Low Signal-to-noise Ratio Conditions Research Articles

A covariance matrix-based spectrum sensing technology exploiting stochastic resonance and filters

Cognitive radio (CR) is designed to implement dynamical spectrum sharing and reduce the negative effect of spectrum scarcity caused by the exponential increase in the number of wireless devices. CR requires that spectrum sensing should detect licenced signals quickly and accurately and enable coexistence between primary and secondary users without interference. However, spectrum sensing with a low signal-to-noise ratio (SNR) is still a challenge in CR systems. This paper proposes a novel covariance matrix-based spectrum sensing method by using stochastic resonance (SR) and filters. SR is implemented to enforce the detection signal of multiple antennas in low SNR conditions. The filters are equipped in the receiver to reduce the interference segment of noise frequency. Then, two test statistics computed by the likelihood ratio test (LRT) or the maximum eigenvalues detector (MED) are constructed by the sample covariance matrix of the processed signals. The simulation results exhibit the spectrum sensing performance of the proposed algorithms under various channel conditions, namely, additive white Gaussian noise (AWGN) and Rayleigh fading channels. The energy detector (ED) is also compared with LRT and MED. The simulation results demonstrate that SR and filter implementation can achieve a considerable improvement in spectrum sensing performance under a strong noise background.

FFBV Algorithm Design for Soft Synchronization FMCW Radar

Whether in military or civilian use, frequency-modulated continuous-wave (FMCW) radars play a very important role, but common FMCW radars need to collect both radar echo signals and hardware synchronization signals during echo signal processing. Therefore, this article proposes a new synchronization algorithm, i.e., the four-threshold frequency band variance (FFBV) synchronization algorithm. Then, we combine theoretical derivation and experimental verification to analyze the performance of the FFBV synchronization algorithm. With assistance of the FFBV synchronization algorithm, the soft synchronization FMCW radar can achieve the same functions without hardware synchronization signals. First, we analyze the principle behind the FMCW radar based on intermittent ramp signals. Second, we analyze the design of the FFBV synchronization algorithm. In addition, we verify the performance of the algorithm when the received signal is corrupted by the additive white Gaussian noise (AWGN). Then, we analyze the performance from two aspects, including the performance of the algorithm under different signal-to-noise ratio (SNR) conditions, as well as the performance comparison with other common synchronization algorithms. Finally, experimental results show that the FFBV synchronization algorithm has achieved good performance in solving the signal synchronization issue of the FMCW radar under the condition of low SNR. Especially, the SNR required by the FFBV synchronization algorithm is 2 and 6.5 dB lower than that required by the three-threshold synchronization algorithm and variance synchronization algorithm, respectively, under the same condition that the accuracy is 90%.

Gerschgorin disk estimator method for source number estimation based on peak-to-average power ratio

Gerschgorin disk estimator (GDE) method is difficult to detect the number of signal sources effectively under low signal-to-noise ratio (SNR). In view of this situation, we propose GDE method based on peak-to-average power ratio (GDE-PAR) by combining the peak-to-average power ratio (PAR) with the Gerschgorin disk radius. We extract the eigenvectors from the received data and use them as the weights of the data. The PAR is used to modify the corresponding Gerschgorin disk radius, and the number of signal sources is determined by GDE method. This paper adopts Matlab simulation on the Gerschgorin disk radius before and after correction under different SNR conditions. In the case of double target of equal intensity and double target of unequal intensity, three target of equal intensity and three target unequal intensity using Monte Carlo method, we use Akaike information theory criterion (AIC), minimum description length (MDL) criterion, PAR method and GDE-PAR method to estimate the number of signal sources respectively. The results show that under the conditions of low SNR and multi-target of unequal intensity, the probability of successful detection of source by GDE-PAR method is higher than that of AIC, MDL criterion and PAR method.

Adaptive Multi-Trace Carving for Robust Frequency Tracking in Forensic Applications

In the field of information forensics, many emerging problems involve a critical step that estimates and tracks weak frequency components in noisy signals. It is often challenging for the prior art of frequency tracking to i)achieve a high accuracy under noisy conditions, ii)detect and track multiple frequency components efficiently, or iii)strike a good trade-off of the processing delay versus the resilience and the accuracy of tracking. To address these issues, we propose Adaptive Multi-Trace Carving (AMTC), a unified approach for detecting and tracking one or more subtle frequency components under very low signal-to-noise ratio (SNR) conditions and in near real time. AMTC takes as input a time-frequency representation of the system's preprocessing results (such as the spectrogram), and identifies frequency components through iterative dynamic programming and adaptive trace compensation. The proposed algorithm considers relatively high energy traces sustaining over a certain duration as an indicator of the presence of frequency/oscillation components of interest and track their time-varying trend. Extensive experiments using both synthetic data and real-world forensic data of power signatures and physiological monitoring reveal that the proposed method outperforms representative prior art under low SNR conditions, and can be implemented in near real-time settings. The proposed AMTC algorithm can empower the development of new information forensic technologies that harness very small signals.

