  With the increasing demand for multi-carrier communication in high-mobility
scenarios, it is urgent to design new multi-carrier communication waveforms
that can resist large delay-Doppler spreads. Various multi-carrier waveforms in
the transform domain were proposed for the fast time-varying channels,
including orthogonal time frequency space (OTFS), orthogonal chirp division
multiplexing (OCDM), and affine frequency division multiplexing (AFDM). Among
these, the AFDM is a strong candidate for its low implementation complexity and
ability to achieve optimal diversity. This paper unifies the waveforms based on
the discrete affine Fourier transform (DAFT) by using the chirp slope factor
"k" in the time-frequency representation to construct a unified design
framework for high-mobility communications. The design framework is employed to
verify that the bit error rate performance of the DAFT-based waveform can be
enhanced when the signal-to-noise ratio (SNR) is sufficiently high by adjusting
the chirp slope factor "k".
