Noise Probability Density Function Research Articles

Algorithms for Indicating the Beginning of Accidents Based on the Estimate of the Density Distribution Function of the Noise of Technological Parameters

A technology has been developed, which allows for calculating the probability density function of noise, its maximum and inflection points, using the discrete values of a signal corrupted by an additive random noise. Computational experiments have been conducted. It has been demonstrated that knowledge of those characteristics of noise allows systems of monitoring, control, diagnostics, forecasting, identification, management, etc. to register not only the initial period of fault origin, but also the moment when preventive maintenance measures, routine or major overhaul works are required.

Non-Gaussian Systems Control Performance Assessment Based on Rational Entropy.

Control loop Performance Assessment (CPA) plays an important role in system operations. Stochastic statistical CPA index, such as a minimum variance controller (MVC)-based CPA index, is one of the most widely used CPA indices. In this paper, a new minimum entropy controller (MEC)-based CPA method of linear non-Gaussian systems is proposed. In this method, probability density function (PDF) and rational entropy (RE) are respectively used to describe the characteristics and the uncertainty of random variables. To better estimate the performance benchmark, an improved EDA algorithm, which is used to estimate the system parameters and noise PDF, is given. The effectiveness of the proposed method is illustrated through case studies on an ARMAX system.

Performance comparison between matched filter and locally optimal detector for composite hypothesis test with inaccurate noise

This study considers the performance comparison between the matched filter (MF) and the locally optimal (LO) detector when the noise information is not accurate. For a given binary hypothesis testing problem, the authors derive the condition under which the LO detector performs worse than the MF with the assumptions of large number samples and low signal-to-noise ratio. The condition is an inequality, which involves the noise probability density function (pdf) used in the LO detector, the real noise pdf, and the noise variance. Simulations show that the condition is theoretically sound under both known and unknown noise pdf's.

Detection of Magnetic Anomaly Signal Based on Information Entropy of Differential Signal

Magnetic anomaly detection is an effective approach for detecting the visually obscured ferromagnetic target, and its performance is mainly limited by background geomagnetic noise. In contrast to the traditional detection methods that rely on several a priori assumptions regarding the target or the probability of magnetic noise consisting of external geomagnetic noise and intrinsic sensor noise, we present, in this letter, a new estimator of information entropy for differential signal acquired by a pair of magnetic sensors to detect any changes in the magnetic noise pattern. First, the magnetic noise probability density function (PDF) of differential signal is estimated by using the kernel smoothing method. Then, the minimum entropy detector based on the magnetic noise PDF of differential signal is used to detect the magnetic anomaly target. Finally, according to the probabilities of false alarm, the detection threshold can be obtained to be used for abnormal judgment. In order to verify the effectiveness of the proposed method, the experiment is conducted, and the results demonstrate that the proposed method has better detection performance than that of traditional methods.

Pressure transient measurement statistics and gauge metrology

Downhole pressure transient measurements are usually affected by random noise caused by the intrinsic noise of the measuring device (the pressure gauge), environmental noise, and/or wellbore pressure fluctuations. The interpretation of pressure transients depends on the characterization of the noise signal and the obtaining of an accurate reservoir pressure response. This article presents a new procedure to characterize acquired formation pressure measurements, their statistical properties, and standard deviation by assuming independent and identically distributed random measurement noise. Apparent accuracy and apparent resolution of measurements are introduced. An automated methodology is developed to obtain and characterize the probability density function of the random noise. This new methodology will replace the conventional manual technique of selectively zooming on pressure curves and measuring their variations.Pressure data from a drillstem test (DST) were used to illustrate the automatic calculation of the apparent resolution. The noise affecting the DST data was then fully characterized and its density function computed. The dataset was also used to introduce and illustrate a new methodology for the analysis of pressure gauge drift using the distribution of slopes extracted from the local linearization of the pressure data. This methodology was able to identify gauges suspected of slight pressure drift that was not detectable visually.

