Recently, synchrosqueenzing transform (SST)-based time-frequency analysis (TFA) methods have been developed for achieving the highly concentrated TF representation (TFR). However, SST-based methods suffer from two drawbacks. The first one is that the TFRs are unsatisfactory when dealing with the multicomponent signals, the instantaneous frequencies (IFs) of which are closely adjacent or intersected. Besides, the exhaustive adjustment of window length is required for SST-based methods to obtain the optimal TFR. To tackle these problems, in this article, we first analyze the concentration of TFRs for SST-based methods. A deep learning (DL)-based end-to-end replacement scheme for SST-based methods, named TFA-Net, is then proposed, which learns complete basis functions to obtain various TF characteristics of time series. The 2-D filter kernels are subsequently used for energy concentration. Different from the two-step SST-based methods where the TF transform and energy concentration are separated, the proposed end-to-end architecture makes the basis functions used for extracting TF features more beneficial to energy concentration. The comprehensive numerical experiments are conducted to demonstrate the effectiveness of the TFA-Net. The applications of the proposed method to real-world vital signs, undersea voices and micro-Doppler signatures show its great potential in analyzing nonstationary signals.

Frequency estimation of 2-D multicomponent sinusoidal signals is a fundamental issue in the statistical signal processing community that arises in various disciplines. In this article, we extend the DeepFreq model by modifying its network architecture and apply it to 2-D signals. We name the proposed framework 2-D ResFreq. Compared with the original DeepFreq framework, the 2-D convolutional implementation of the matched filtering module facilitates the transformation from time-domain signals to frequency-domain signals and reduces the number of network parameters. The additional upsampling layer and stacked residual blocks are designed to perform superresolution. Moreover, we introduce frequency amplitude information into the optimization function to improve the amplitude accuracy. After training, the signals in the test set are forward-mapped to 2-D accurate and high-resolution frequency representations. Frequency and amplitude estimation are achieved by measuring the locations and strengths of the spectral peaks. We conduct numerical experiments to demonstrate the superior performance of the proposed architecture in terms of its superresolution capability and estimation accuracy.

Frequency estimation of multiple sinusoidals is fundamental in statistical signal processing. In this article, we focus on 1-D complex signals and propose a complex-valued network for frequency estimation, referred to as cResFreq, which overcomes the drawbacks of DeepFreq and 2-D ResFreq, that is, the performance loss associated with processing complex-valued signals by a real-valued network. First, weights of a hidden layer are optimized to approximate varieties of complex-valued complete basis vectors, and the locally uncorrelated noise suppression is realized by convolutional kernels. The feature maps/coarse frequency representations after a modulus operation are subsequently processed by real-valued residual blocks for obtaining a high-resolution frequency representation. Numerical experiments exhibit the superior performance of the proposed method in terms of resolution, estimation accuracy, and detection capability for weak components. Finally, the cResFreq is applied to realize the superresolution of range profiles in radar systems. The results based on the synthetic and real signals demonstrate that the HRRPs obtained by the cResFreq provide more target details, which shows promise in automatic target recognition (ATR). The codes can be found in https://github.com/panpp-git/cResFreq .

The potential of microwave Doppler radar in non-contact vital sign detection is significant; however, prevailing radar-based heart rate (HR) and heart rate variability (HRV) monitoring technologies often necessitate data lengths surpassing 10 s, leading to increased detection latency and inaccurate HRV estimates. To address this problem, this paper introduces a novel network integrating a frequency representation module and a residual in residual module for the precise estimation and tracking of HR from concise time series, followed by HRV monitoring. The network adeptly transforms radar signals from the time domain to the frequency domain, yielding high-resolution spectrum representation within specified frequency intervals. This significantly reduces latency and improves HRV estimation accuracy by using data that are only 4 s in length. This study uses simulation data, Frequency-Modulated Continuous-Wave radar-measured data, and Continuous-Wave radar data to validate the model. Experimental results show that despite the shortened data length, the average heart rate measurement accuracy of the algorithm remains above 95% with no loss of estimation accuracy. This study contributes an efficient heart rate variability estimation algorithm to the domain of non-contact vital sign detection, offering significant practical application value.

The accuracy of on-grid frequency estimation methods suffers from the quantization error of discrete grids. In this article, a deep unfolded network for off-grid frequency estimation is proposed, dubbed OGFreq. In the OGFreq, there exist two kinds of variables. One is the batch-oriented dictionary for frequency-domain transform, and the other one is the instance-specific on-grid frequency and off-grid bias. As the dictionary is required to be universally applicable among all observed signals, network layers are designed and network weights are updated to approximate the transform bases in a data-driven way. Besides, instance-specific on-grid frequencies and off-grid biases are solved by unfolding the iterative soft-threshold algorithm (ISTA). In addition, the instance-specific hyperparameters for sparsity in ISTA are obtained by an encoder–decoder soft-threshold (EDS) module with the attention mechanism. In this way, the dictionary, on-grid frequency, and off-grid bias are learned in a unified data-driven framework. Numerical experiments show that the OGFreq obtains 4% lower false negative rate (FNR) when the SNR is 20 dB. Moreover, the computational complexity is one order of magnitude lower than the iteration-based off-grid frequency estimation methods. Finally, the robustness of the OGFreq is discussed when extended to the impulse noise and damped signals.

To overcome the limitations of LiDAR and camera systems in cost and weather-resilient performance, millimeter-wave radar has emerged as a complementary solution for object identification and surveillance. Previous studies have indicated promising prospects for Frequency-Modulated Continuous Wave (FMCW) radar in action recognition tasks, primarily through classifying micro-Doppler features in the radar's slow-time dimension. However, these features are highly sensitive to the direction of target motion, causing significant variations when observed from different angles. To address these challenges while enhancing cost-efficiency and environmental robustness, we introduce a Stacked Dual-Path Feature Fusion Network (SDP-Net). The design of the model is validated using an unsupervised image clustering algorithm. We also present lightweight variants of SDP-Net to ensure broad hardware compatibility and demonstrate robust omnidirectional motion recognition using monostatic radar. Comparative evaluation on both simulated and measured data sets confirms that our approach outperforms existing recognition methods.