Using Sequence-to-Sequence Models for Carrier Frequency Offset Estimation of Short Messages and Chaotic Maps

Deep Learning methods have produced good carrier frequency offset estimations for short message sequences in comparison with methods based on the Fast Fourier Transform. However, these performance gains were observed for short ranges of frequency offsets, sequences with predefined pilot symbols and periodic modulation schemes. Chaotic modulation has an advantage over periodic signals in offering security through the continuous changes produced by parameterising the chaotic map function. However, synchronisation of chaotic map parameters in coherent receivers is dependent on the carrier recovery of phase and frequency which dramatically reduces the demodulation performance under high noise levels. This article presents a stacked sequence-to-sequence neural network architecture for blind carrier frequency offset estimation of both periodic and chaotic modulation schemes. The results obtained demonstrate better performance than conventional methods in low SNR for the Additive White Gaussian Noise channel. While this technique operates without feature engineering, the results demonstrate that data augmentation produces a higher degree of accuracy for such models, indicating the benefit of integration with conventional signal pre-processing steps as part of the deep learning pipeline. The proposed neural network architecture is shown to perform carrier frequency offset estimation, not only for the selected periodic modulations, but also in the case of highly non-linear chaotic maps. This suggests the applicability of deep learning methods for synchronisation in waveforms that employ chaotic modulation schemes for secure communication and for applications where short and sporadic messaging are required (e.g., Internet of Things).