A novel parameter estimation of chirp signal in α-stable noise

Wang, Chunyang

doi:10.1587/elex.14.20161053

Cited by 11 publications

(4 citation statements)

References 8 publications

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“…As a result, based on the pulse characteristics of α-stable noise, FRFT can remove the sharp spikes of the echo signal and convert the non-Gaussian noise into a Gaussian-like distribution, and then uses energy concentration of FRFT to gain accurate initial frequency and chirp rate estimates of the chirp signal. The simulation results show that the approach has high anti-noise performance when predicting chirp signal parameters in α-stable noise, and the estimated effects are consistent with noise-free signals [8].…”

Section: State-of-the-art Methodsmentioning

confidence: 57%

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Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Razzaq

Hussain

2022

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Deep learning (DL) and machine learning (ML) are widely used in many fields but rarely used in the frequency estimation (FE) and slope estimation (SE) of signals. Frequency and slope estimation for frequency-modulated (FM) and single-tone sinusoidal signals are essential in various applications, such as wireless communications, sound navigation and ranging (SONAR), and radio detection and ranging (RADAR) measurements. This work proposed a novel frequency estimation technique for instantaneous linear FM (LFM) sinusoidal wave using deep learning. Deep neural networks (DNN) and convolutional neural networks (CNN) are classes of artificial neural networks (ANNs) used for the frequency and slope estimation for LFM signals under additive white Gaussian noise (AWGN) and additive symmetric alpha stable noise (SαSN). DNN is composed of input, output, and two hidden layers, where several nodes in the first and second hidden layers are 25 and 8, respectively. CNN is the content input layer; many hidden layers include convolution, batch normalization, ReLU, max pooling, fully connected, and dropout. The output layer consists of a fully connected softmax and classification layers. SαS distributions are impulsive noise disturbances found in many communication environments such as marine systems, their distribution lacks a closed-form probability density function (PDF), except for specific cases, and infinite second-order statistics, hence geometric SNR (GSNR) is used in this work to determine the effect of noise in a mixture of Gaussian and SαS noise processes. DNN is a machine learning classifier with few layers for reducing FE and SE complexity. CNN is a deep learning classifier, designed with many layers, and proved to be more accurate than DNN when dealing with big data and finding optimal features. Simulation results show that SαS noise can be much more harmful to the FE and SE of FM signals than Gaussian noise. DL and ML can significantly reduce FE complexity, memory cost, and power consumption as compared to the classical FE based on time–frequency analysis, which are important requirements for many systems, such as some Internet of Things (IoT) sensor applications. After training CNN for frequency and slope estimation of LFM signals, the performance of CNN (in terms of accuracy) can give good results at very low signal-to-noise ratios where time–frequency distribution (TFD) fails, giving more than 20 dB difference in the GSNR working range as compared to the classical spectrogram-based estimation, and over 15 dB difference with Viterbi-based estimate.

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Section: State-of-the-art Methodsmentioning

confidence: 57%

“…Ref. [8] analyzes the characteristics of α-stable noise, and the chirp signal in α-stable noise is converted into Gaussian-like distribution. Then, fractional Fourier transform was used to estimate the initial frequency and chirp rate of signal in α-stable noise.…”

Section: State-of-the-art Methodsmentioning

confidence: 99%

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Razzaq

Hussain

2022

Information

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“…The α-stable distribution Fractal Fract. 2023, 7, 822 3 of 21 does not have a closed-form probability density function, and is commonly represented by the following characteristic function [16,17]…”

Section: Impulsive Noise Modelmentioning

confidence: 99%

Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise

Wang,

Guo,

Yang

2023

Fractal Fract

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Due to the short duration and high amplitude characteristics of impulsive noise, these parameter estimation methods based on Gaussian assumptions are ineffective in the presence of impulsive noise. To address this issue, a LFM signal parameter estimation method is proposed based on FOTD and CFRFT. Firstly, the mathematical expression of FOTD is presented and its tracking performance is verified. Secondly, the tracked signal is subjected to discrete time CFRFT, and a mathematical optimization model for LFM signal parameter estimation is established on the fractional spectrum characteristic. Finally, a correction method for non-standard SαS distributed noise is proposed, and the performance of parameter estimation under both standard and non-standard SαS distributions are analyzed. The simulation results show that this method not only effectively suppresses the impact of impulsive noise on the fractional spectrum of LFM signal, but also has better parameter estimation accuracy and stability in the low GSNR. The proposed method is particularly effective under the measured noise environment, as it successfully suppresses the impact of impulsive noise and achieves high-precision parameter estimation.

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“…The instantaneous frequency, which characterizes the changes in frequency content across time is a necessary aspect of FM transmissions. A signal's IF is a time derivative of its instantaneous phase (θ(t)) as follows [11][12][13]:…”

Section: Instantaneous Frequency and Frequency Modulationmentioning

confidence: 99%

Instantaneous Frequency and Chirp Rate Estimation for Noisy Quadratic FM Signals by CNN

Saleem,

M. Hussain

2023

Jour. Kufa Math. Comp.

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Deep learning and machine learning are widely employed in various domains. In this paper, Artificial Neural Network (ANN) and Convolution Neural Network (CNN) are used to estimate the Instantons Frequency (IF), Linear Chirp Rate (LCR), and Quadratic Chirp Rate (QCR) for Quadratic Frequency Modulated (QFM) signals under Additive White Gaussian (AWG) noise and Additive Symmetric alpha Stable (ASαS) noise. SαS distributions are impulsive noise disturbances except for a few circumstances, lack a closed-form Probability Density Function (PDF), and an infinite second-order statistic. Geometric SNR (GSNR) is used to determine the impulsiveness of mixture noise for Gaussian and SαS noise. ANN is a machine learning classifier with few layers that reduce FE, LCRE, and QCRE complexity and achieve high accuracy. CNN is a deep learning classifier that is built with multiple layers of FE, LCRE, and QCRE. CNN is more accurate than ANN when dealing with large amounts of data and determining optimal features. The results reveal that SαS noise is substantially more damaging to FE, LCRE, and QCRE than Gaussian noise, even when the magnitude is modest, and it is less damaging when alpha is greater than one. After training DCNN for FE, LCRE, and QCRE estimation of QFM signals. The 2D-CNN model accuracy achieved 98.7603 and 1D-CNN is 75.8678 for ten epochs. ANN model accuracy achieved 37.5 for 1000 epochs. The accuracy of TFD (spectrogram & pspectrum) for frequency estimation of QFM signals was 38.4254 by spectrogram and 38.6746 by pspectrum.

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A novel parameter estimation of chirp signal in α-stable noise

Cited by 11 publications

References 8 publications

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Parameter Estimation of LFM Signals Based on FOTD-CFRFT under Impulsive Noise

Instantaneous Frequency and Chirp Rate Estimation for Noisy Quadratic FM Signals by CNN

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