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

Abstract

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.