Model-Order-Adaptive Channel Estimation for AFDM Systems with Fractional Delay and Doppler

2026-10-07

AI Summary

This study addresses the challenging problem of channel estimation in affine frequency division multiplexing (AFDM) systems under fractional delays, Doppler shifts, and an unknown number of propagation paths. An adaptive estimation algorithm based on a modified space-alternating generalized expectation-maximization (SAGE) framework is proposed. By leveraging dual-pilot initialization and statistical residual testing, the method achieves adaptive model order selection. Furthermore, it reveals the frequency wrapping mechanism induced by fractional delays and incorporates a support pruning strategy with coarse-to-fine joint optimization, thereby overcoming the limitations of conventional fixed-order approaches. Experimental results demonstrate that the proposed algorithm significantly reduces both the normalized mean square error (NMSE) and bit error rate (BER). It maintains robust performance even in high-mobility scenarios at 600 km/h, comprehensively outperforming existing baseline methods.

Abstract

Affine frequency division multiplexing (AFDM) has emerged as a promising waveform for high-mobility communications owing to its ability to exploit multipath diversity. However, channel state information (CSI) acquisition remains challenging in channels with fractional delay and Doppler and an unknown number of propagation paths. In this paper, we investigate the channel estimation for AFDM systems. We first analyze the AFDM response in the presence of fractional-delay-induced frequency wrapping. The analysis reveals that fractional delay may displace the dominant extremum and generate informative secondary extrema. Then, we develop a model-order-adaptive channel estimator within an improved space-alternating generalized expectation-maximization (SAGE) framework. A dual-pilot reference symbol is employed for path and delay initialization, while pilot observations across multiple AFDM symbols provide temporal information for Doppler estimation. New paths are identified through statistically controlled residual tests, whereas unsupported or redundant paths are removed by conditional support pruning. The delay, Doppler frequency, and complex gain of each retained path are subsequently estimated through a coarse-to-fine procedure and refined using the exact AFDM likelihood. Simulation results demonstrate that the proposed method achieves lower normalized mean squared error (NMSE) and bit error rate (BER) than representative SAGE, sparse-recovery, and Bayesian benchmarks. It also provides reliable path detection and model-order estimation and maintains robust performance at terminal velocities of up to 600~km/h.

Problem

• AFDM
• channel estimation
• fractional delay
• fractional Doppler
• model-order adaptation

Innovation

• Affine Frequency Division Multiplexing (AFDM)
• Model-Order-Adaptive Channel Estimation
• Space-Alternating Generalized Expectation-Maximization (SAGE)
• Fractional Delay and Doppler
• High-Mobility Communications