Novel Form of MMSE Estimation via Exact Moment Value of Noise and Higher Order Taylor Series in AWGN

Minimum mean-square-error (MMSE) and maximum a posteriori (MAP) estimations are considered basic approaches commonly used in denoising methods. In most cases, MMSE estimation yields better performance in reducing noise than MAP estimation does. However, the calculation according to MMSE estimation is more difficult than that of MAP estimation, because MMSE estimation relies on integration and its results mainly contain special functions, while MAP estimation relies on differentiation. The previous research work presented MMSE estimation in the form of differentiation, which is in the approximation form. But in this letter, we will present MMSE estimation in the differentiation form by using the actual moment value of the probability density function of Gaussian noise together with the higher order Taylor series. This will provide higher efficiency of noise reduction than the formerly presented method.

On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models With Input Cost Constraints

We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the noise probability density function, one which dictates the type of the optimal input. In Layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cut-off rate equal to the logarithm of the noise PDF evaluated at the input-output function. Furthermore, we prove a converse statement that says whenever the cost grows slower than the cut-off rate, the optimal input has necessarily an unbounded support. In addition, we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties. We argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cut-off rate. Our results are valid for any cost function that is super-logarithmic. They summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models, such as Gaussian mixtures, generalized-Gaussians and heavy-tailed noise models, that we state along with numerical computations.

Variability of Hydroacoustic Noise Probability Density Function at the Output of Automatic Gain Control System

This research presents results of the estimation of temporal variability of the hydroacoustic noise probability density function (PDF) in shallow waters within the frequency band of 0.03–3.3 kHz; the studies were conducted near the Primorsky Aquarium on Russky Island, Vladivostok, Russia. Signals were received via unidirectional hydrophone and automatic gain control of the received signals. The hydrophone was attached to a drifting buoy via an elastic suspension; the received signals were transmitted by cable to a boat drifting with the buoy. The results of the comparison of the sea noise probability density function (PDF) estimates at the output of a system with automatic gain control (AGC) with similar results for a white Gaussian noise in the same frequency band are described.

Performance Analysis of Coded Massive MIMO-OFDM Systems Using Effective Matrix Inversion

In this paper, we derive the bit error rate and pairwise error probability (PEP) for massive multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems for different $M$ -ary modulations based upon the approximate noise distribution after channel equalization. The PEP is used to obtain the upper-bounds for convolutionally coded and turbo coded massive MIMO-OFDM systems for different code generators and receive antennas. In addition, complexity analysis of the log-likelihood ratio (LLR) values is performed using the approximate noise probability density function. The derived LLR computations can be time-consuming when the number of receive antennas is very large in massive MIMO-OFDM systems. Thus, a reduced complexity approximation is introduced using Newton’s interpolation with different polynomial orders and the results are compared with the exact simulations. The Neumann large matrix approximation is used to design the receiver for a zero-forcing equalizer by reducing the number of operations required in calculating the channel matrix inverse. Simulations are used to demonstrate that the results obtained using the derived equations match closely the Monte Carlo simulations.

Entropy optimization based filtering for non-Gaussian stochastic systems

This paper is concerned with the entropy optimization based filter design for a class of multivariate dynamic stochastic systems with simultaneous presence of non-Gaussian process noise and measurement noise. The filter consists of time update and measurement update two steps, where the selection of the filter gain in the measurement update equation is a key issue to be addressed. Different from the classic Kalman filter theory, entropy rather than variance is employed as the filtering performance criterion due to the non-Gaussian characteristic of the estimation error. Following the establishment of the relationship between the probability density functions of random noises and estimation error, two kinds of entropy based performance indices are provided. On this basis, the corresponding optimal filter gains are obtained respectively by using the gradient optimization technique. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed filtering algorithms.

An Approach for Despeckling a Sequence of Ultrasound Images Based on Statistical Analysis

In this paper, a denoising approach taking into account the statistical properties of the ultrasound image is proposed. In the proposed method, the time correlation between the different frames of a video sequence are taken into consideration to find the maximum a posteriori probability estimate of a noisy pixel. The proposed algorithm is tested on both synthetic and real ultrasound images to verify the effectiveness of the system. The paper provides a model for time correlation of the noise between different frames of the ultrasound video data. To simulate the speckle noise in a natural image, an attempt is made to study the probability density function of speckle noise in an ultrasound video sequence. From our analysis, it is concluded that the speckle noise is multiplicative Gaussian in nature. Certain statistical tests are also conducted to verify the effectiveness of our proposed method. Experimental results show that the proposed despeckling method shows superior performance than its counterparts.

