Noise enhanced binary hypothesis-testing in a new framework

• The noise enhanced model, which can increase the detection probability and decrease the false-alarm probability.
• Determination of the optimal additive noise to minimize the false-alarm without decreasing detection probability.
• Derivation of the suitable additive noise corresponding to our noise enhanced model.
• Derivation of the sufficient conditions for two limit cases and our noise enhanced model.
• Determination of the additive noise probability density function which can minimize the Bayes risk.

In this paper, the noise enhanced system performance in a binary hypothesis testing problem is investigated when the additive noise is a convex combination of the optimal noise probability density functions (PDFs) obtained in two limit cases, which are the minimization of false-alarm probability (PFAPFA) without decreasing detection probability (PDPD) and the maximization of PDPD without increasing PFAPFA, respectively. Existing algorithms do not fully consider the relationship between the two limit cases and the optimal noise is often deduced according to only one limit case or Bayes criterion. We propose a new optimal noise framework which utilizes the two limit cases and deduce the PDFs of the new optimal noise. Furthermore, the sufficient conditions are derived to determine whether the performance of the detector can be improved or not via the new noise. In addition, the effects of the new noise are analyzed according to Bayes criterion. Rather than adjusting the additive noise again as shown in other algorithms, we just tune one parameter of the new optimal noise PDF to meet the different requirements under the Bayes criterion. Finally, an illustrative example is presented to study the theoretical results.