Noise Power Estimation Research Articles

An Efficient Sparse Recovery STAP Algorithm for Airborne Bistatic Radars Based on Atomic Selection under the Bayesian Framework

The traditional sparse recovery (SR) space-time adaptive processing (STAP) algorithms are greatly affected by grid mismatch, leading to poor performance in airborne bistatic radar clutter suppression. In order to address this issue, this paper proposes an SR STAP algorithm for airborne bistatic radars based on atomic selection under the Bayesian framework. This method adopts the idea of atomic selection for the process of Bayesian inference, continuously evaluating the contribution of atoms to the likelihood function to add or remove atoms, and then using the selected atoms to estimate the clutter support subspace and perform sparse recovery in the clutter support subspace. Due to the inherent sparsity of clutter signals, performing sparse recovery in the clutter support subspace avoids using a massive number of atoms from an overcomplete space-time dictionary, thereby greatly improving computational efficiency. In airborne bistatic radar scenarios where significant grid mismatch exists, this method can mitigate the performance degradation caused by grid mismatch by encrypting grid points. Since the sparse recovery is performed in the clutter support subspace, encrypting grid points does not lead to excessive computational burden. Additionally, this method integrates out the noise term under a new hierarchical Bayesian model, preventing the adverse effects caused by inaccurate noise power estimation during iterations in the traditional SR STAP algorithms, further enhancing its performance. Our simulation results demonstrate the high efficiency and superior clutter suppression performance and target detection performance of this method.

An asymptotically exact estimate of the median noise eigenvalue of sample covariance matrices

The Dominant Mode Rejection beamformer [Abraham & Owsley (1990)] averages the noise subspace eigenvalues of the sample covariance matrix (SCM) to estimate the background noise power. This noise power estimate from snapshot deficient SCMs can be unreliable for large arrays in time-varying environments with limited snapshots. Median filtering offers robustness to outliers and subspace mismatch for these challenging problems. Recent numerical experiments [Campos Anchieta & Buck (2022)] identified a simple regression relating the median sample eigenvalue to the true background power for snapshot deficient SCMs. However, the complicated expression of the Marchenko-Pastur (MP) distribution for the noise eigenvalues of the SCM thwarted prior attempts to find a closed form estimator for the MP distribution median. This talk exploits a coordinate transform to obtain a closed-form median of the MP distribution that is exact for the leading term in the power series expansion of the distribution. The new median estimator is more accurate than the previous numerical regression when the ratio of sensors to snapshots is 2 or more. Given the central role of SCM eigenvalues in principal component analysis and constant false alarm rate detectors, the new median expression should find application in other data science algorithms for underwater acoustics. [Work supported by ONR Code 321US.]

On the Radial-Based Estimation of Colored Noise Power in Weather Radars

On the Radial-Based Estimation of Colored Noise Power in Weather Radars

Expectation-maximization vector approximate message passing-based frequency-domain turbo equalization for underwater acoustic communications.

Channel equalization plays a crucial role in single-carrier underwater acoustic (UWA) communications. Recently, a frequency-domain turbo equalization (FDTE) scheme enabled by the vector approximate message passing (VAMP) algorithm, was proposed, and it outperformed classic linear minimum mean square error FDTE at acceptable complexity cost. The operation of the VAMP-FDTE requires knowledge of noise power, which is predetermined before the equalization starts. In practice, however, it is difficult to obtain prior knowledge of noise power due to factors of unknown channel estimation errors and dynamic underwater environments. Motivated by this fact, we propose an enhanced VAMP-FDTE scheme, which learns the noise power knowledge during the equalization process via the expectation-maximization (EM) algorithm. The EM-based noise power estimation makes use of intermediate results of the VAMP-FDTE and, thus, only incurs a small extra computational overhead. The improved VAMP-FDTE, named EM-VAMP-FDTE, was tested by experimental data collected in shallow-sea horizontal UWA communication trials with MIMO configuration. It showed better performance than the existing VAMP-FDTE scheme, attributed to the online noise power learning.

Virtual covariance matrix reconstruction-based adaptive beamforming for small aperture array.

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different conditions.

Robust noise-power estimation via primal–dual algorithms with measurements from a subset of network nodes

Noise power or signal variance is an important performance parameter or indicator used for many applications in signal processing and wireless communications. This paper investigates power estimation of random noises on sensor networks by using measurements taken over a subset of nodes. In many circumstances, the power values are typically smooth on the network, that is, the powers measured by neighboring nodes tend to have similar values. Using this smoothness, the power-estimation problem is formulated as a regularized optimization problem involving minimization of a sum of non-negative log-likelihood and the total variation. To find its optimal solution, a primal–dual hybrid gradient (PDHG) algorithm is developed, which uses primal–dual updates to achieve good estimation results. To further improve the estimation performance, two variants of the PDHG algorithm are also proposed: one has faster convergence by using a variable step-size searching strategy, and the other is robust to outliers and can identify abnormal nodes by using an outlier-rejection scheme. Several numerical experiments confirm the efficiency of our proposed algorithms.

