Low complexity equalization for AFDM in doubly dispersive channels

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.