Instantaneous Frequency Estimation for Frequency-Modulated Signals under Gaussian and Symmetric α-Stable Noise

Frequency estimation for frequency-modulated (FM) and single-tone sinusoidal signals is essential in various applications, such as wireless communications, sonar and radar measurements. In this paper, methods for estimating the instantaneous frequency (IF) under Additive White Gaussian Noise (AWGN) and Additive Symmetric alpha-alpha Stable Noise (S alpha SN) are investigated. Two MATLAB algorithms were considered based on the maximum likelihood for the Short Time Fourier Transform (STFT). S alpha S distributions commonly used to model impulsive noise disturbances; however, the S alpha S distribution lacks a closed-form Probability Density Function (PDF), except in specific cases (Gaussian, Cauchy, and levy distributions). As the second-order statistic is infinite for alphastable noise, Geometric SNR (GSNR) is used to determine the noise's impulsiveness in a mixture of Gaussian and S alpha S noise processes. Results showed that S alpha S noise is much more harmful for frequency estimation than Gaussian noise, even if it is a small capacity, and it is less destructive when alpha is more than one.