Fisher-information condition for enhanced signal detection via stochastic resonance

Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.Fabing Duan, François Chapeau-Blondeau, Derek Abbot

Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals

This paper presents a thorough evaluation of a bistable system versus a matched filter in detecting bipolar pulse signals. The detectability of the bistable system can be optimized by adding noise, i.e. the stochastic resonance (SR) phenomenon. This SR effect is also demonstrated by approximate statistical detection theory of the bistable system and corresponding numerical simulations. Furthermore, the performance comparison results between the bistable system and the matched filter show that (a) the bistable system is more robust than the matched filter in detecting signals with disturbed pulse rates, and (b) the bistable system approaches the performance of the matched filter in detecting unknown arrival times of received signals, with an especially better computational efficiency. These significant results verify the potential applicability of the bistable system in signal detection field.Comment: 15 pages, 9 figures, MikTex v2.

Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance

The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not

Weak-periodic stochastic resonance in a parallel array of static nonlinearities

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.Yumei Ma, Fabing Duan, François Chapeau-Blondeau and Derek Abbot

MSE distortion for colored noise with grouped thresholds

<div>MSE distortion versus the noise level for group sizes $M=1,~2,~3,~5,~10$, and $120$ (from top to bottom), and the array size $N=120$. Within each group, the threshold element size is equal, i.e. $N/M$, and the threshold levels are equally spaced and set as $\theta_m=m\sigma_x/(M+1)$ for $m=1,~2,\cdots,M~(M\leq N)$. (B) Colored noise with the correlation time $\tau=0.1$~s.The solid red lines correspond to the MSE distortion for stationary input, and the dashed blue lines represent the MSE distortion for non-stationary input.</div