho, Lehnert, James S.
• Format: Article
• Language: English
• Subjects: Bandwidth; Binary phase shift keying; Constellation rotation; Constellations; Criteria; dFT-spread OFDM; Discrete Fourier transforms; Equalizers; Error analysis; Fourier transforms; frequency-domain spectrum shaping; Linear receivers; nyquist criterion; OFDM; Orthogonal Frequency Division Multiplexing; Peak to average power ratio; Power amplifiers; Pulse shaping methods; Rotation; Signal to noise ratio; square-root raised cosine; Symbols; Trigonometric functions; widely-linear zero-forcing equalizer
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2021.3056106

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 \pi /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.