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

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 signal. In addition, we derive the analytical power spectral density of AFDM and evaluate its spectral characteristics in comparison with other multicarrier schemes, considering 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 Cramér-Rao bounds for channel parameter estimation, showing that the chirped modulation peculiar of AFDM increases the estimation variance but enables the resolution of Doppler ambiguities. Our findings provide the necessary theoretical and practical foundations for the implementation of AFDM in realistic wireless transceivers.