Cross-correlated Noises Research Articles

MIMO SAR Waveform Separation Based on Costas‐LFM Signal and Co‐arrays for Maritime Surveillance

In case of bright targets over a dark background, the cross-correlation noise of Multiple input and multiple output (MIMO) Synthetic aperture radar (SAR) orthogonal waveforms in the same frequency coverage will increase which can degrade the image. An Interpulse Costas hopping and intra-pulse Slope coded linearly frequency modulated (IPC-SCLFM) waveform is designed and analyzed to decrease the autocorrelation and cross-correlation noise. Besides a novel acquisition mode of “MIMO Coprime SAR” (MIMO-Cop SAR) is proposed with Coprime arrays (Co-arrays) in receive across the SAR line of flight based on digital beamforming. An improved processing by multiplying values at each pixel of two coarrays images is proposed to suppress the cross-correlation noise. MIMO-Cop SAR can effectively suppress the crosscorrelation noise, reduce the amount of data to be stored and get high signal-to-noise ratio in a simple way. The effectiveness of MIMO-Cop SAR for maritime surveillance is demonstrated by the simulation experiments.

Robust image alignment for cryogenic transmission electron microscopy

Cryo-electron microscopy recently experienced great improvements in structure resolution due to direct electron detectors with improved contrast and fast read-out leading to single electron counting. High frames rates enabled dose fractionation, where a long exposure is broken into a movie, permitting specimen drift to be registered and corrected. The typical approach for image registration, with high shot noise and low contrast, is multi-reference (MR) cross-correlation. Here we present the software package Zorro, which provides robust drift correction for dose fractionation by use of an intensity-normalized cross-correlation and logistic noise model to weight each cross-correlation in the MR model and filter each cross-correlation optimally. Frames are reliably registered by Zorro with low dose and defocus. Methods to evaluate performance are presented, by use of independently-evaluated even- and odd-frame stacks by trajectory comparison and Fourier ring correlation. Alignment of tiled sub-frames is also introduced, and demonstrated on an example dataset. Zorro source code is available at github.com/CINA/zorro.

Multiple cross-correlation noise induced transition in a stochastic bistable system

Based on the stochastic equivalent rules, the Fokker–Planck Equation for a general one-dimensional nonlinear system subjected to N-component noises and cross-correlation noises is derived, and the greatest advantage of the method lies in its simplicity. Applying this method, the effects of multiple sources of noise and the correlation forms of noises among them (i.e., two multiplicative noises, an additive noise and the correlation between the three noises) on the steady-state properties and the mean first passage time (MFPT) of a stochastic bistable system are discussed in details. The results show rich transition phenomena, such as the reentrance-like noise-induced phenomenon and the switch between the bimodal and the unimodal structure for different noise intensities. Moreover, the effects of the cross-correlation among the three noise sources on the MFPT are also discussed, and the noise-enhanced stability phenomenon and the resonant activation phenomenon are observed. The numerical results are in basic agreement with the theoretical predictions.

Optimal Linear Estimators for Systems With Finite-Step Correlated Noises and Packet Dropout Compensations

This paper is concerned with the optimal estimation problem for discrete-time stochastic systems with finite-step auto- and cross-correlated noises and multiple packet dropouts induced by the unreliable networks. When a packet transmitted from the sensor to the data processing center is lost, its predictor is used as the compensation. The optimal linear estimators including filter, predictor and smoother that depend on the packet arriving rate are proposed in the linear minimum variance sense via an innovative analysis approach. They are computed in terms of the solutions of some auto- and cross-covariance matrices. A tracking system example is given to demonstrate the effectiveness of the proposed algorithms.

Stochastic stability and state shifts for a time-delayed cancer growth system subjected to correlated multiplicative and additive noises

In the present paper, we investigate the stationary probability distribution(SPD) and the mean treatment time of a time-delayed cancer growth system induced by cross-correlated intrinsic and extrinsic noises. Our main results show that the resonant-like phenomenon of the mean first-passage time (MFPT) appears in the tumor cell growth model due to the interaction of all kinds of noises and time delay. Due to the existence of the resonant-like peak value, by increasing the intensity of multiplicative noise and time delay, it is possible to restrain effectively the development of the cancer cells and enhance the stability of the system. During the process of controlling the diffusion of the tumor cells, it contributes to inhibiting the development of cancer by increasing the cross-correlated noise strength and weakening the additive noise intensity and time delay. Meanwhile, the proper multiplicative noise intensity is conducive to the process of inhibition. Conversely, in the process of exterminating cancer cells of a large density, it can exert positive effects on eliminating the tumor cells by increasing noises intensities and the value of time delay.