Fast Sparse-TSVD Super-Resolution Method of Real Aperture Radar Forward-Looking Imaging

Most existing super-resolution imaging methods fail to work in low signal-to-noise ratio (SNR) condition due to the ill-posed antenna measurement matrix, but the sparse-truncated singular value decomposition (TSVD) method can effectively suppress noise and improve azimuth resolution in low SNR condition. However, the current sparse-TSVD method encounters large computation cost, resulting in a slow algorithm speed. In this work, a fast sparse-TSVD super-resolution imaging method of real aperture radar is proposed. First, the proposed method is based on the results of TSVD, using the truncated unitary matrix and diagonal matrix to reconstruct the signal convolution model. The dimension of the reconstructed antenna measurement matrix reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times N$ </tex-math></inline-formula> , and the dimension of the reconstructed echo matrix reduces from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times 1$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times 1$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is azimuth sampling points and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is truncation parameter, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \gg k$ </tex-math></inline-formula> . Much of the expensive matrix– multiplication computation can then be performed on the smaller matrices, thereby accelerating the algorithm. Second, an objective function is established as the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l_{1}}$ </tex-math></inline-formula> constraint based on the regularization strategy. Lastly, this article employs iterative reweighted least square (IRLS) method to solve the objective function, and the dimension of the reversed matrix is lessened from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N \times N$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \times k$ </tex-math></inline-formula> , speeding up the algorithm further. The simulation and real data verify that the proposed algorithm not only improves the azimuth resolution in low SNR condition but also increases computational efficiency compared with the sparse-TSVD method.

Passive Extraction of Signal Feature Using a Rectifier with a Mechanically Switched Inductor for Low Power Acoustic Event Detection.

Analog hardware used for signal envelope extraction in low-power interfaces for acoustic event detection, owing to its low complexity and power consumption, suffers from low sensitivity and performs poorly under low signal to noise ratios (SNR) found in undersea environments. To overcome those problems, in this paper, we propose a novel passive electromechanical solution for the signal feature extraction in low frequency acoustic range (200–1000 Hz), in the form of a piezoelectric vibration transducer, and a rectifier with a mechanically switched inductor. A simulation study of the novel solution is presented, and a proof-of-concept device is developed and experimentally characterized. We demonstrate its applicability and show the advantages of the passive electromechanical device in comparison to the active electrical solution in terms of operation with lower input signals (<20 mV compared to 40 mV), and higher robustness in low SNR conditions (output voltage loss for −10 dB ≤ SNR < 40 dB of 1 mV, compared to 10 mV). In addition to the signal processing performance improvements, compared to our previous work, the utilization of the presented novel passive feature extractor would also decrease power consumption of a detector’s channel by over 76%, enabling life-time extension and/or increased quality of detection with larger number of channels. To the best of our knowledge, this is the first solution presented in the literature that demonstrates the possibility of using a passive electromechanical feature extractor in a low-power analog wake-up event detector interface.

Development of ZJU High-Spectral-Resolution Lidar for Aerosol and Cloud: Extinction Retrieval

The retrieval of the extinction coefficients of aerosols and clouds without assumptions is the most important advantage of the high-spectral-resolution lidar (HSRL). The standard method to retrieve the extinction coefficient from HSRL signals depends heavily on the signal-to-noise ratio (SNR). In this work, an iterative image reconstruction (IIR) method is proposed for the retrieval of the aerosol extinction coefficient based on HSRL data, this proposed method manages to minimize the difference between the reconstructed and raw signals based on reasonable estimates of the lidar ratio. To avoid the ill-posed solution, a regularization method is adopted to reconstruct the lidar signals in the IIR method. The results from Monte-Carlo (MC) simulations applying both standard and IIR methods are compared and these comparisons demonstrate that the extinction coefficient and the lidar ratio retrieved by the IIR method have smaller root mean square error (RMSE) and relative bias values than the standard method. A case study of measurements made by Zhejiang University (ZJU) HSRL is presented, and their results show that the IIR method not only obtains a finer structure of the aerosol layer under the condition of low SNR, but it is also able to retrieve more reasonable values of the lidar ratio.

