Widely-Linear Nyquist Criterion for DFT-Spread OFDM with Frequency-Domain Spectrum Shaping

In this paper, the Nyquist criterion for ordinary linear modulation is generalized to the discrete-Fourier transform-spread (DFT-spread) orthogonal frequency-division multiplexing (OFDM). In particular, the DFT-spread OFDM of constellation-rotated PAM symbols is considered with frequency-domain spectrum shaping (FDSS). This includes the DFT-spread OFDM of π/2-BPSK symbols as a special case, which is supported by the 5th generation New Radio standard. Unlike the conventional Nyquist criterion with a linear receiver, the new criterion is to remove intersymbol interference in the output of a widely-linear receiver. It is shown that not only the folded spectrum but also the shifted and reverse-folded spectrum is crucial in the criterion, 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 with FDSS.