Message Passing-Initialized Approximated-Variance Expectation Propagation (MPI-AVEP) Detector for AFDM Waveform

High-mobility communications in 6G systems face challenges due to Doppler shifts that degrade the performance of traditional orthogonal frequency division multiplexing (OFDM). Affine frequency division multiplexing (AFDM) offers high spectral efficiency but requires efficient detection to exploit its diversity gain. We introduce expectation propagation (EP) as an effective detector for AFDM, improving decoding by estimating the joint posterior distribution of symbols. However, EP incurs high complexity due to matrix inversion, and the Neumannseries approximation (NSA), which is widely used to reduce matrix inversion complexity, fails in AFDM systems due to ill-conditioned channel matrices. To address this, we propose a message passing-initialized approximated-variance EP (MPI-AVEP). It exploits the quasi-banded structure of AFDM channel matrices to reduce the total complexity. The MPI-AVEP achieves performance similar to traditional EP while reducing complexity from cubic to linear in the number of subcarriers. Thus, it offers a practical solution for high-mobility communication systems.