Probability Distribution Of Noise Research Articles

Range uncertainty distribution of direct-detection laser radar with a peak-detecting routine

A stochastic model was firstly developed to derive the range uncertainty distribution of a peak detecting laser radar. An analytical solution was obtained, which can describe the probability density distribution of range data obtained by a peak detecting laser radar under different signal amplitudes, waveforms as well as noise distributions. The results show that the probability density distribution is proportional to the second derivative of the laser signal waveform and the probability distribution of differential noise.

Robust spectrum sensing based on statistical tests

Spectrum sensing, in particular, detecting the presence of licensed or incumbent users in licensed spectrum, is one of the pivotal tasks in cognitive radio network. In this study, the authors tackle the spectrum sensing problem by using statistical test theory and derive novel spectrum sensing approaches. The authors apply the classical Kolmogorov–Smirnov (KS) test under the assumption that the noise probability distribution is known. However, as in practice, the exact noise distribution is unknown, a sensing method for Gaussian noise with unknown noise power is proposed in this article and referred to t-sensing. The proposed sensing scheme is asymptotically robust and can be applied to non-Gaussian noise distributions. A closed form equation determining the miss-detection probability for the t-sensing is derived. The authors compare with the performance of our sensing algorithms with the energy detector and Anderson–Darling (AD) sensing methods proposed in literature. Simulation results show that the proposed sensing methods outperform both ED- and AD-based sensing, especially for the case when the received signal-to-noise ratio is low.

A theoretical investigation into the 3D point spreading situation of a scanning holographic imaging system based on random phase encoding

In this paper, by analyzing variance and noise probability distribution of the reconstructed image, a point spreading situation of adjacent section under the conventional optical scanning holography (OSH) method and a new one based on random-phase encoding (RPE) are studied. Simulation results show that, compared to the conventional OSH at the same de-focus distance, the RPE-OSH can lead the distribution of reconstructed adjacent sections to be more homogeneous and manifested as a speckle-like pattern on the in-focus image. Further study shows that the complex amplitude probability distribution of adjacent section meets the shape of Gaussian curve, and noise can be filtered out by some corresponding filters. So aliasing and interference on the in-focus image can be removed.

Stochastic resonance in binary composite hypothesis-testing problems in the Neyman–Pearson framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their inputs via the stochastic resonance (SR) effect. In this paper, the effects of SR are studied for binary composite hypothesis-testing problems. A Neyman-Pearson framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum, and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches to obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results.

Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M -ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results.

OPTIMAL DIRECTED CURRENT OF A BROWNIAN MOTOR UNDER A NON-GAUSSIAN NOISE GENERATED BY A MULTIPLICATIVE PROCESS

Unidirectional motion is achieved when a particle, moving under the influence of an underlying noise source, is subjected to a ratchet asymmetric periodic potential. Here, we investigate how deviations from the Gaussian nature of the noise distribution function impacts the average particle's current. The input noise is considered to be produced by a Langevin process including both multiplicative and additive random noise sources. The resulting input random signal has a power-law amplitude distribution and a finite correlation time. These features are controlled by the average of the multiplicative noise. We show that the average particle's velocity depends non-monotonically on the degree of non-Gaussianity of the input noise. It exhibits a maximum at an intermediate value of the effective power-law exponent that characterizes the asymptotic decay of the noise probability distribution function.

An investigation of speech enhancement using wavelet filtering method

This paper investigates the utilization of wavelet filters via multistage convolution by Reverse Biorthogonal Wavelets (RBW) in high and low pass band frequency parts of speech signal. Speech signal is decomposed into two pass bands of frequency; high and low, and then the noise is removed in each band individually in different stages via wavelet filters. This approach provides better outcomes because it does not cut the speech information, which occurs when utilizing conventional thresholding. We tested the proposed method via several noise probability distribution functions. Subjective evaluation is engaged in conjunction with objective evaluation to accomplish optimal investigation method. The method is simple but has surprise high quality results. The method shows superiority over Donoho and Johnstone thresholding method and Birge-Massart thresholding strategy method.

CRLB Based Optimal Noise Enhanced Parameter Estimation Using Quantized Observations

In this letter, optimal additive noise is characterized for parameter estimation based on quantized observations. First, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. Then, it is proven that optimal additive ¿noise¿ can be represented by a constant signal level, which means that randomization of additive signal levels is not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Finally, a numerical example is presented to explain the theoretical results.

Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distributionA new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requiresa prioriknowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to themaxdiscriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.

