| Summary: | Estimating parameters from sinusoidal signals contaminated by noise is a critically important topic extensively applied in fields such as radar systems, communication systems, biomedical engineering, and power systems. Frequency, as the most crucial parameter and intrinsic characteristic of sinusoidal signals, constitutes a classic problem in signal processing, demanding accurate estimation.
Gaussian white noise stands as the most prevalent noise in nature, prompting significant attention toward extracting signal frequencies from sinusoidal signal samples corrupted by Gaussian white noise. Existing traditional frequency estimation methods mainly encompass periodogram methods, linear prediction methods, parametric modeling methods, autocorrelation phase methods, and subspace methods. However, these studies predominantly focus on enhancing estimation accuracy under high signal-tonoise ratio (SNR) environments. In numerous practical scenarios, signal sequences obtained may be short and contain substantial noise due to complex environmental factors.
With advancements in big data technology and computational power, deep learning (DL) has emerged as a new branch in the field of machine learning. Neural networks constitute the core of deep learning algorithms, characterized by their flexibility and excellent fitting capability, enabling automatic adaptation to various signal types and environmental conditions. In order to estimate the frequency of sinusoidal signals tainted by Gaussian white noise, this study develops three deep learning-based estimators: Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN) estimators. Additionally, two traditional frequency estimation methods, namely periodogram-based quadratic interpolation and multiple signal classification (MUSIC), are utilized as benchmark algorithms for evaluating their performance. Amongthethree neural network frequency estimators, the performance of RNN-based and CNN-based estimators surpasses that of the MLP-based estimator. However, their performance is more stable compared to the two traditional estimators, making them more suitable for complex scenarios encountered in practical applications. Moreover, the performance of deep learning-based frequency estimation methods does not significantly deteriorate, unlike traditional methods, when the input signal sequence length is very short. Even when the input signal SNR is-30dB, the estimation error of neural network estimators is at least 30dB lower than traditional methods. Furthermore, this study investigates the impact of different SNR ranges between the training and evaluation phases on the performance of deep learning methods.
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