Adaptive Bistable Stochastic Resonance Based Weak Signal Reception in Additive Laplacian Noise

Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.

Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise

This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio （SNR） is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.

Stochastic resonance in a stochastic bistable system with additive noises and square-wave signal

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated.

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density（PSD） and signal-to-noise ratio（SNR） are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.

Bistable Stochastic Resonance Enhanced 4-ary PAM Signal Detection under Low SNR

To boost the performance of 4-ary pulse amplitude modulated(PAM) at low signal-to-noise ratio(SNR), bistable stochastic resonance(BSR) system is introduced into digital communications system and get a reliable signal detection scheme. In this paper, we first analyse BSR system for different amplitudes of 4-ary PAM signals. The steadystate of the bistable system will be statistically distinct, and the feasibility of the proposed detection scheme is confirmed. On this basis, we present a detailed study on steady-state transitions of the BSR system, and an explicit expression of the bistable system parameters is derived. By setting the bistable system parameters, bistable system, 4-ary PAM signal, and noise reach the resonance state, and the BSR-based detection scheme is implemented. Moreover, we derive an analytical expression to calculate the symbol error rate(SER) of 4-ary PAM signals with the BSR-based detection under additive white Gaussian noise(AWGN). Finally, the simulation results validate that BSR-based detection scheme can improve the detection performance while efficiently reducing the symbol error rate.

Control of stochastic resonance in bistable systems by using periodic signals

According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance.

Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.

Effects of error feedback on a nonlinear bistable system with stochastic resonance

In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing.

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.

Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system

Coupling-induced logical stochastic resonance(LSR) can be observed in a noise-driven coupled bistable system where the behaviors of system can be interpreted consistently as a specific logic gate in an appropriate noise level. Here constant coupling is extended to time-varying coupling, and then we investigate the effect of time-varying coupling on LSR in a periodically driven coupled bistable system. When coupling intensity oscillates periodically with the same frequency with periodic force or relatively high frequency, the system successfully yields the desired logic output. When coupling intensity oscillates irregularly with phase disturbance, large phase disturbance reduces the area of optimal parameter region of coupling intensity and response speed of logic devices. Although the system behaves as a desired logic gate when the frequency of time-periodic coupling intensity is precisely equal to that of periodic force, the desired logic gate is not robust against tiny frequency difference and phase disturbance. Therefore, periodic coupling intensity with high frequency ratio is an optimal option to obtain a reliable and robust logic operation.

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper,we study the phenomenon of stochastic resonance(SR)in a periodically driven bistablesystem with correlations between multiplicative and additive white noise terms when there are two different kinds oftime delays existed in the deterministic and fluctuating forces,respectively.Using the small time delay approximationand the theory of signal-to-noise ratio(SNR)in the adiabatic limit,the expression of SNR is obtained.The effects ofthe delay time γ in the deterministic force,and the delay time θ in the fluctuating force on SNR are discussed.Based onthe numerical computation,it is found that:(i)There appears a reentrant transition between one peak and two peaksand then to one peak again in the curve of SNR when the value of the time delay θ is increased,(ii)SR can be realizedby tuning the time delay γ or θ with fixed noise,i.e.,delay-induced stochastic resonance(DSR)exists.

Stochastic Resonance in a Bistable System with Time-Delayed Feedback Loops

<Abstract>The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplicative Gaussian coloured noise and additive Gaussian white noise is investigated.Firstly,the analytic expression of the quasi-steady distribution function Ps(x,t) is derived by applying the unified eoloured noise approximation and the Novikov Theorem;Secondly,the expression of the signal-to-noise ratio (SNR) is obtained in the adiabatic limit to quantify the stochastic resonance.Finally,the effects of the linear coefficient a,the nonlinear coefficient b,the linear time-delayed feedback coefficient c and the delay time τ on P_s(x,t) and SNR~± are discussed.It is found that the effects of the linear coefficient and the nonlinear coefficient,the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient,the positive delayed time and the negative delayed time on P_s(x,t) and SNR~± are different,respectively.This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.

Signal modulating noise effect in bistable stochastic resonance systems and its analog simulation

The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.

Application of Stochastic Resonance Signal Recovery

Stochastic resonance（SR） enhances the nonlinear system behavior with the assistance of noise, including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum, while the time-waveform is distorted. The distortion analysis was made both from the particle＇s dynan-fics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle＇s motion track in the bistable system and the suggested recovery system, the influences of noise and system parameters on the recovery course were discussed. Moreover, the pulse distortion appearing the recovery waveform caused by the particle＇s transitions at the bistable potential＇ inflexions was explained. Due to different characteristics, cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system＇s response to the SR output. Meanwhile, the recovery system is optional, as parameter-tuned or parameter-fixed. Since the method requires no average processing, it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged ha noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly, the system parameters are tuned in a wider range than the traditional SR processing methods.

