Noise-Improved Bayesian Estimation With Arrays of One-Bit Quantizers

Abstract

Abstract-A noisy input signal is observed by means of a parallel array of one-bit threshold quantizers, in which all the quantizer outputs are added to produce the array output. This parsimonious signal representation is used to implement an optimal Bayesian estimation from the output of the array. Such conditions can be relevant for fast real-time processing in large-scale sensor networks. We demonstrate that, for input signals of arbitrary amplitude, the performance in the estimation can be improved by the addition of independent noises onto the thresholds in the array. These results constitute a novel instance of the phenomenon of suprathreshold stochastic resonance in arrays, by which nonlinear transmission or processing of signals with arbitrary amplitude can be improved through cooperative coupling with noise.

Exploring $Bona~Fide$ Optimal Noise for Bayesian Parameter Estimation

“…Proof of Theorem 2 is presented in Appendix A. Although this theorem leads to a negative aspect of the added noise to the optimal MMSE estimatorθ ms (x), it also indicates the possibility of noise benefits in some suboptimal estimators beyond the restricted conditions of [12], [20], [22]- [25], [27], [30], [31], [33], [36]- [43], [45]- [49]. In practice, the MMSE estimatorθ ms (x) is usually too computationally intensive to implement [51], [54], thus we will exploit the optimal added noise in some easily implementable suboptimal estimators as follows.…”

“…For the first situation, the performances of some easily implemented suboptimal estimators were shown to be substantially improved by exploiting the benefits of added noise [22], [32], [34]- [38], [42], [46]- [49]. In the second situation, rich results from utilizing various kinds of noise have been reported for quantized observations [1], [2], [12]- [14], [20], [21], [23]- [25], [27], [30], [31], [33], [36]- [43], [45]- [49]. For instance, Papadopoulos et al developed a methodology of additive control input before signal quantization at the sensor to achieve the maximum possible performance for quantizer-based networks [23].…”

“…Modeling the suprathreshold stochastic resonance as stochastic quantization, McDonnell et al systematically studied the optimal linear and nonlinear decoding schemes associated with the information bound on the MSE [12]. The optimal Bayesian estimators constructed by the quantizer outputs were also explicitly derived, and a basic mechanism was provided for the performance improvement of optimal Bayesian estimator by increasing the noise level [24], [25], [30], [31].…”

Noise Benefits in Combined Nonlinear Bayesian Estimators

“…Recently, the noise benefit in nonlinear estimators [4]- [18] and detectors [19]- [33] has attracted great attentions of researchers in the field of signal processing, because the accuracy of an estimator and the detectability of a detector can be enhanced by design via intentionally adding noise. Sufficient or necessary conditions have been derived for the existence of the optimal added noise PDF [6]- [8], [16], [23]- [26], and the explicit or approximate forms of optimal added noise PDFs [7]- [13], [15], [16] have also been of great interest.…”

“…Sufficient or necessary conditions have been derived for the existence of the optimal added noise PDF [6]- [8], [16], [23]- [26], and the explicit or approximate forms of optimal added noise PDFs [7]- [13], [15], [16] have also been of great interest. Among these investigations, it was found that a parallel array of estimators can benefit from mutually independent added noise components in comparison to a single estimator [4], [5], [7]- [13]. From the parameter estimation standpoint, Uhlich [7] proposed a novel noise-enhanced estimator by averaging estimates from the same observation added by artificial noise components, and discussed its superiority over the original estimator and the noise-modified estimator derived by Chen et al [6].…”