Stabilization of the Barkhausen Noise Parameters

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The Barkhausen noise was measured in nonoriented Fe–3%Si steel with different average grain sizes. Air gaps between the yoke and the measured objects were also varied during the measurements. The change of the grain size was achieved by different combinations of cold rolling and heat treatment processes. The rise of the gap size degraded the level of the Barkhausen noise and caused that the parameters of the Barkhausen noise, such as the amplitude of the Barkhausen noise's envelope, decreased. In order to suppress the influence of the air gap size on the measurement results, we analyzed the amplitude probability distribution of the Barkhausen noise and we found that the distribution at small levels of the voltage practically does not change with the grain size, but it increases with rise of the gap size. This change of the amplitude probability distribution with the gap size was used to correct the amplitude of the Barkhausen noise's envelope. It was shown that the correction essentially increases the precision of the evaluation of the grain size at varying air gap. Similar technique can be used also to decrease the error of evaluation of other microstructural changes of ferromagnetic materials using the Barkhausen noise method, without measuring and feedback setting the defined waveform of the magnetic field in the sample. For this method to be applicable, several conditions should be met, especially the level of the Barkhausen noise should be essentially higher than the level of the disturbing noise. </para>

Decentralized Spectrum Access Amongst Cognitive Radios—An Interacting Multivariate Global Game-Theoretic Approach

This paper studies decentralized dynamic spectrum access using the theory of multivariate global games. We consider a network of cognitive radios (CRs) where each CR obtains noisy multivariate measurements of the quality of several logical channels and needs to decide which channel to access. Assuming the CRs are rational devices, each CR determines which channel to access, based on its expected throughput and Bayesian estimate of the intention of other CRs. We formulate conditions for which the Bayesian Nash equilibrium (BNE) of the resulting global game is monotonically increasing in the quality of the logical channel. This leads to a simple characterization of the competitive optimal behavior of the system as a function of the prior probability distribution of spectrum hole occupancy, channel quality and observation noise. In obtaining the characterization of the BNE, we extend recent results in univariate global games to the multivariate case.

Markov Chain Analysis of Thermally Induced Soft Errors in Subthreshold Nanoscale CMOS Circuits

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The development of future nanoscale CMOS circuits, characterized by lower supply voltages and smaller dimensions, raises the question of logic stability of such devices with respect to electrical noise. This paper presents a theoretical framework that can be used to investigate the thermal noise probability distributions for equilibrium and nonequilibrium logic states of CMOS flip-flops operated at subthreshold voltages. Representing the investigated system as a 2-D queue, a symbolic solution is proposed for the moments of the probability density function for large queues where Monte Carlo and eigenvector methods cannot be used. The theoretical results are used to calculate the mean time to failure of flip-flops built in a current 45-nm silicon-on-insulator technology modeled in the subthreshold regime including parasitics. As a predictive tool, the framework is used to investigate the reliability of flip-flops built in a future technology described in the International Technology Roadmap for Semiconductors. Monte Carlo simulations and explicit symbolic calculations are used to validate the theoretical model and its predictions. </para>

On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary PSK systems with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> > 2. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.

Detection of Transient Events in the Presence of Background Noise

We describe a method to detect and count transient burstlike signals in the presence of a significant stationary noise. To discriminate a transient signal from the background noise, an optimum threshold is determined using an iterative algorithm that yields the probability distribution of the background noise. Knowledge of the probability distribution of the noise then allows the determination of the number of transient events with a quantifiable error (wrong-positives). We apply the method, which does not rely on the choice of free parameters, to the detection and counting of transient single-molecule fluorescence events in the presence of a strong background noise. The method will be of importance in various ultra sensing applications.

Simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifiers in DPSK applications

A thorough simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifier (SOA) is very important for predicting its performance in differential phase-shift keyed (DPSK) applications. In this paper, standard deviation and probability distribution of differential phase noise at the SOA output are obtained from the statistics of simulated differential phase noise. By using a full-wave model of SOA, the noise performance in the entire operation range can be investigated. It is shown that nonlinear phase noise substantially contributes to the total phase noise in case of a noisy signal amplified by a saturated SOA and the nonlinear contribution is larger with shorter SOA carrier lifetime. It is also shown that Gaussian distribution can be useful as a good approximation of the total differential phase noise statistics in the whole operation range. Power penalty due to differential phase noise is evaluated using a semi-analytical probability density function (PDF) of receiver noise. Obvious increase of power penalty at high signal input powers can be found for low input OSNR, which is due to both the large nonlinear differential phase noise and the dependence of BER vs. receiving power curvature on differential phase noise standard deviation.

A NOVEL SCHEME OF IMPLEMENTING HIGH-SPEED HIGH-PROBABILITY-RESOLUTION DIGITAL AWGN GENERATORS

Digital noise generators are basic components in communication channel emulators which are used to make the test and verification of communication systems easy and fast. In this paper, a novel scheme of implementing high-speed high-probability-resolution digital AWGN generator is proposed based on a derived universal algorithm for any white f(x)-distributed noise generation. The precision and the hardware complexity of the proposed AWGN generator are discussed in detail. Implemented with FPGA, the presented AWGN generator is utilized to test a high-speed UWB communication system and performs well with excellent precision in noise probability distribution. The proposed novel scheme of implementing digital noise generators is important and helpful in building communication channel emulators to test and verify communication systems.