Low‐density parity check coded orthogonal frequency division multiplexing for PLC in non‐Gaussian noise using LLRs derived from effective noise probability density functions

In this study, the performance of irregular low-density parity check (LDPC) coded orthogonal frequency division multiplexing (COFDM) utilising 4096 quadrature amplitude modulation (4096-QAM) is investigated over multipath power-line communication (PLC) channel. The effective complex-valued ratio distributions of the noise samples at the zero-forcing equaliser output considering both frequency-selective multipath PLCs, background and impulsive noise are derived, in addition to the condition for optimum detection of 4096-QAM and the bit error rate (BER). Moreover, the performance of the LDPC decoder is improved by computing the log-likelihood ratios (LLRs) required for soft decoding based on the derived probability density functions. Numerical results obtained using the newly derived LLRs demonstrate a significant performance improvement compared to the conventional receiver that uses blanking impulsive noise mitigation method and LLR computed based on the Gaussian distribution. Furthermore, EXtrinsic Information Transfer chart analysis demonstrates that the proposed approach requires fewer iterations for convergence compared to the conventional receiver. Finally, utilising channel bandwidth of 22.4 MHz, the proposed system offers an improvement of 111 Mbps over the conventional system to reach a maximum data throughput of 256 Mbps for a signal-to-noise ratio of 39 dB and BER of 10 -5 .

Image despeckling with non-local total bounded variation regularization

A non-local total bounded variational (TBV) regularization model is proposed for restoring images corrupted with data-correlated speckles and linear blurring artifacts. The energy functional of the model is derived using maximum a posteriori (MAP) estimate of the noise probability density function (PDF). The non-local total bounded variation prior regularizes the model while the data fidelity is derived using the MAP estimator of the noise PDF. The computational efficiency of the model is improved using a fast numerical scheme based on the Augmented Lagrange formulation. The proposed model is employed to restore ultrasound (US) and synthetic aperture radar (SAR) images, which are usually speckled and blurred. The numerical results are presented and compared. Furthermore, a detailed theoretical study of the model is performed in addition to the experimental analysis.

1/f Noise in Optical Output and Non-Gaussianity in Voltage Noise of GaAs Nanoscale Light-Emitting Structures

The 1/[Formula: see text] noise investigation in nanoscale light-emitting diodes (LEDs) and lasers, based on GaAs and its solid solutions, is presented here. Spectra of 1/[Formula: see text] noise [Formula: see text] in the voltage across terminals of device, and [Formula: see text] in emitted light intensity, as well as the cross-spectrum [Formula: see text], were measured. It was found that the noise in the leakage current, and in the additional nonlinear current, of devices is transformed into the noise in optical output intensity in spontaneous emission regime. We measured the histogram as the estimate of the probability density function of the voltage noise. The obtained data in lasers characterize the non-Gaussianity and/or nonstationarity of the noise in the regime of induced radiation. In contrast, in LEDs the deviation of noise from Gaussianity practically was not observed.

Heavy-Tailed Noise Suppression and Derivative Wavelet Scalogram for Detecting DNA Copy Number Aberrations.

