Joint Fractional Delay and Doppler Frequency Estimator Under Spectrum Wrapping Phenomenon for LEO-ICAN AFDM Signals

TL;DR

This work tackles the challenge of jointly estimating fractional delay and Doppler for AFDM-based LEO-ICAN links, where spectrum wrapping introduces model mismatch. It delivers a rigorous input-output derivation under fractional delay to expose the envelope of the effective DAFT-domain channel and then proposes a low-complexity, LOS-focused estimator: a closed-loop PSPR-based fractional Doppler compensation followed by an open-loop ELG-based fractional delay estimation. Compared with integer-estimation and AML baselines, the proposed method yields higher accuracy, reduced computational load, and smaller guard-interval overhead, validated by extensive simulations with $N=256$ subcarriers. The results support AFDM as a robust waveform for high-Doppler, high-dynamics V2X scenarios in LEO-ICAN deployments, with potential extensions to multipath channels in future work.

Abstract

With the rapid development of low earth orbit (LEO) satellites, the design of integrated communication and navigation (ICAN) signals has attracted increasing attention, especially in the field of vehicle-to-everything (V2X). As a new-generation waveform, Affine Frequency Division Multiplexing (AFDM) features high robustness against Doppler effects, a simple modulation structure, and low pilot overhead, making it a promising candidate for high-dynamic LEO satellite scenarios. However, LEO-ICAN AFDM signals face challenges in fractional delay and Doppler frequency estimation. Existing studies that ignore its inherent spectrum wrapping phenomenon may lead to deviations of varying degrees in model construction. This paper conducts an in-depth derivation of AFDM's input-output relationship under fractional cases, reveals the envelope characteristics of its equivalent channel, and proposes a joint estimation algorithm based on peak-to-sidelobe power ratio (PSPR) detection and early-late gate (ELG) to estimate fractional Doppler frequency and delay. Simulations show that the algorithm has low complexity, low guard interval overhead, and high precision compared with traditional methods.

Figures (7)

• Figure 1: Block diagram of AFDM modulation and demodulation
• Figure 2: Time and frequency(TF) representation of AFDM, and it can be observed that spectrum discontinuity occurs within the dashed elliptical boxes.
• Figure 3: Schematic diagram of $\Upsilon(m, m')$, $\Theta(m, m')$, and $|\mathcal{F}(m, m')|$ under $m$ index (with $m^{\prime}=0$), illustrating the periodic sinc sampling sequence, sinc envelope, and the total magnitude respectively.
• Figure 4: Schematic diagram of piece-wise summation index.
• Figure 5: Plot of ELG factor $\mathcal{A}(\iota)$ versus fractional delay $\iota$

Theorems & Definitions (1)

• proof : Proof of Theorem \ref{['thm1']}