Optimal cosmic microwave background map-making in the presence of cross-correlated noise

We present an extension of the ROMA map-making algorithm for the generation of optimal cosmic microwave background polarization maps. The new code allows for a possible cross-correlated noise component among the detectors of a CMB experiment. A promising application is the forthcoming LSPE balloon-borne experiment, which is devoted to the accurate observation of CMB polarization at large angular scales. We generalized the noise covariance matrix in time domain to account for all the off-diagonal terms due to the detector cross-talk. Hence, we performed preliminary forecasts of the LSPE-SWIPE instrument. We found that considering the noise cross-correlation among the detectors results in a more realistic estimate of the angular power spectra. In particular, the extended ROMA algorithm has provided a considerable reduction of the spectra error bars. We expect that this improvement could be crucial in constraining the B-mode polarization at the largest scales.

Distributed fusion estimation with square-root array implementation for Markovian jump linear systems with random parameter matrices and cross-correlated noises

This study presents the distributed fusion estimation of discrete-time Markovian jump linear systems with random parameter matrices and cross-correlated noises in sensor networks. The recursive linear minimum mean square error estimator is proposed based on the Gram-Schmidt orthogonalization procedure under a centralized framework. In order to avoid the loss of positive semidefiniteness and reduce dynamical range, its square-root array implementation is presented by recursively triangularizing the square roots of relevant positive semidefinite matrices. Furthermore, via the information filter form, the distributed fusion estimation with square-root array implementation is derived from the centralized fusion structure, incorporated with consensus strategy. A maneuvering target tracking simulation in a sensor network validates the proposed method.

Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system

The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from “on” → “off” of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching “off” → “on”. A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified.

Stochastic dynamical features for a time-delayed ecological system of vegetation subjected to correlated multiplicative and additive noises

In this paper, the generalized potential function, the stationary probability distribution function (SPDF), the mean development time and the mean shrinking time of a time-delayed vegetation growth system induced by cross-correlated internal and external noises are investigated. Our main results are designed to reveal the fact that the resonant phenomenon of the mean first-passage time (MFPT) takes place in the vegetation growth model because of the interaction of different types of noises and time delay. It can inhibit the vegetation system from developing rapidly and reduce the stability of the system by increasing of intensity of multiplicative noise and time delay. Meanwhile, it can produce beneficial effect on maintaining the stability of the vegetation system by increasing the strength of correlated noise. However, it can exert complicated effect on the stability of system by increasing the intensity of additive noise in different cases. During the spread process of the vegetation, it plays a positive role in propelling the development of vegetation by reducing the cross-correlated noise strength and increasing the multiplicative, additive noise intensities and time delay. On the contrary, in the decline process of vegetation system, it plays a crucial part in maintaining the vegetation biomass by increasing the strength of cross-correlated noise and weaken the multiplicative, additive noise intensities and time delay.

Quantum Hall realization of polarized intensity interferometry

We combine the ideas of intensity interferometry, polarization optics and Bell's measurement into an experimental proposal which is hosted in a $\nu\,$=$\,2$ quantum Hall (QH) edge state. Our interferometer comprises of a single gate, that separates the spin resolved edge states of $\nu$\,=\,$2$ state. An analog of waveplate (from polarization optics) is realized by exposing the individual edges to nano-magnets over a finite length which facilitates coherent manipulation of the electron spin on the edge. We show that the in-plane rotation of magnetization direction of the nano-magnets results in oscillations observed solely in the cross-correlated noise which arises from two particle interference. Through numerical simulations we demonstrate that our proposal is well within the reach of recent experimental developments of spin manipulations on the QH edge.

