Robustness of null broadening against source motion

Adaptive and Robust Beamforming

At present, commonly used methods of weak signal detection such as the wavelet threshold denoising method, digital filtering method, the Fourier frequency domain transformation etc. can achieve the lowest detection of signal-to-noise ratio (SNR) of -10 dB, and the bidirectional ring coupled Duffing oscillator can reach the lowest detected SNR of -20 dB. But the discharge pulse signal with a lower SNR often appears in on-site testing, so the existing detection methods are difficult to meet the practical requirements of weak signal detection. In order to effectively solve the problem, a new method for weak pulse signal detection is proposed based on an extended-Duffing oscillator. The main idea of this method is to make the Duffing oscillator model transform to an extended-Duffing oscillator model by using the general time scale transformation. This approach can effectively expand the frequency detection range for weak signal detection. In addition, because the critical amplitude of the Duffing system depends on various parameters, such as system parameters, initial values, driving signal frequency, and calculation step of Runge - Kutta method etc.. However, the Melnikov method is an approximate analytical method, which does not take into account the factors such as initial values and calculation step, therefore, the Melnikov method is not suitable for numerical simulations, and lack of practicality. For this, the critical amplitude of chaos with high accuracy is determined only through the simulation experiment. Experimental results show that the critical amplitude is equal to 0.825010 when the incentive angular frequency of the extended-Duffing oscillator equals 10000 rad/s, and the extended-Duffing oscillator changes from the critical chaotic state to the large scale cycle state for small changes (10-6) of the driving amplitude. The simulation results show that the extended-Duffing oscillator not only has a good noise immunity performance, but also can effectively detect weak partial discharge pulse signal so that the signal-to-noise ratio can be lower than -40 dB. This method further expands the detection range and application fields of weak signals.

Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron

Weak signal detection is a significant problem in modern detection such as mechanical fault diagnosis. The uniqueness of chaos and good learning ability of neural networks provide new ideas and framework for weak signal detection field. In this paper, Elman neural network is applied to detect and recover weak pulse signal in chaotic noise. For detection problem of weak pulse signal under chaotic noise, based on short-term predictability of chaotic observations, phase space reconstruction for observed signals is carried out. And Elman deep learning adaptive detection model (EDAD model) is established for weak pulse signal detection, and a hypothesis test is used to detect weak pulse signal from the prediction error. For the recovery of weak pulse signal under chaotic noise, a double-layer Elman deep neural network recovery model (DEDR model) is proposed, which is based on the Elman deep learning network model and single-point jump model for weak pulse signal, and it is optimized with goal of minimizing mean square prediction error of the Elman model. The profile least squares method is applied to estimate parameters of the DEDR model for difficult recovery of weak pulse signal because the DEDR model is essentially a semiparametric model with parametric and nonparametric parts. In the end, simulation experiments show that the model built in this paper can effectively detect and recover weak pulse signal in the background of chaotic noise.

This research work concentrates on developing new methodologies for weak signal detection, which are further used in the watermark detection application. The proposed detectors perform comparable to or better than most of the state-of-the-art techniques. Stochastic resonance plays a significant role in weak signal detection. Injection of precalculated noise is a big concern for us. Noises i.e., symmetric and asymmetric have been utilized for getting an improved version of the weak signal detector. With equality and non-equality constraints, we use the particle swarm optimization method to optimize the objective function. After that, we investigate a new detector based on the fractional operator. The noisy signal is convolved with the coefficients of fractional order filter. The proposed method has been tested with different standard performance parameters. The results of the proposed detector have been compared with state-of-the-art detectors such as a threshold detector (TD), neural network-based detector etc. The robustness of the proposed detector with respect to the parameters of signal and noise has also been explored. The problem of weak DC signal detection present in non-Gaussian noise is always a troublesome because of the non-linearity of the test statistic. We have used the concept of stochastic resonance in a conventional neural network-based detector. A predefined noise is injected during the back-propagation algorithm in order to minimize the error. The reduction in errors (in terms of enhancement in the probability of detection, $$P_D$$ at a constant value of the probability of false alarm, $$P_{FA}$$ ) and faster convergence give a right justification to use the concept of stochastic resonance in the neural network-based detector.

Constructive Role of Internal Noise for the Detection of Weak Signal in Cell System

Weak signal detection is a basic and important problem in radar systems. The detectable range of a radar is determined by the radar equation. This equation shows that the performance of a radar is improved by increasing the receiver output SNR. For the purpose of improving the SNR, the process called integration of pulses has been used. We propose new methods based on the wavelet transform for the improvement of the SNR. The wavelet transform is a tool for time-frequency domain signal analysis and is sensitive to the transient signals. By computer simulations, we show that the receiver output SNR after the wavelet transform is applied becomes about 8 dB greater than that of the original signals. This value corresponds to a 60 percent improvement of the radar detectable range. >

The adaptive beamforming is one of the key techniques for array signal processing. However, the matrix inversion operation in the existing methods will cost a large amount of computational complexity, which results in poor real-time processing ability. In order to reduce the amount of computational cost, a fast and robust adaptive beamforming method based on complex-valued radial basis function (CRBF) neural network is proposed. In the proposed method, the CRBF neural network is established, thus the direct matrix inversion is avoided by the nonlinear mapping processing from the array covariance matrix to the adaptive weight vector, and therefore the calculation speed of adaptive weight vectors is increased. Based on the simulation results, the proposed method is verified that the speed of adaptive beamforming is increased compared with sample matrix inversion (SMI) algorithm method and an improved performance is achieved compared with that of conventional real-valued RBF neural network beamformer.

