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.

Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism.We propose a novel composite multistable stochastic-resonance(NCMSR)model combining the Gaussian potential model and an improved bistable model.Compared with the traditional multistable stochastic resonance method,all the parameters in the novel model have no symmetry,the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters.The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation,the NCMSR model has a higher utilization of noise.Taking the output signal-to-noise ratio as the index,weak periodic signal is detected based on the NCMSR model in Gaussian noise andαnoise environment respectively,and the detection effect is good.The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race.The outstanding advantages of this method in weak signal detection are verified,which provides a theoretical basis for industrial practical applications.

Quantum stochastic filters for nonlinear time-domain filtering of communication signals

Principles and performances of quantum stochastic filters are studied for nonlinear time-domain filtering of communication signals. Filtering is realized by combining neural networks with the nonlinear Schroedinger equation and the time-variant probability density function of signals is estimated by solution of the equation. It is shown that obviously different performances can be achieved by the control of weight coefficients of potential fields. Based on this characteristic, a novel filtering algorithm is proposed, and utilizing this algorithm, the nonlinear waveform distortion of output signals and the denoising capability of the filters can be compromised. This will make the application of quantum stochastic filters be greatly extended, such as in applying the filters to the processing of communication signals. The predominant performance of quantum stochastic filters is shown by simulation results.

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.

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.

Stochastic Resonance in a Single-Mode Laser Driven by Quadratic Colored Pump Noise:Effects of Biased Amplitude Modulation Signal

A single-mode laser noise model driven by quadratic colored pump noise and biased amplitude modulationsignal is proposed.The analytic expression of signal-to-noise ratio is calculated by using a new linearized procedure.Itis found that there are three different typies of stochastic resonance in the model:the conventional form of stochasticresonance,the stochastic resonance in the broad sense,and the bona fide SR.

Implication of two-coupled tri-stable stochastic resonance in weak signal detection

Stochastic resonance （SR） has been proved to be an effective approach to extract weak signals overwhelmed in noise. However, the detection effect of current SR models is still unsatisfactory. Here, a coupled tri-stable stochastic resonance （CTSSR） model is proposed to further increase the output signal-to-noise ratio （SNR） and improve the detection effect of SR. The effects of parameters a, b, c, and r in the proposed resonance system on the SNR are studied, by which we determine a set of parameters that is relatively optimal to implement a comparison with other classical SR models. Numerical experiment results indicate that this proposed model performs better in weak signal detection applications than the classical ones with merits of higher output SNR and better anti-noise capability.

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.

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio （SNR） of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.

Re-scaling and adaptive stochastic resonance as a tool for weak GNSS signal acquisition

Weak global navigation satellite system（GNSS） signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance（SR）. The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.

Stochastic Resonance in Linear Region of a Single-Mode Laser: Effects of Amplitude Modulation of Signal

A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross- correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio （SNR） is calculated. It is found that the phenomena of stochastic resonance （SR） respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model： the conventional form of SR, the SR in the broad sense, and the bona fide SR.

Parameter-induced stochastic resonance with a periodic signal

In this paper conventional stochastic resonance （CSR） is realized by adding the noise intensity. This demonstrates that tuning the system parameters with fixed noise can make the noise play a constructive role and realize parameter- induced stochastic resonance （PSR）. PSR can be interpreted as changing the intrinsic characteristic of the dynamical system to yield the cooperative effect between the stochastic-subjected nonlinear system and the external periodic force. This can be realized at any noise intensity, which greatly differs from CSR that is realized under the condition of the initial noise intensity not greater than the resonance level. Moreover, it is proved that PSR is different from the optimization of system parameters.

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.

Harmonic stochastic resonance-enhanced signal detecting in NW small-world neural network

The harmonic stochastic resonance-enhanced signal detecting in Newman-Watts small-world neural network is studied using the Hodgkin-Huxley dynamical equation with noise. If the connection probability p, coupling strength gsyn and noise intensity D matches well, higher order resonance will be found and an optimal signal-to-noise ratio will be obtained. Then, the reasons are given to explain the mechanism of this appearance.

Novel Woods-Saxon stochastic resonance system for weak signal detection

We propose a joint exponential function and Woods–Saxon stochastic resonance(EWSSR)model.Because change of a single parameter in the classical stochastic resonance model may cause a great change in the shape of the potential function,it is difficult to obtain the optimal output signal-to-noise ratio by adjusting one parameter.In the novel system,the influence of different parameters on the shape of the potential function has its own emphasis,making it easier for us to adjust the shape of the potential function.The system can obtain different widths of the potential well or barrier height by adjusting one of these parameters,so that the system can match different types of input signals adaptively.By adjusting the system parameters,the potential function model can be transformed between the bistable model and the monostable model.The potential function of EWSSR has richer shapes and geometric characteristics.The effects of parameters,such as the height of the barrier and the width of the potential well,on SNR are studied,and a set of relatively optimal parameters are determined.Moreover,the EWSSR model is compared with other classical stochastic resonance models.Numerical experiments show that the proposed EWSSR model has higher SNR and better noise immunity than other classical stochastic resonance models.Simultaneously,the EWSSR model is applied to the detection of actual bearing fault signals,and the detection effect is also superior to other models.

Stochastic resonance in a gain-noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance （SR） is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio （SNR） separately with the pump noise self-correlation time τ, the noise correlation coefficient between the real part and the imaginary part of the quantum noise λq, the attenuation coefficient γ＇ and the deterministic steady-state intensity I0. In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of and λq, but also by the dependence of SNR on the laser system variables of γ and I0. Thus our investigation extends the characteristic quantity of SR proposed before.

A sign-function receiving scheme for sine signals enhanced by stochastic resonance

To address the problem that it is difficult to detect an intermediate frequency(IF)signal at the receiving end of a communication system under extremely low signal-to-noise ratio(SNR)conditions,we propose a stochastic resonance(SR)-enhanced sine-signal detection method based on the sign function.By analyzing the SR mechanism of the sine signal and combining it with the characteristics of a dual-sequence frequency-hopping(DSFH)receiver,a periodic stationary solution of the Fokker-Planck equation(FPE)with a time parameter is obtained.The extreme point of the sine signal is selected as the decision time,and the force law of the electromagnetic particles is analyzed.A receiving structure based on the sign function is proposed to maximize the output difference of the system,and the value condition of the sign function is determined.In order to further improve the detection performance,in combination with the central-limit theorem,the sampling points are averaged N times,and the signal-detection problem is transformed into a hypothesis-testing problem under a Gaussian distribution.The theoretical analysis and simulation experiment results confirm that when N is 100 and the SNR is greater than 20 dB,the bit-error ratio(BER)is less than 1.5×10^(-2) under conditions in which the signal conforms to the optimal SR parameters.

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.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance （ESR） in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio （SNR） is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.