From the point of information theory, the baseband binary pulse amplitude modulated (PAM) signals transmission, via tuning the nonlinear receiver's parameters, is studied over an additive white Gaussian noise (AWGN) channel. It is demonstrated that the channel capacity of baseband binary communication systems, for a given signal added noise, can be maximized by optimal designed receivers. This new form of stochastic resonance (SR) is referred to as parameter-induced stochastic resonance (PSR) in a broad sense. PSR effect does not require that the input signals are subthreshold. The characteristic behavior of channel capacity versus transmission bit rate is also studied. For reproducing the original binary signals more correctly, time scale transformation method and the approach of ensemble average probability of error bits are introduced. We observe a marked enhancement of the channel capacity for binary PAM signals transmission by PSR in numerical simulations. With this theory and method, the practical applications are considered.
We analyze the parametric estimation that can be performed on a signal buried in noise based on the parsimonious representation provided by a parallel array of threshold devices. The Fisher information contained in the array output about the input parameter is used as the measure of performance in the estimation task. For estimation on a suprathreshold input signal, we establish that enhancement of the Fisher information can be obtained by addition of independent noises to the thresholds in the array. Similar improvement by noise is also shown to be possible for the estimation error of the maximum likelihood estimator. These results extend the applicability of the recently introduced nonlinear phenomenon of suprathreshold stochastic resonance.
Two methods of realizing aperiodic stochastic resonance (ASR) by adding noise and tuning system parameters in a bistable system, after a scale transformation, can be compared in a real parameter space. In this space, the resonance point of ASR via adding noise denotes the extremum of a line segment, whereas the method of tuning system parameters presents the extrema of a parameter plane. We demonstrate that, in terms of the system performance, the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system. Besides, adding noise can be viewed as a specific case of tuning system parameters. Further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold, and the conventional ASR effects might not occur in some suprathreshold optimal systems.
Conventional stochastic resonance can be viewed as an amplitude effect, in which a small (subthreshold) input signal receives assistance from noise to trigger a stronger response from a nonlinear system. We demonstrate another mechanism of improvement by the noise, which is more of a temporal effect. An intrinsically slow system has difficulty to respond to a fast (suprathreshold) input, and the noise plays a constructive role by spurring the system for a more efficient response. The possibility of this form of stochastic resonance is established and studied here in a double-well bistable dynamic system, driven by a suprathreshold random binary signal, with the noise accelerating the switching between wells.
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