Binary Time-Frequency Mask for Improved Malay Speech Intelligibility at Low SNR Condition

A binary masking is often seen as a medium to enhance speech signal especially in hearing aid and speech recognition applications due to its simplicity and efficient approach for supervised source separation. High intelligibility could be obtained by applying the binary time-frequency masking to noisy speech signal. Since the issue of linear filtering algorithms might affect the intelligibility of noisy speech signal, so, this paper presents the binary time-frequency mask for improved Malay speech intelligibility at low SNR condition. The clean Malay speech signals that were contaminated by car and train noise with different signal to noise ratio (SNR) and local criterion (LC) level in forming the binary mask are analysed. The performance of intelligibility improvement was evaluated using a normalized sub band enveloped correlation (nSec). Overall results showed that the proposed approach produces slightly improved speech intelligibility at low SNR value.

Fractional Fourier transform based underwater multi-targets direction-of-arrival estimation using wideband linear chirps

In underwater applications, linear chirp signal with linearly instantaneous frequency over the signal bandwidth also known as a linear frequency modulated (LFM) signal is often used in active sonar to realize direction of arrival (DOA) estimation of targets. For this kind of wideband signal, traditional array signal processing method firstly transforms the time domain signal into frequency domain using fast Fourier transform (FFT) and then does beamforming for each sub-band. Different from FFT based signal processing method, this paper uses fractional Fourier transform (FRFT) for preprocessing of wideband LFM signals. By FRFT preprocessing, the wideband LFM signals are transformed into narrowband signals in the fractional Fourier domain, avoiding the influence of cross-interference terms. This paper compares the performance of FRFT based DOA estimation using conventional beamforming (CBF), minimum variance distortionless response (MVDR) and robust Capon beamforming (RCB) respectively. Then the revised RCB (RRCB) algorithm is proposed to solve the DOA estimation problem with a small number of snapshots. Simulations are carried out for single target and multi-targets DOA estimation using FFT based and FRFT based array signal processing method respectively. Simulation results show that FRFT based array signal processing method can achieve much narrower main lobe and higher main-to-side lobe ratio in low signal-to–noise ratio conditions. Besides, it can realize accurate DOA estimation of two adjacent targets while FFT based array signal processing method fails.

A Novel 2-D Geometry Reconstruction Approach for Space Debris via Interpolation-Free Operation under Low SNR Conditions

Two unsolved key issues in inverse synthetic aperture radar (ISAR) imaging for non-cooperative rapidly spinning targets including high computational complexity and poor imaging performance in the case of low signal-to-noise ratio (SNR) are addressed in this work. In the strip-map imaging mode of SAR, it is well known that azimuth spatial invariant characteristics exist, and inspired by this, we propose a fast ISAR imaging approach for spinning targets. Our approach involves two steps. First, a precise analytic expression in the range-Doppler (RD) domain is produced using the principle of stationary phase (POSP). Second, a novel interpolation kernel function is designed to remove two-dimensional (2-D) spatial-variant phase errors, and the corresponding fast implementation steps that only require Fourier transform and multiplications are also presented. Finally, a well-focused ISAR image is obtained by compensating the azimuth high-order terms. Compared with current imaging methods, our approach avoids multi-dimensional search and interpolation operations and exploits the 2-D coherent integrated gain; the proposed method is of low computational cost and robustness in the low SNR condition. The effectiveness of the proposed approach is confirmed by numerically simulated experiments.

Beamforming technique based on adaptive diagonal loading in wireless access networks

The technique of beamforming which determines the directionality of array sensors plays an important part in wireless access networks, due to small snapshots and variational signal-to-noise ratio(SNR) in practical applications, the performance of traditional sampling matrix inversion(SMI) beamforming algorithm often degrades drastically. Therefore, an adaptive diagonal loading sampling matrix inversion(ADL-SMI) algorithm is proposed, it calculates the loading value according to the characteristic structure of the covariance matrix. Simulative results show that beam formed by the proposed algorithm has a high quality under the conditions of high or low SNR, and still performs well under the case of small snapshots. Comparing with SMI and the traditional diagonal loading algorithm, the ADL-SMI is robuster and easier to be realized.

