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.
Highlights
Stochastic resonance (SR) is a nonlinear phenomenon where the transmission of a coherent signal by certain nonlinear systems can be improved by the addition of noise [1,2,3,4,5,6,7,8,9,10,11,12]
Since the signal-to-noise ratio (SNR) gain of a locally optimal nonlinearity is given by the Fisher information of the noise distribution, we demonstrated that the SNR gain of a locally optimal nonlinearity certainly exceeds unity for a weak periodic signal in additive non-Gaussian noise, and SR does not exist in an updated locally optimal nonlinearity [58]
It is demonstrated that the internal array noise components are incapable of further improving the SNR gain for locally optimal processing
Summary
Stochastic resonance (SR) is a nonlinear phenomenon where the transmission of a coherent signal by certain nonlinear systems can be improved by the addition of noise [1,2,3,4,5,6,7,8,9,10,11,12]. The establishment of a locally optimal nonlinearity needs the complete descriptions of the noise PDF and the noise level When this is not feasible, we propose instead a parallel array of suboptimal but implemented threshold nonlinearities for transmitting a weak periodic signal, in order to improve the SNR gain via the SR phenomenon. With a sufficiently large array size, the fact of the SNR gain exceeding unity is shown for a wide range of underlying noise distributions These interesting results demonstrate that a parallel array of threshold nonlinearities can be practically exploited, and is useful for nonlinear signal processing
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