Saturation-enhanced dynamic regressor extension for robust carrier frequency estimation of disturbed amplitude-modulated signals

Hoang D.L., Pyrkin A.A. Saturation-enhanced dynamic regressor extension for robust carrier frequency estimation of disturbed amplitude-modulated signals. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2026, vol. 26, no. 4, pp. 753–762. doi: 10.17586/2226-1494-2026-26-4-753-762

This paper considers the problem of carrier frequency estimation from measurements of an amplitude-modulated signal in the presence of unknown bounded disturbances and a time-varying envelope. Existing identification methods based on regression transformations usually require a small-disturbance condition, which limits their practical applicability. The scientific novelty of this work consists in the development of a robust carrier-frequency estimation algorithm that preserves the regression structure of delay-based signal parameterization and does not require the assumption of small disturbance magnitude. The proposed method is based on the parameterization of the measured signal using delayed measurements, which makes it possible to reduce the problem to a linear regression model. To estimate the unknown parameter, an adaptive algorithm with a saturation nonlinearity is used, limiting the influence of large regression errors. After estimating the regression parameter, the carrier frequency is reconstructed. The effectiveness of the proposed method is verified through numerical experiments for amplitude-modulated signals under noise and impulsive disturbances. A comparison with a normalized gradient algorithm and a power-transformed regression method is performed. The simulation results demonstrate a faster reduction of the estimation error and improved robustness of the proposed algorithm. The obtained results show the advantage of the proposed method over existing frequency-estimation algorithms under strong disturbances. The method can be applied to radio-signal processing, communication systems, and modulation-recognition algorithms. Future research directions include the development of discrete-time implementations of the algorithm and its extension to multi-component signals.

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