  Affine Frequency Division Multiplexing (AFDM), which is based on discrete
affine Fourier transform (DAFT), has recently been proposed for reliable
communication in high-mobility scenarios. Two low complexity detectors for AFDM
are introduced here. Approximating the channel matrix as a band matrix via
placing null symbols in the AFDM frame in the DAFT domain, a low complexity
MMSE detection is proposed by means of the $\rm{LDL}$ factorization.
Furthermore, exploiting the sparsity of the channel matrix, we propose a low
complexity iterative decision feedback equalizer (DFE) based on weighted
maximal ratio combining (MRC), which extracts and combines the received
multipath components of the transmitted symbols in the DAFT domain. Simulation
results show that the proposed detectors have similar performance, while
weighted MRC-based DFE has lower complexity than band-matrix-approximation
LMMSE when the channel impulse response has gaps.