Diurnal variations of ELF transients and background noise in the Schumann resonance band

Schumann resonances (SR) are resonant electromagnetic waves in the Earth‐ionosphere cavity, induced primarily by lightning discharges, with a fundamental frequency of about 8 Hz and higher‐order modes separated by approximately 6 Hz. The SR are made up of the background signal resulting from global lightning activity and extremely low frequency (ELF) transients resulting from particularly intense lightning discharges somewhere on the planet. Since transients within the Earth‐ionosphere cavity due to lightning propagate globally in the ELF range, we can monitor and study global ELF transients from a single station. Data from our Negev Desert (Israel) ELF site are collected using two horizontal magnetic induction coils and a vertical electric field ball antenna, monitored in the 5–40 Hz range with a sampling frequency of 250 Hz. In this paper we present statistics related to the probability distribution of ELF transients and background noise in the time domain and its temporal variations during the day. Our results show that the ELF signal in the time domain follows the normal distribution very well. The σ parameter exhibits three peaks at 0800, 1400, and 2000 UT, which are related to the three main global lightning activity centers in Asia, Africa, and America, respectively. Furthermore, the occurrence of intense ELF events obeys the Poisson distribution, with such intense events occurring every ∼10 s, depending on the time of the day. We found that the diurnal changes of the σ parameter are several percent of the mean, while for the number of intense events per minute, the diurnal changes are tens of percent about the mean. We also present the diurnal changes of the SR intensities in the frequency domain as observed at our station. To better understand the diurnal variability of the observations, we simulated the measured ELF background noise using space observations as input, as detected by the Optical Transient Detector (OTD). The most active center which is reflected from both ELF measurements and OTD observations is in Africa. However, the second most active center on the basis of ELF measurements appears to be Asia, while OTD observations show that the American center is more active than the Asian center. These differences are discussed. This paper contributes to our understanding of the origin of the SR by comparing different lightning data sets: background electromagnetic radiation and optical emission observed from space.

Aspects of signal-dependent noise characterization

An automated method is presented for analyzing signal-dependent noise. Signal-dependent noise is present in many types of data-acquisition processes and has been investigated by other researchers with various methods. Regardless of the noise analysis methods, often the starting point is based on a particular signal-dependent noise model, which also forms the basis for our study. The approach determines whether the estimated noise variance is dependent on the signal by approximating the functional relation within the constraints of the assumed signal-noise model. The method relies on the Fourier attributes of the signal and noise and uses the wavelet expansion for separating these components. The technique does not rely on the underlying noise and signal probability distributions. Two-dimensional simulations as well as mammography data are used to illustrate the merits of the approach.

Optimal and Near-Optimal Signal Detection in Snapping Shrimp Dominated Ambient Noise

The optimal detection of signals requires detailed knowledge of the noise statistics. In many applications, the assumption of Gaussian noise allows the use of the linear correlator (LC), which is known to be optimal in these circumstances. However, the performance of the LC is poor in warm shallow waters where snapping shrimp noise dominates in the range 2-300 kHz. Since snapping shrimp noise consists of a large number of individual transients, its statistics are highly non-Gaussian. We show that the noise statistics can be described accurately by the symmetric alpha-stable family of probability distributions. Maximum-likelihood (ML) and locally optimal detectors based on the detailed knowledge of the noise probability distribution are shown to demonstrate enhanced performance. We also establish that the sign correlator, which is a nonparametric detector, performs better than the LC in snapping shrimp noise. Although the performance of the sign correlator is slightly inferior to that of the ML detector, it is very simple to implement and does not require detailed knowledge of the noise statistics. This makes it an attractive compromise between the simple LC and the complex ML detector

Decentralized Estimation in an Inhomogeneous Sensing Environment

We consider decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth-constrained sensor network with a fusion center. The sensor noises are assumed to be additive, zero mean, spatially uncorrelated, but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment. The classical best linear unbiased estimator (BLUE) linearly combines the real-valued sensor observations to minimize the mean square error (MSE). Unfortunately, such a scheme cannot be implemented in a practical bandwidth-constrained sensor network due to its requirement to transmit real-valued messages. In this paper, we construct a decentralized estimation scheme (DES) where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal-to-noise ratio (SNR). The resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter. The proposed DES is universal in the sense that each sensor compression scheme requires only the knowledge of local SNR, rather than the noise probability distribution functions (pdf), while the final fusion step is also independent of the local noise pdfs. We show that the MSE of the proposed DES is within a constant factor of 25/8 of that achieved by the classical centralized BLUE estimator.