Wirtinger gradient descent optimization for reducing Gaussian noise in lensless microscopy

Lensless microscopy is an imaging technique that records diffraction measurements without using any lens and recovers the complex object profile via phase retrieval. The successful reconstruction of lensless imaging experiments often requires the captured images to have a high signal-to-noise ratio (SNR), but high SNR is hard to guarantee in practice. Here we report a novel iterative algorithm for reducing Gaussian noise in lensless microscopy. Our method incorporates the Gaussian noise model in the Wirtinger gradient descent optimization process to perform phase retrieval. The reported algorithm is tested on both the multi-angle illumination and multi-height detection schemes of lensless microscopy for diversity measurements. As demonstrated by simulations and experiments, the method is able to obtain better reconstructions under low SNR conditions, in comparison with the traditional Gerchberg Saxton method. We have provided open-source implementation code for non-commercial use.

Waveform centroid discrimination of pulsed Lidar by combining EMD and intensity weighted method under low SNR conditions

In this study, we report on a self-adaptive waveform centroid algorithm combing EMD and intensity-weighted (IW) method for the accurate Lidar ranging under low signal-to-noise ratio (SNR) conditions. Empirical mode decomposition (EMD), discrete cosine transformation (DCT) and inverse discrete cosine transformation (IDCT) are utilized to filter out the high-frequency interference in Lidar pulse signal. A time window is set to adaptive select the effective data. The centroid points are calculated by the intensity-weighted (IW) waveform centroid algorithm with the selected data. The proposed algorithm is experimentally tested, achieving an average error of about 153 ps, 209 ps and 232 ps under the SNR of 5.1 dB, 2.7 dB and 1.8 dB, respectively, which exerts better precision compared to the wavelet soft thresholding with intensity-weighted (WL-IW) algorithm and EMD with peak selection (EMD-PK) algorithm. Furthermore, the proposed algorithm is fairly robust with remarkable detection success rates of above 96% under low SNR conditions. The proposed waveform centroid algorithm has the potential for pulsed Lidar’s ranging tasks in harsh environment.

Intra‐pulse modulation radar signal recognition based on CLDN network

Automatic modulation classification of radar signals, which plays a significant role in both civilian and military applications, is researched in this study through a deep learning network. In this study, a novel network combined a shallow convolution neural network (CNN), long short-term memory (LSTM) network and deep neural network (DNN) is proposed to recognise six types of radar signals with different signal-to-noise ratio (SNR) levels from -14 to 20 dB. First, raw signal sequences in the time domain, frequency domain and autocorrelation domain are as input for a shallow CNN. Then the features extracted by CNN will be the input of LSTM network. Finally, DNNs will output the signal modulation types directly. The simulation results demonstrate that the accuracies in autocorrelation domain are all more than 90% at -6 dB and close to 100% when SNR > -2 dB. The recognition performances of the three domains are compared. Compared with other recognition methods, the proposed method has higher average accuracy and better performance under low SNR condition. The measured results show that the proposed method has achieved high accuracies of common four kinds of measured radar signals.

Robust calibration method for distributed ISAR time‐varying frequency errors based on the contrast maximisation principle

The linear time-varying frequency errors (LTFE) caused by the mismatch of transmitter and receiver oscillators can defocus the imaging result of distributed inverse synthetic aperture radar (ISAR) seriously. The LTFE calibration method based on the entropy minimization principle is sensitive to signal-to-noise ratio (SNR), and its performance is degraded significantly under low SNR conditions. In addition, this method uses enumeration algorithm to solve the optimization problem, which has a heavy computation burden. Therefore, a robust calibration method based on the contrast maximization principle is proposed. Compared with image entropy, image contrast has better anti-noise ability because it has better sensitivity property, namely, the change of image contrast is sharper than the change of image entropy. In the proposed method, the estimation of frequency error coefficient is modelled as an unconstrained optimization problem with image contrast as cost function, and the particle swarm optimization (PSO) algorithm is used to search the global optimal solution. Then, the LTFE can be calibrated by the estimated frequency error coefficient. The proposed method has better robustness, which can work well under low SNR conditions. Besides, it has higher computational efficiency. Simulations are carried out to verify the effectiveness and robustness of the proposed method.

