  Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier
waveform for high mobility communications, is introduced here. AFDM is based on
discrete affine Fourier transform (DAFT), a generalization of discrete Fourier
transform, which is characterized by two parameters that can be adapted to
better cope with doubly dispersive channels. First, we derive the explicit
input-output relation in the DAFT domain showing the effect of AFDM parameters
in the input-output relation. Second, we show how the DAFT parameters
underlying AFDM have to be set so that the resulting DAFT domain impulse
response conveys a full delay-Doppler representation of the channel. Then, we
show analytically that AFDM can achieve full diversity in doubly dispersive
channels, where full diversity refers to the number of multipath components
separable in either the delay or the Doppler domain, due to its full
delay-Doppler representation. Furthermore, we present a low complexity
detection method taking advantage of zero-padding. We also propose an embedded
pilot-aided channel estimation scheme for AFDM, in which both channel
estimation and data detection are performed within the same AFDM frame.
Finally, simulations corroborate the validity of our analytical results and
show the significant performance gains of AFDM over state-of-the-art
multicarrier schemes in high mobility scenarios.
