AFDM Channel Estimation in Multi-Scale Multi-Lag Channels

TL;DR

AFDM is evaluated for multi-scale multi-lag underwater acoustic channels where each path has distinct delay and Doppler characteristics, including Doppler time scaling. The paper derives the CFR in the DAFT domain and shows that DTS spreads path energy, motivating two estimators: AFDM-IMI for low-to-moderate DTS and AFDM-OMP for high DTS. By leveraging CFR structure, mutual incoherence properties, and a CFR overlap probability metric, the authors demonstrate improved channel estimation accuracy and BER over OFDM and OCDM. Numerical results confirm AFDM’s advantage in MSML settings, highlighting its potential for robust, high-mobility UWA communications.

Abstract

Affine Frequency Division Multiplexing (AFDM) is a brand new chirp-based multi-carrier (MC) waveform for high mobility communications, with promising advantages over Orthogonal Frequency Division Multiplexing (OFDM) and other MC waveforms. Existing AFDM research focuses on wireless communication at high carrier frequency (CF), which typically considers only Doppler frequency shift (DFS) as a result of mobility, while ignoring the accompanied Doppler time scaling (DTS) on waveform. However, for underwater acoustic (UWA) communication at much lower CF and propagating at speed of sound, the DTS effect could not be ignored and poses significant challenges for channel estimation. This paper analyzes the channel frequency response (CFR) of AFDM under multi-scale multi-lag (MSML) channels, where each propagating path could have different delay and DFS/DTS. Based on the newly derived input-output formula and its characteristics, two new channel estimation methods are proposed, i.e., AFDM with iterative multi-index (AFDM-IMI) estimation under low to moderate DTS, and AFDM with orthogonal matching pursuit (AFDM-OMP) estimation under high DTS. Numerical results confirm the effectiveness of the proposed methods against the original AFDM channel estimation method. Moreover, the resulted AFDM system outperforms OFDM as well as Orthogonal Chirp Division Multiplexing (OCDM) in terms of channel estimation accuracy and bit error rate (BER), which is consistent with our theoretical analysis based on CFR overlap probability (COP), mutual incoherent property (MIP) and channel diversity gain under MSML channels.

Figures (6)

• Figure 1: The per-entry amplitude of the CFR matrix $\mathbf{\bar{H}}$ of: (a) OFDM in non-scaled LTV channel; (b) OFDM in MSML channel; (c) AFDM in non-scaled LTV channel; and (d) AFDM in MSML channel under $P=5$, $l_\textrm{max}=19$, $Q_\textrm{max}=1$ and Doppler factor in order of $10^{-3}$.
• Figure 2: The occurrence probability of diversity order $\rho$ and the CCDF of PEP associated with OFDM, OCDM and AFDM, respectively, under Doppler factor in the order of (a) (c) $10^{-4}$ and (b) (d) $10^{-2}$.
• Figure 3: (a) Output $\mathbf{z}$ for the same input $\mathbf{s}$ under different $\left(l_i,Q_i\right)$ combination; and (b) the corresponding matrices $\mathbf{\Psi}_1$ and $\mathbf{\Psi}_2$.
• Figure 4: The MIP of OFDM-OMP, OCDM-OMP, and AFDM-OMP under MSML channels.
• Figure 5: The performance indicators of OFDM-OMP, OCDM-OMP, and AFDM-OMP under MSML channels: (a) NMSE (b) BER.