Impact of two types of time delays and cross-correlated multiplicative and additive noises on stability and stochastic resonance for a metapopulation system

In this paper, we investigate the stability and the shift between the extinction state and the stable one of a large density and the stochastic resonance (SR) for a metapopulation system subjected to two types of time delay terms, cross-correlation noises and multiplicative signal. By using the fast descent method and the method of small delay approximation, the expressions of the effective potential function and the signal-to-noise ratio (SNR) are obtained. We denote by Q the intensity of the multiplicative noise, and M the intensity of the additive noise, θ and τ the two time delay terms introduced into the metapopulation system. Our main results show some facts that time delay θ and the strength of correlation noise λ can restrain the development of the metapopulation, while the other term of time delay τ can accelerate the expansion of the population from the extinction state to the large stable one. We discover that it is possible to enhance the signal-to-noise ratio by adjusting the intensities of the multiplicative, additive noises and the time delays of the stochastic metapopulation system

Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

In this paper, the transition between the stable state of a big density and the extinction state and stochastic resonance (SR) for a time-delayed metapopulation system disturbed by colored cross-correlated noises are investigated. By applying the fast descent method, the small time-delay approximation and McNamara and Wiesenfeld’s SR theory, we investigate the impacts of time-delay, the multiplicative, additive noises and colored cross-correlated noise on the SNR and the shift between the two states of the system. Numerical results show that the multiplicative, additive noises and time-delay can all speed up the transition from the stable state to the extinction state, while the correlation noise and its correlation time can slow down the extinction process of the population system. With respect to SNR, the multiplicative noise always weakens the SR effect, while noise correlation time plays a dual role in motivating the SR phenomenon. Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon. Conversely, it could motivate the SR effect to increase the strength of the cross-correlation noise in the SNR-β plot, while the increase of additive noise intensity will firstly excite SR, and then suppress the SR effect.

Multi-Channel Autonomous Information System Performance with Positional Signal State Analyzers at the Channel Outputs

The article presents a statement of technique to research performances of multi-channel combo standalone information systems with positional analyzers of the signal states at the channel outputs. In most cases, in considered multi-channel systems there has been impossible to coincide in time the random moments of signals coming from the objects through various channels in all ways of encounter environment and conditions of practical application. The analyzer makes decision on the signal using the discrete operations on the quantized signals of the certain duration from the channel outputs. The analyzer performance is described by a set of Boolean algebra functions defined for all possible states of the signals at the outputs of the channels, and in the general case is specified in a perfect disjunctive normal form. To determine the validity or falsity of functions of the algebra of logics, which are calculated statements concerning the available or unavailable useful signal at the system input, on the authority of the Poretsky’s theorem and the theory of coincidence in time of the random pulse flow of the channels response because of uncorrelated and correlated noise, are obtained dependences to calculate the probabilities of false alarms and omissions of the signals in discrete combined systems. It is shown that the flows of false alarms because of noise at the channel outputs in the system are Poisson streams. On the basis of the ordinary Poisson flows the paper justifies the relationships for calculating the false alarms of the system with uncorrelated and correlated noise in the channels. The paper also justifies the relationships for performance of multichannel combined systems with positional analyzers of the channels states. Based on the obtained relationships was calculated the average coincidence frequency of the extended pulses of the channel response in a dualchannel system, depending on the noise cross-correlation coefficient with different extended pulse durations and relative response thresholds in the channels. The impact of cross-correlation noise has been analysed. The obtained results enable us to examine the performance of the multichannel autonomous information systems with positional analyzers of the signal states at the outputs of channels operating under uncorrelated and correlated noise.

Frequency and bias dependent modeling of induced gate noise and cross-correlation noise in 40 nm metal-oxide-semiconductor field-effect transistors

With the development of down-scaling of CMOS technology for low power, mixed-signal, and high frequency applications, the optimal high frequency performance is shown to be shifted from lower moderate inversion toward weak inversion regimes. High-frequency noise model is a prerequisite for designing the radio frequency and millimeter-wave circuits, and is essential for the noise analysis of nanoscale metal-oxide-semiconductor field-effect transistors (MOSFETs). In this paper, based on the physical structure of 40 nm MOSFET and by considering the drift-diffusion equation and charge conservation law, accurate physics-based unified high-frequency noise model is developed for induced gatecurrent noise and its cross-correlation with drain-current noise under different bias conditions, which is used to describe the frequency and bias dependence of 40 nm MOSFET from weak inversion to strong inversion regime. Especially, the effective gate overdrive is explicitly included in unified noise model to offer excellent accuracy, continuity and smoothness, and this makes the proposed analytical models convenient to directly reflect the relationship between the noise model and bias condition. Besides, new analytical model is derived for the induced-gate current noise and its cross-correlation term of weakly inverted MOSFET. These simple expressions not only serve as the asymptotic limit for the validation of the proposed physics-based unified model, but also provide a clearer insight into and better understanding of the gate noise behavior and their cross-correlation in the weak-inversion region. Moreover, in terms of the proposed subthreshold noise model, the charge of weak inversion rather than the normal effective channel thickness approximation is involved. In this way, the model accuracy can be improved. Furthermore, a detailed derivation and discussion are presented by analyzing the physics-based noise generation mechanism of transistor including the channel thermal noise and the shot noise based on the small-signal equivalent circuit of the 40 nm MOSFET device. Using these expressions it is possible to extract the values of all the noise model parameters directly from measurement. The proposed model is demonstrated by using noise data from both measurement and the noise simulation. Excellent agreement between simulated and measured noise data shows that the proposed model can be used for predicting the noise behavior of 40 nm MOSFET under different dimensions and operating conditions. The applicability of reported model for drain-current noise is also verified. As far as small-signal (i.e., linear) bias-dependent operation is concerned, it is shown how most of the findings of this work can also be used to predict the data of long channel devices in the strong-inversion regimes.

Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements

This paper deals with state estimation problem for linear uncertain systems with correlated noises and incomplete measurements. Multiplicative noises enter into state and measurement equations to account for the stochastic uncertainties. And one-step autocorrelated and cross-correlated process noises and measurement noises are taken into consideration. Using the latest received measurement to compensate lost packets, the modified multi-step random delays and packet dropout model is adopted in the present paper. By augmenting system states, measurements and new defined variables, the original system is transformed into the stochastic parameter one. On this basis, the optimal linear estimators in the minimum variance sense are designed via projection theory. They depend on the variances of multiplicative noises, the one-step correlation coefficient matrices together with the probabilities of delays and packet losses. The sufficient condition on the existence of steady-state estimators is then given. Finally, simulation results illustrate the performance of the developed algorithms.

Stochastic multiresonance induced by correlated noise from a gene transcriptional regulatory system driven by amplitude-modulated signal

We analyzed the signal-to-noise ratio (SNR) theoretically by studying a gene transcriptional regulatory model driven by additive amplitude modulation signal and cross-correlated noises. By using the general two-state approach for this model, we obtained the analytic expression of SNR under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the periodic signal. More interestingly, the phenomenon of stochastic multiresonance can be observed in the curve of the SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation coefficient for controlling the SNR under fixed noise intensity, as well as a guidance in the design for the related experiments.

Modeling Channel Thermal Noise and Induced Gate Noise in Junctionless FETs

This paper presents analytical expressions for channel noise, induced gate noise (IGN), and cross-correlation noise in a long-channel junctionless (JL) double-gate MOSFET. The analytical relationships, which have been derived from a coherent charge-based model, are validated with technology computer-aided design simulations, and the figures of merit have been compared with the inversion mode FETs. For a given current, we found that the channel thermal noise is very similar for both architectures, whereas the IGN is slightly decreased in the JL FETs.

Time Dependence of Entropy Flux and Entropy Production for a Time-Delayed Dynamical System Driven by Cross-Correlated Noises

We study the relaxation of a dissipative dynamical system with time delay and cross-correlated noises in the absence and presence of a non-equilibrium constraint in terms of the information entropy flux and production for the case of small delays. Based on the delay Fokker-Planck equation and the entropy balance equation, the time dependence of the entropy flux and entropy production of the system is derived when the delay time is small. Our calculation shows how the relaxation time depends on the delay time. We also consider how the non-equilibrium constraint is affected by the system parameters, such as the cross-correlation intensity, strength of dissipation, and delay time. The interplay among the non-equilibrium constraint, dissipation, time delay, and inter-correlated noises reveals some interesting extremal nature in the time dependence of the entropy flux and entropy production.

Relaxation Times and Correlation Functions under the Influence of Cross-Correlated Colored Noises for the Model of Resonant Tunneling

Relaxation Times and Correlation Functions under the Influence of Cross-Correlated Colored Noises for the Model of Resonant Tunneling

STOCHASTIC MULTIRESONANCE INDUCED BY ADDITIVE AMPLITUDE MODULATION SIGNAL AND NOISE IN A GENE TRANSCRIPTIONAL REGULATORY MODEL

We investigate the stochastic resonance (SR) and stochastic multiresonance phenomena in a gene transcriptional regulatory system driven by additive amplitude modulation signal and cross-correlated noise. By using the general two-state approach, we obtained the analytic expression of signal-to-noise ratio (SNR) under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the signal. More interestingly, stochastic multiresonance can be observed in the curve of SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation noise for controlling SNR under fixed noise intensity in the study of stochastic gene transcriptional regulatory process.