Motivated by the convergence of terrestrial cellular networks with satellite networks, we consider an adaptation of offset quadrature phase shift keying (OQPSK), used with single-carrier waveform in traditional satellite systems, to discrete Fourier transform spread (DFT-s-) orthogonal frequency-division multiplexed (OFDM) waveform employed in the uplink of terrestrial systems. We introduce a new order-one constellation modulation, termed repeated-and-offset QPSK (RO-QPSK), derive its basic properties, and compare it with pi/2-BPSK with frequency-domain spectral shaping (FDSS), as supported in 5G. RO-QPSK naturally produces a Hann-window-shaped spectrum, resulting in a very low maximum peak-to-average power ratio (PAPR) on the order of 2 dB. Moreover, with single-tap equalization and symbol combining at the receiver, RO-QSPK can improve the signal-to-interference-plus-noise (SINR) compared to pi/2-BPSK with FDSS, in narrowband and/or moderately frequency-selective channels, as encountered in satellite communications. A moderate FDSS can also be combined with RO-QSPK to further reduce the PAPR while providing similar performance. Of independent interest, general SINR expressions for DFT-s-OFDM are also provided.

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