Effects of stochastic resonance for linear-quadratic detector

In this paper, the stochastic resonance (SR) effects of the fixed linear-quadratic (L-Q) detector in binary hypothesis testing problems is investigated. The effects include the improvement of the overall performance of the detector wherein the output signal-to-noise ratio (SNR) of receiver and the detection probability (PD) are increased and the false-alarm probability (PFA) is reduced at the same time. The SNR of a noise modified detector is derived. Since the improvement of the SNR does not mean the improvement of detection performance, the noise enhanced detection performance in terms of PFA and PD are discussed graphically and elaborated through an example of Gaussian background noise. Furthermore, the conditions are deduced to determine whether the overall performance of the detector can be improved or not. In addition, the form of the suitable noise probability distribution function (PDF) is determined and the PDF of noise that satisfies the conditions to improve the overall performance of detector are derived. Finally, an illustrative example is presented to verify the theoretical results.