AFDM-FTN: A Spectrally Efficient Waveform for High-Mobility Communications

This paper proposes an affine frequency division multiplexing (AFDM)-aided faster-than-Nyquist (FTN) waveform, termed AFDM-FTN, to enhance spectral efficiency (SE) in high-mobility communication scenarios. We first derive the AFDM-FTN input-output relationship and analyze the FTN-induced interference pattern in AFDM-FTN. To address the channel estimation challenges, a low-complexity channel estimator based on the basis expansion model (BEM) is developed. By exploiting the intrinsic characteristics of the AFDM channel matrix and the FTN coefficient matrix, a multi-layer message passing (MLMP) algorithm is proposed that leverages the sparsity of the time-domain (TD) channel and the FTN coefficient matrix, where belief messages are iteratively propagated across the TD channel, FTN, and transform layers. Building upon the BEM-assisted channel estimation and MLMP, a low-complexity joint channel estimation and data detection scheme (BEM-MLMP-JCED) is further developed to iteratively refine channel estimation with the aid of transmitted data. Finally, the channel estimation lower bound, the mean square error (MSE) performance of the BEM-MLMP-JCED, and the computational complexity are analyzed. Simulation results demonstrate that the proposed AFDM-FTN system with BEM-MLMP-JCED achieves comparable BER to conventional AFDM while providing enhanced SE and reduced complexity compared to benchmark receivers.