Source number estimation based on a novel multi-view meta-hierarchical classification framework

Accurately measuring the direction of arrival (DOA) is one of the most important issues in multiple sensor/antenna array monitoring scenarios. However, as a necessary parameter of almost all state-of-the-art DOA estimation methods, the source number is normally hard to determine using the traditional Akaike information criterion or minimum description length methods, especially in low or very low signal-to-noise ratio (SNR) conditions. In this paper, we propose to estimate the source number in a data-driven manner by employing a novel multi-view meta-hierarchical classification framework. Specifically, there are two collaborative views and two hierarchical classification layers employed for generating meta-features. Then, the obtained meta-features are re-learned by the final meta-classification layer to estimate the final prediction of the source number. Experimental results illustrated that the proposed method can estimate the source number accurately and reliably even in low SNR conditions.

A TV Forward-Looking Super-Resolution Imaging Method Based on TSVD Strategy for Scanning Radar

Because of the poor performance of the conventional total variation (TV) super-resolution imaging method in low signal-to-noise ratio (SNR) condition, a TV super-resolution imaging method based on the truncated singular value decomposition (TSVD) strategy is proposed. First, based on the regularization theory, the TV function is selected as the constraint term to construct objective function. Second, to solve the problem of noise amplification faced by the conventional TV method, this article reconstructs the objective function based on the TSVD strategy, which improves the antinoise performance by discarding small singular values of antenna convolution matrix. Finally, due to the nondifferentiable property of reconstructed objective function, this article utilizes the iterative reweighted norm (IRN) method. Since the influence of the noise is weakened by the TSVD strategy, the proposed method can achieve super-resolution imaging and contour preservation in low SNR condition. The simulation and experimental results demonstrate the effectiveness of the proposed method.

Enhanced Loran skywave delay estimation based on artificial neural network in low SNR environment

This study proposes a high precision algorithm to estimate the Enhanced Loran skywave delay. It is based on the artificial neural network. The algorithm establishes a neural network model between the receiving Enhanced Loran signal and the skywave propagation delay. By training a large number of data, the neural network model can more accurately reflect the relationship between the receiving signal and the skywave delay. This is an innovative application of the skywave delay estimation algorithm in the Enhanced Loran receiving system, especially in low signal-to-noise ratio (SNR) environments. The experimental results show that the accuracy of this algorithm is about hundreds of nanoseconds in the condition of normal receiving SNR. The accuracy of the algorithm is about us in the condition of low SNR, while the previous algorithm cannot be used in this case. It has also been proved by the off-air data.

Accurate DOA Estimation With Adjacent Angle Power Difference for Indoor Localization

Indoor localization with high accuracy plays a key role in the field of Internet of Things in 5th-Generation (5G) era. With the introduction of Multiple Input Multiple Output (MIMO) technology in 5G, the direction-of-arrival (DOA) method is highly feasible in indoor localization. However, the direction of arrival is susceptible to complex indoor environment. To improve the accuracy and stability of DOA estimation, an adjacent angle power difference (AAPD) method is proposed based on Orthogonal Matching Pursuit (OMP). This method uses OMP to obtain an initial estimate of the direction, and then, adjusts the estimation by calculating the difference power of adjacent points at initial value point to get the fractional DOA. In the scenario of continuous movement, beamforming is further applied, which reduces the amount of calculation. Both simulation and experimental results show that the proposed method can achieve high accuracy and eliminate the error jitter. Compared with the classical Multiple Signal Classification (MUSIC) method for DOA estimation, the proposed method can increase accuracy by 46% under the condition of low SNR (Signal-to-Noise Ratio). The probability that the measurement error does not exceed 5° in the actual movement tests is 97.5%.

Automatic Modulation Recognition for Radar Signals via Multi-Branch ACSE Networks

Automatic modulation recognition (AMR) for radar signals plays a significant role in electronic warfare. Conventional recognition methods may suffer from the recognition accuracy and the computation complexity under low signal-to-noise ratio (SNR) conditions. In this paper, a novel multi-branch Asymmetric Convolution Squeeze-and-Excitation (ACSE) networks using multi-domain features and fusion strategy based on a support vector machine is proposed to recognize eight kinds of radar signals. First, features of radar signals in the frequency domain, the autocorrelation domain, and the time-frequency domain are extracted. Then the obtained multi-domain features are converted as the input of the proposed networks which owns the representational power and learning ability. Finally, the outputs of multi-branch ACSE networks are fused via the fusion strategy to obtain the final results. Via simulations, the robustness and effectiveness of the fusion strategy are verified. The results on the simulation dataset prove that the proposed method can achieve more than 93% accuracy at -10dB for all modulations. Compared with four newly proposed networks, the multi-branch ACSE networks achieves better performance under low SNR conditions. And the results on measured signals show that the proposed method outperforms other comparison methods, especially for binary frequency-shift keying (BFSK) signals.