Improved Ultrafast Power Doppler Imaging Using United Spatial-Angular Adaptive Scaling Wiener Postfilter.

Ultrafast power Doppler imaging (uPDI) using high-frame-rate plane-wave transmission is a new microvascular imaging modality that offers high Doppler sensitivity. However, due to the unfocused transmission of plane waves, the echo signal is subject to interference from noise and clutter, resulting in a low signal-to-noise ratio (SNR) and poor image quality. Adaptive beamforming techniques are effective in suppressing noise and clutter for improved image quality. In this study, an adaptive beamformer based on a united spatial-angular adaptive scaling Wiener (uSA-ASW) postfilter is proposed to improve the resolution and contrast of uPDI. In the proposed method, the signal power and noise power of the Wiener postfilter are estimated by uniting spatial and angular signals, and a united generalized coherence factor (uGCF) is introduced to dynamically adjust the noise power estimation and enhance the robustness of the method. Simulation and in vivo data were used to verify the effectiveness of the proposed method. The results show that the uSA-ASW can achieve higher resolution and significant improvements in image contrast and background noise suppression compared with conventional delay-and-sum (DAS), coherence factor (CF), spatial-angular CF (SACF), and adaptive scaling Wiener (ASW) postfilter methods. In the simulations, uSA-ASW improves contrast-to-noise ratio (CNR) by 34.7 dB (117.3%) compared with DAS, while reducing background noise power (BNP) by 52 dB (221.4%). The uSA-ASW method provides full-width at half-maximum (FWHM) reductions of [Formula: see text] (59.5%) and [Formula: see text] (56.9%), CNR improvements of 25.6 dB (199.9%) and 42 dB (253%), and BNP reductions of 46.1 dB (319.3%) and 12.9 dB (289.1%) over DAS in the experiments of contrast-free human neonatal brain and contrast-free human liver, respectively. In the contrast-free experiments, uSA-ASW effectively balances the performance of noise and clutter suppression and enhanced microvascular visualization. Overall, the proposed method has the potential to become a reliable microvascular imaging technique for aiding in more accurate diagnosis and detection of vascular-related diseases in clinical contexts.

Brillouin-Scattering Induced Noise in DAS: A Case Study

In the paper, the effect of spontaneous Brillouin scattering (SpBS) is analyzed as a noise source in distributed acoustic sensors (DAS). The intensity of the SpBS wave fluctuates over time, and these fluctuations increase the noise power in DAS. Based on experimental data, the probability density function (PDF) of the spectrally selected SpBS Stokes wave intensity is negative exponential, which corresponds to the known theoretical conception. Based on this statement, an estimation of the average noise power induced by the SpBS wave is given. This noise power equals the square of the average power of the SpBS Stokes wave, which in turn is approximately 18 dB lower than the Rayleigh backscattering power. The noise composition in DAS is determined for two configurations, the first for the initial backscattering spectrum and the second for the spectrum in which the SpBS Stokes and anti-Stokes waves are rejected. It is established that in the analyzed particular case, the SpBS noise power is dominant and exceeds the powers of the thermal, shot, and phase noises in DAS. Accordingly, by rejecting the SpBS waves at the photodetector input, it is possible to reduce the noise power in DAS. In our case, this rejection is carried out by an asymmetric Mach-Zehnder interferometer (MZI). The rejection of the SpBS wave is most relevant for broadband photodetectors, which are associated with the use of short probing pulses to achieve short gauge lengths in DAS.

Application of empirical mode decomposition for denoising and ground clutter removal on weather radar signals

Proper detection and estimation of signal and noise power measurements are important to generate the best quality of meteorological data products such as Reflectivity, Velocity and Spectrum width. In order to obtain the best quality radar products, it is desirable to compute meteorological parameters by estimating noise power and removal of ground clutter. This paper attempts to study the Empirical Mode Decomposition (EMD) denoising techniques on weather radar signals in the presence of noise and ground clutter. Different methods of EMD based denoising techniques have been considered and applied to the weather signals to check the best performance of the denoising and clutter removal technique. The limitations of these methods are brought out through simulation analysis. To overcome these limitations, this paper proposes a new method for denoising and clutter removal in weather signals. This method is a modified version of the correlation-based EMD Interval Threshold (IT) measurements. Moments have been estimated from these techniques and compared with conventional methods like Pulse pair techniques.

