Continuous-Time Analysis of AFDM: Pulse-Shaping, Fundamental Bounds and Impact of Hardware Impairments

TL;DR

This paper develops a continuous-time analytical framework for AFDM, highlighting the importance of bandlimited pulses, spectral characteristics, and hardware impairments, and provides bounds for channel estimation in high-mobility wireless systems.

Contribution

It introduces a continuous-time model for AFDM, analyzes spectral and hardware effects, and derives channel estimation bounds, advancing practical understanding of AFDM in real-world scenarios.

Findings

Strictly bandlimited pulses are essential for multicarrier structure.

Spectral analysis shows differences with other schemes under realistic conditions.

Chirped modulation enables Doppler ambiguity resolution despite increased estimation variance.

Abstract

Affine frequency division multiplexing (AFDM) has recently emerged as a resilient waveform candidate for high-mobility next-generation wireless systems. However, current literature mostly focuses on discrete time (DT) models, often overlooking effects and hardware non-idealities of actual continuous time (CT) signal generation. In this paper, we bridge this gap by developing a CT-analytical framework based on the affine Fourier series (AFS) representation, which allows us to demonstrate that strictly bandlimited pulses and subcarrier suppression strategies are essential to maintain the multicarrier structure of the transmitted signal. In addition, we derive the analytical power spectral density of AFDM and compare its spectral characteristics in comparison with those of other multicarrier schemes, taking into account the impact of realistic truncated pulse-shaping. Furthermore, we analyze the sensitivity of the CT model to phase noise, carrier frequency offset, and sampling jitter, providing a theoretical analysis of communication performance. Finally, we derive closed-form Cram\'er-Rao bounds for channel parameter estimation, showing that the chirped modulation peculiar of AFDM increases estimation variance but enables the resolution of Doppler ambiguities. Our findings lay the necessary theoretical and practical foundations for the implementation of AFDM in realistic wireless transceivers.