  Affine frequency division multiplexing (AFDM) is an emerging multicarrier
waveform that offers a potential solution for achieving reliable communications
over time-varying channels. This paper proposes two maximum-likelihood (ML)
estimators of symbol time offset and carrier frequency offset for AFDM systems.
One is called joint ML estimator, which evaluates the arrival time and carrier
frequency offset by comparing the correlations of samples. Moreover, we propose
the other so-called stepwise ML estimator to reduce the complexity. Both
proposed estimators exploit the redundant information contained within the
chirp-periodic prefix inherent in AFDM symbols, thus dispensing with any
additional pilots. To further mitigate the intercarrier interference resulting
from the residual frequency offset, we design a mirror-mapping-based scheme for
AFDM systems. Numerical results verify the effectiveness of the proposed time
and carrier frequency offset estimation criteria and the mirror-mapping-based
modulation for AFDM systems.