Tensor train factorization under noisy and incomplete data with automatic rank estimation

As a powerful tool in analyzing multi-dimensional data, tensor train (TT) decomposition shows superior performance compared to other tensor decomposition formats. Existing TT decomposition methods, however, either easily overfit with noise, or require substantial fine-tuning to strike a balance between recovery accuracy and model complexity. To avoid the above shortcomings, this paper treats the TT decomposition in a fully Bayesian perspective, which includes automatic TT rank determination and noise power estimation. Theoretical justification on adopting the Gaussian-product-Gamma priors for inducing sparsity on the slices of the TT cores is provided, thus allowing the model complexity to be automatically determined even when the observed tensor data is noisy and contains many missing values. Furthermore, using the variational inference framework, an effective learning algorithm on the probabilistic model parameters is derived. Simulations on synthetic data demonstrate that the proposed algorithm accurately recovers the underlying TT structure from incomplete noisy observations. Further experiments on image and video data also show its superior performance to other existing TT decomposition algorithms.

Noise-power estimation and performance improvement for SR-based receiver with few-bit ADC

Noise-power estimation and performance improvement for SR-based receiver with few-bit ADC

Spectral minima tracking for improving the energy detection under noise power uncertainty

Spectrum sensing involves identifying the unused license bands in Cognitive Radio Networks. Energy Detection (ED) is the most widely studied form of spectrum sensing. ED detects potentially unknown signals and it is mainly characterized by its low complexity. However, the ED performance is considerably deteriorated by the presence of noise uncertainty (NU). To increase the robustness of ED in NU scenarios, in this work we propose to use an adaptive detection threshold, which is calculated from the noise power estimate obtained at each sensing interval. The noise power is estimated using the technique called Spectral Minima Tracking (SMT). Moreover, a correlation analysis is conducted to quantify the degree of relationship between the parameters of the SMT technique and the resulting noise power estimate. The findings made in the correlation analysis allowed to adjust the parameters of the SMT technique, and thus giving place to the improvement of the quality of the noise power estimate. Simulation results show an improvement in the detection rate of the adaptive ED due to the reduction of the bias in the noise power estimate, as compared to the non-adaptive ED.

Using Discrete Wavelet Transform and Wiener filter for Image De-nosing

In this paper we proposed an algorithm for image de-nosing based on; the two level discrete wavelet transform (DWT), and Wiener filter, also this paper describe estimate noise power. At first The DWT transform noisy image into sub-bands, consist of lowfrequencyand high-frequencies, and then estimate noise power for each sub-band. The noise power is computed through two important computations; compute square of variance for each sub-band then compute the mean of the variance. After compute the variance apply the wiener filter on each sub-band by using local window nn , finally perform inverse DWT to obtain de-noised image. Our algorithm tested on the two color images and also compared with Normal Shrink filter and Wiener filter.

Joint Frame Detection and Channel Parameter Estimation for OOK Free-Space Optical Communications

We consider a free-space optical (FSO) communication link for packet-based transmissions over a turbulence fading channel. The modulation format is on-off keying (OOK) and a unique-word (UW) composed by a known synch pattern is periodically inserted in the data stream to identify the start of frame. Since an avalanche photo-diode (APD) is used for direct detection of the OOK symbols, the photocurrent signal provided by the APD is plagued by a mixture of thermal and shot noise with signal-dependent power. Our goal is the detection of the UW position in the received stream, along with the estimation of the unknown channel attenuation and noise variances. The aforementioned problem has recently been studied by ignoring any information conveyed by data symbols surrounding the UW. In this work, further investigation is conducted in order to determine the maximum likelihood (ML) solution that, in addition to the UW, exploits all the information-bearing symbols belonging to the observation window. The relevant Cramér-Rao bound (CRB) is also evaluated to establish the ultimate accuracy achievable in the estimation process. Since the true ML estimator leads to a computationally intractable multi-dimensional optimization problem, we develop suitable approximations that enable accurate frame synchronization with affordable complexity. We also present an iterative solution to refine the channel and noise power estimates provided by the UW detection procedure. Numerical simulations demonstrate the superiority of the proposed synchronization and estimation schemes with respect to existing alternatives.

An adaptive algorithm for sampling over diffusion networks with dynamic parameter tuning and change detection mechanisms

Recently, we proposed a sampling algorithm for diffusion networks that locally adapts the number of nodes sampled according to the estimation error. Thus, it reduces the computational cost associated with the learning task when the error is low in magnitude, e.g., during steady state, and maintains the sampling of the nodes otherwise, which enables fast convergence during the transient. However, its performance depends crucially on the choice of the parameter responsible for penalizing the sampling, which is a function of the variance of the measurement noise across the network. Inappropriate choices affect the tracking capability of the algorithm. In this paper, we propose a different solution, which automatically adjusts its own parameters based on the noise power estimation. Although its computational cost is slightly increased, this modification removes the need for a priori knowledge of the noise variance across the network, and increases its robustness to the presence of noisy nodes in the network. Furthermore, by implementing an adaptive reset system for the sampling mechanism, we are able to significantly improve the tracking capability of the original algorithm.