Most existing array comparative genomic hybridization (array CGH) data processing methods and evaluation models assumed that the probability density function (pdf) of noise in array CGH data is a Gaussian distribution. However, in practice, such noise distribution is peaky and heavy-tailed. Therefore, a Gaussian pdf is not adequate to approximate the noise in array CGH data and hence introduces wrong detections of chromosomal aberrations and leads misunderstanding on disease pathogenesis. A more accurate and sufficient model of noise in array CGH data is necessary and beneficial to the detection of DNA copy number variations. We analyze the real array CGH data from different platforms and show that the distribution of noise in array CGH data is fitted very well by generalized Gaussian distribution (GGD). Based on our new noise model, we propose a novel array CGH processing method combining the advantages of both the smoothing and segmentation approaches. The new method uses generalized Gaussian bivariate shrinkage function and one-directional derivative wavelet scalogram in generalized Gaussian noise. In the smoothing step, with the new generalized Gaussian noise model, we derive the heavy-tailed noise suppression algorithm in stationary wavelet domain. In the segmentation step, the 1D Gaussian derivative wavelet scalogram is employed to detect break points. Both real and simulated array CGH data with different noises (such as Gaussian noise, GGD noise, and real noise) are used in our experiments. We demonstrate that our new method outperforms other state-of-the-art methods, in terms of both root mean squared errors and receiver operating characteristic curves.

Single‐cell and multi‐cell performance analysis of OFDM index modulation

This paper addresses the achievable rate of single cell and sum rate of multi-cell orthogonal frequency division multiplexing (OFDM) index modulation (IM). The single cell achievable rate of OFDM-IM with Gaussian input is calculated using a multi-ary symmetric channel. Then, the cumulative distribution function (CDF) of multi-cell OFDM-IM is investigated by stochastic geometry. Furthermore, it is proved in this paper that the probability density function (PDF) of noise plus intercell-interference (ICI) in multi-cell OFDM-IM with quadrature amplitude modulation (QAM) follows a mixture of Gaussians (MoG) distribution. Next, parameters of the MoG distribution are estimated using a simplified expectation maximization (EM) algorithm. Upper bound of sum rates of multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are compared and discussed.

Statistical Analysis of Indoor RSSI Read-outs for 433 MHz, 868 MHz, 2.4 GHz and 5 GHz ISM Bands

Abstract This paper presents statistical analysis of RSSI read-outs recorded in indoor environment. Many papers concerning indoor location, based on RSSI measurement, assume its normal probability density function (PDF). This is partially excused by relation to PDF of radio-receiver's noise and/or together with influence of AWGN (average white Gaussian noise) radio-channel – generally modelled by normal PDF. Unfortunately, commercial (usually unknown) methods of RSSI calculations, typically as “side-effect” function of receiver's AGC (automatic gain control), results in PDF being far different from Gaussian PDF. This paper presents results of RSSI measurements in selected ISM bands: 433/868 MHz and 2.4/5 GHz. The measurements have been recorded using low-cost integrated RF modules (at 433/868 MHz and 2.4 GHz) and 802.11 WLAN access points (at 2.4/5 GHz). Then estimated PDF of collected data is shown and compared to normal (Gaussian) PDF.

Statistical Analyses of ASE Noise

The evolution of ASE noise and the generation of nonlinear phase shift are analyzed based on the travelling wave solution of ASE noise and its probability density function by solving the Fokker-Planck equation including dispersion effect. Nonlinear effect has strong impact on ASE noise. After the transmission in non-zero dispersion shift fibers + dispersion compensation fibers, due to the nonlinear effect, ASE noise is enhanced. Detailedly, the real part of ASE decreases but the image part increases greatly compared to that with dispersion effect only. Nonlinear phase shift, related to the image part of ASE noise, occurs in this kind of link. The impact of signal intensity on ASE noise induces fluctuations to the both curves of ASE noise and nonlinear phase shift as functions of time, respectively. Furthermore, it results in the non-Gaussian distribution of ASE noise probability density function (side-bands occurring) and brings more than 1 dB additive BER.

Practical optimal nonlinear filter with estimated noise probability density function

Practical optimal nonlinear filter with estimated noise probability density function

Tropical littoral ambient noise probability density function model based on sea surface temperature.

Ambient noise variability in tropical shallow water presents a critical challenge for sonar designers and operators due to site-specific sea surface fluctuations. Sea surface temperature (SST) is a direct measure of energy balance defining the local climate of the region and hence ambient noise characteristics. In this work, an ambient noise probability density function (pdf) model for a spectral band of 3-10 kHz has been designed based on the statistical distribution of SST and validated using real field data. This will enable early ambient noise prediction compared to existing wind speed based models to facilitate structured mitigation strategies for improving sonar performance.