Enhanced Detection of Rolling Element Bearing Fault Based on Stochastic Resonance

Early bearing faults can generate a series of weak impacts. All the influence factors in measurement may degrade the vibration signal. Currently, bearing fault enhanced detection method based on stochastic resonance（SR） is implemented by expensive computation and demands high sampling rate, which requires high quality software and hardware for fault diagnosis. In order to extract bearing characteristic frequencies component, SR normalized scale transform procedures are presented and a circuit module is designed based on parameter-tuning bistable SR. In the simulation test, discrete and analog sinusoidal signals under heavy noise are enhanced by SR normalized scale transform and circuit module respectively. Two bearing fault enhanced detection strategies are proposed. One is realized by pure computation with normalized scale transform for sampled vibration signal, and the other is carried out by designed SR hardware with circuit module for analog vibration signal directly. The first strategy is flexible for discrete signal processing, and the second strategy demands much lower sampling frequency and less computational cost. The application results of the two strategies on bearing inner race fault detection of a test rig show that the local signal to noise ratio of the characteristic components obtained by the proposed methods are enhanced by about 50% compared with the band pass envelope analysis for the bearing with weaker fault. In addition, helicopter transmission bearing fault detection validates the effectiveness of the enhanced detection strategy with hardware. The combination of SR normalized scale transform and circuit module can meet the need of different application fields or conditions, thus providing a practical scheme for enhanced detection of bearing fault.

Frequency modulated weak signal detection based on stochastic resonance and genetic algorithm

Stochastic resonance system is subject to the restriction of small frequency parameter in weak signal detection,in order to solve this problem,a frequency modulated weak signal detection method based on stochastic resonance and genetic algorithm is presented in this paper. The frequency limit of stochastic resonance is eliminated by introducing carrier signal,which is multiplied with the measured signal to be injected in the stochastic resonance system,meanwhile,using genetic algorithm to optimize the carrier signal frequency,which determine the generated difference-frequency signal in the lowfrequency range,so as to achieve the stochastic resonance weak signal detection. Results showthat the proposed method is feasible and effective,which can significantly improve the output SNR of stochastic resonance,in addition,the system has the better self-adaptability,according to the operation result and output phenomenon,the unknown frequency of the signal to be measured can be obtained,so as to realize the weak signal detection of arbitrary frequency.

Adaptive stochastic resonance method for weak signal detection based on particle swarm optimization

In order to solve the parameter adjustment problems of adaptive stochastic resonance system in the areas of weak signal detection,this article presents a new method to enhance the detection efficiency and availability in the system of two-dimensional Duffing based on particle swarm optimization.First,the influence of different parameters on the detection performance is analyzed respectively.The correlation between parameter adjustment and stochastic resonance effect is also discussed and converted to the problem of multi-parameter optimization.Second,the experiments including typical system and sea clutter data are conducted to verify the effect of the proposed method.Results show that the proposed method is highly effective to detect weak signal from chaotic background,and enhance the output SNR greatly.

Fluctuations and dissipations in stochastic energetic resonance

By analyzing the fluctuations and dissipations of a Brownian particle colliding with the molecules in a fluid, the work exchanged between the Brownian particle constrained in a bistable potential well and an external periodic force is investigated. Characters of the stochastic energetic resonance are found and studied at different intensities of fluctuations and dissipations. The microscopic mechanism of energy exchange between the Brownian particle and the external force is revealed. The method used in this study provides a novel way of controlling the stochastic energetic resonance.

Effect of Asymmetry in a Bistable System Subject to Multiplicative Colored Noise

By the method of the stochastic energetics,we investigate the stochastic resonance (SR) phenomenon of anoverdamped Brown particle in an asymmetric bistable potential,driven by external periodical signal and multiplicativenoise.The expressions have been obtained for the quasi-steady-state probability distribution function.It is found thatthe input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of thenoise strength,whereas the IE turns to be a monotonic function of the correlation time of the noise.The effect ofpotential asymmetry is also studied on SR and IE.

Delay induced transitions in an asymmetry bistable system and stochastic resonance

The delay Fokker-Planck equation is given for an asymmetry bistable system with correlated Gaussian white noises. The small delay approximation based on the probability density approach is used and the approximate stationary probability density function is obtained. The phenomenon of delay induced transitions is found. When a weak periodic signal is added, the phenomenon of stochastic resonance is investigated. Expression of the signal-to-noise ratio (SNR) is obtained by using the two-state theory. It is shown that the time delay can suppress or promote the stochastic resonance phenomenon.