Fusion Test Statistics Based Mixture Detector for Spectrum Sensing

In this paper, two widely used spectrum sensing algorithms, sphericity test and energy detection are considered. The statistics of sphericity test and energy detector with estimated noise power are weighted and fused to propose a mixture detector. The proposed mixture detector based on the fusion test statistics can simultaneously utilize the power information and correlation feature of the received signals. Specifically, the theoretical optimal weight is derived by maximizing the deflection coefficient of the mixture detector. Besides, the analytical expressions for the decision threshold, false alarm probability and detection probability of this algorithm are derived by moment-matching Beta approximation. Numerical examples are provided to illustrate the validity of theoretical analysis. And simulations show that the proposed mixture detector with optimal weight can improve the spectrum sensing performance compared with existing algorithms.

The Impact of Channel Type on Spectrum Sensing

In this letter, we investigate the impact of channel correlation and line-of-sight (LOS) on the performance of spectrum sensing, focusing on energy detection (ED) with estimated noise power and the sphericity test (ST). We derive the expected value and variance of the test statistic for ED with estimated noise power, showing that detection probability decreases with channel correlation but increases with LOS propagation. For the ST, we show that detection improves with increased LOS, but the effects of correlation are complex. Depending on the system parameters correlation can improve or degrade detection performance. The analysis is corroborated by means of simulations for correlated Rayleigh, Ricean and ray-based channel models. Finally, we leverage these results to investigate the performance of the recently proposed mixture detector (MD).

Solar Monitoring of the NEXRAD WSR-88D Network Using Operational Scan Data

Abstract Solar monitoring is a method in which solar interferences, recorded during operational scanning of a radar, are used to monitor antenna pointing, identify signal processor issues, track receiver chain stability, and check the balance between horizontal and vertical polarization receive channels. The method is used by EUMETNET to monitor more than 100 radars in 20 European countries and it has been adopted by many national weather services across the world. NEXRAD is a network of 160 similar S-band weather radars (WSR-88Ds), which makes it most suitable for assessing the capability of the solar monitoring method on a continental scale. The NEXRAD level-II data contain radial-by-radial noise power estimates. An increase in this estimate is observed when the antenna points close to the sun. Our decoding software extracts these noise power estimates for the horizontal and vertical receive channels (converted to solar flux units) and other relevant metadata, including azimuth, elevation, observation time, and radar location. Here we present results of analyzing one year of solar monitoring data generated by 142 radars from the contiguous United States. We show monitoring results, geographical maps, and statistical outcomes on antenna pointing, solar fluxes, and differential reflectivity biases. We also assess the quality of the radars by defining a figure of merit, which is calculated from the solar monitoring results. The results demonstrate that the solar method provides great benefit for routine monitoring and harmonization of national and transnational operational radar networks.

Energy efficient management for distributed state estimation under DoS attacks

AbstractIn this article, we consider the issue of energy efficient management for distributed state estimation over unknown packet‐dropping communication channels which are exposed to Denial‐of‐Service (DoS) attacks. After a packet is transmitted, the sensor determines whether to retransmit and the retransmission power levels based on the feedback information from the receiving sensor. We formulate the energy efficient management problem as a modified Markov decision problem (MMDP), and proposed an algorithm to seek a retransmission power schedule that achieves optimal tradeoff between energy consumption and communication rate for given channel noise power. In the case of unknown channel state, we design a statistical learning method to estimate channel noise power. Besides, inspired by the hypothesis testing, we design an anomaly detector to guarantee the instantaneity of channel noise power estimation and efficiency of energy management. Furthermore, we derive the optimal gain for each estimator, and provide a sufficient condition for the stability of estimator under the energy management. Finally, we verify the main results by numerical examples.

Sensitivity and Accuracy Enhanced Wavelength Modulation Spectroscopy Based on PSD Analysis

This letter proposes a novel method to implement calibration-free wavelength modulation spectroscopy (CF-WMS) with enhanced sensing sensitivity and accuracy. Compared with traditional 1f-normalized CF-WMS implementation, the proposed method is derived, for the first time, from the power spectral density (PSD) spectrum of transmitted laser. This novel derivation enables estimation of noise power, thus enhancing of sensing sensitivity and retrieval accuracy of gas parameters, particularly in noisy environment. The proposed method is validated by both numerical simulation and condition-controlled experiment, indicating improvement of the detection limit of gas parameters by a factor of 2.64 compared to the traditional method.