There are numerous studies showing that there is a constant increase in the ocean ambient noise level and the ever-growing demand for developing algorithms for detecting weak signals in ambient noise. In this study, we utilize dynamical and statistical complexity to detect the presence of weak ship noise embedded in ambient noise. The ambient noise and ship noise were recorded in the South China Sea. The multiscale entropy (MSE) method and the complexity-entropy causality plane (C-H plane) were used to quantify the dynamical and statistical complexity of the measured time series, respectively. We generated signals with varying signal-to-noise ratio (SNR) by varying the amplification of a ship signal. The simulation results indicate that the complexity is sensitive to change in the information in the ambient noise and the change in SNR, a finding that enables the detection of weak ship signals in strong background ambient noise. The simulation results also illustrate that complexity is better than the traditional spectrogram method, particularly effective for detecting low SNR signals in ambient noise. In addition, complexity-based MSE and C-H plane methods are simple, robust and do not assume any underlying dynamics in time series. Hence, complexity should be used in practical situations.

A new signal detection and estimation method based on the intermittency transition between order and chaos is developed. The corresponding bifurcation process for the Duffing oscillator is discussed in detail, and the length of the laminar phase of the bifurcation is exploited to describe quantitatively the property of sensitivity dependence on the initial condition of the chaotic Duffing system. Estimation and detection of weak signals are carried out through obtaining the value and the probability distribution of the laminar length.

Detecting and processing Global Navigation Satellite System (GNSS) signals indoors and in urban canyons, have gained a great deal of attention due to the problems of very weak signals and hostile environments. The detection of GNSS signals is generally based on the application of a statistical test, derived from the maximum likelihood theory. The work presented here considers a new approach to the detection of weak GNSS signals using a Bayesian technique within a scenario where the search space size is already reduced to a few tens of cells using some kind of assisted information. The search space cells are considered as candidate cells, where each candidate cell is associated with a code delay and a Doppler frequency. For each candidate cell, a posteriori probability is propagated for a fixed number of operation cycles. At the end of the process, the maximum a posterior (MAP) criterion is used to select the correct cell. Simulation results are presented indicating that the proposed method provides a significant performance advantage over other reference schemes. They include a noncoherent integration scheme and another scheme which also utilizes the posterior probabilities as decision statistics but differs in the mechanism of probability propagation.

Stochastic resonance (SR), with its unique noise utilization mechanism, has demonstrated remarkable advantages in the field of mechanical fault diagnosis. However, the performance of SR is highly dependent on the precise matching of noise intensity and system parameters. In practical engineering applications, noise is often uncontrollable and dynamically changing, which limits its applicability. By contrast, vibration resonance (VR) enhances weak signal detection by introducing a controllable external high-frequency excitation. The stiffness-softening effect induced by this excitation can modulate the potential-well characteristics, alter the system’s equilibrium states, and induce bifurcation, thereby effectively amplifying weak fault signals. Based on this, this paper proposes a potential-well parameter decoupled mechanical fault detection method based on time-delay feedback fractional VR (TDF-FVR). By independently adjusting the width and depth of the potential well, the method effectively optimizes the resonance effect to amplify weak fault signals. To achieve this, TDF-FVR system with tunable parameters is constructed, and a quantum genetic algorithm (QGA) is employed to adaptively optimize the system parameters, using the system’s response amplitude gain Q as the objective function to achieve optimal resonance and improve weak fault signal detection performance. Finally, bearing fault experiments verify the effectiveness of the proposed method, which shows excellent performance in weak fault signal detection. Furthermore, comparative results with the optimized wavelet packet transform, fast kurtogram, and feature modal decomposition methods further demonstrate the superiority of the proposed method.

The gain of the output signal-to-noise ratio (SNR) is insufficient in traditional stochastic resonance (SR) method to detect weak signals. In order to obtaining a higher SNR gain, a kind of signal detection method of adaptive stochastic resonance that use cascade system is proposed. To achieve the optimal output, stochastic resonance parameters adjustment is transformed into the multi-parameter optimization of particle swarm optimization. The optimal result in weak signal detection can be reached by adjusting the parameters of two layers subsystem. The weak signal submerged in strong noise background can be extracted through this simple method that has a fast convergence speed. The threshold of the weak signal detection is lowered by this method, and the applicable scope of stochastic resonance can be enlarged.

A 77GHz microstrip antenna array with a small surface providing high side and grating lobe suppression is presented. This may serve as a starting point for 77GHz automotive radar applications. Multiple Wilkinson dividers guarantee both impedance matching at the input port (TX) as well as low return loss for the incoming (RX) signal. Phase shifting is done by adjusting the level of the Wilkinson dividers or by meandered sections of transmission line. The in∞uence of the radiation caused by the feeding network is analyzed and the absolute degradation in side lobe suppression is derived in this paper.

Detection of weak and extremely weak light signals amplified by linear and four-wave mixing laser amplifiers is analyzed. Photoelectron distributions are found for different input photon statistics over a wide range of gain. Signal-to-noise ratios are calculated and analyzed for preamplification schemes using linear and four-wave mixing amplifiers. Calculations show that the high signal-to-noise ratio (much higher than unity), ensuring reliable detection of weak input signals, can be attained only with a four-wave mixing preamplification scheme. Qualitative dependence of the signal-to-noise ratio on the quantum statistical properties of both signal and idler waves is demonstrated.