Weak-Periodic Stochastic Resonance in a Parallel Array of Static Nonlinearities

Abstract

This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.

Double-maximum enhancement of signal-to-noise ratio gain via stochastic resonance and vibrational resonance

“…(24). The standardized Gaussian noise distribution is with α = 2 and a minimal Fisher information I (f ξ 0 ) of unity [42,43]. For processing a weak signal in Gaussian white noise, the optimum processor is the matched filter.…”

“…The possibility of the maximal SNR gain exceeding unity is demonstrated for weak signals corrupted by the external non-Gaussian noise. The approach by which internal noise is added has received considerable attention for enhancing the array performance within the framework of stochastic resonance [9,16,22,23,42]. However, in many practical operating devices, the internal noise type or level may be not controllable.…”

Stochastic Resonance in an Array of Dynamical Saturating Nonlinearity with Second-Order

“…Stochastic resonance (SR) establishes a phenomenon where the additive noise can enhance the performance of some certain nonlinear systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Benzi initially observed the SR effect in climate model several decades ago [1].…”

“…stochastic pooling networks [5], scalefree networks [6] and small-world networks [7].Recently, the SR in some physical system focuses on the noisy bistable system, such as the bistable fractrional-order system, asymmetric bistable system and fractional harmonic oscillator and so on [8][9][10]. The SR effects can be measured by signal-to-noise ratio, the fisher information [11], etc.…”

Stochastic Resonance for a Time-Delayed Metapopulation System Driven by Multiplicative and Additive Noises

“…Chapeau et al [23] discussed the SR phenomenon for an isolated dynamical saturating system for processing a noisy sinusoidal noise. Duan et al [24−26] investigated SR in a parallel array of nonlinear dynamical elements, the effects of fisher information as a metric of locally optimal processing on weak-periodic-signal SR. Ma et al [27] studied the weak period SR in a parallel array of static nonlinearities. Jia [28] discussed the influence of correlation noises and time delay on SR in a cancer growth system.…”