Variational Inference-Based Frequency-Domain Equalization for Faster-Than-Nyquist Signaling in Doubly Selective Channels

This work deals with frequency-domain equalization for faster-than-Nyquist (FTN) signaling in doubly selective channels (DSCs). To handle the interference of frequency-domain symbols, the minimum mean square error (MMSE) equalizer involves high complexity in DSCs. To overcome the problem, we propose low-complexity receivers based on two variational methods, i.e., mean field (MF) and Bethe approximations. Compared with the MF method, the Bethe approximation takes into account the conditional dependencies of pairwise symbols. By only considering a small set of the frequency-domain symbols that have strong interference to each other, the complexity of the proposed algorithms increases linearly with the block length. Simulation results demonstrate that the proposed algorithms for FTN signaling are able to perform close to the MMSE equalizer in DSCs while with significantly reduced computational complexity.