  Affine frequency division multiplexing (AFDM) is a multi-chirp waveform and a
promising solution for ultra-reliable communication under doubly dispersive
channels. In this paper, we propose two pilot aided channel estimation schemes
for AFDM, named single pilot aided (SPA) and multiple pilots aided (MPA)
respectively. Pilot, guard and data symbols in the discrete affine Fourier
transform (DAFT) domain are arranged appropriately at the transmitter. While at
the receiver, channel estimation is performed with the aid of an estimation
threshold and a mapping table. The bit error performance of AFDM applying the
proposed channel estimation schemes shows only marginal loss compared to AFDM
with ideally known channel state information. Moreover, extensions of the SPA
scheme to multiple-input multiple-output (MIMO) and multi-user uplink/downlink
are presented.
