Study Of Signal Detection Algorithm Based On Noise Enhanced

From an atom to the whole universe, noise exists everywhere. It is an essential research to understand and handle the distribution and characteristic of noise in modern science. In general, noise always exists with useful signal, and more noise in the system often leads to less channel capacity, worse detectability. Nevertheless, with the development of stochastic resonance(SR) the theory, the positive role of noise in the signal detection have been recognized by people, which also called noise enhanced detection. In this paper, a noise enhanced binary hypotheses testing problem for a fixed detector is explored. Firstly, the derivation of the noise enhanced detection probability according to Neyman-Pearson criterion is introduced. Secondly, the noise enhanced model which can enhance the detection and false alarm probabilities simultaneously is investigated. Finally, the noise enhanced output signal-to-noise ratio(SNR) with improving the detection performance for a fixed linear-quadratic(L-Q) detector is studied。The main contributions of this paper can be summarized as follows:Under the premise of most researches focus on how to increase the detection probability while ignoring the importance of decreasing false alarm probability, a more practical noise enhanced model is proposed, which can which can increase the detection probability and decrease the probability at the same time. Further, the detection and false alarm probabilities with different degree of improvement can be achieved by adjusting a variable parameter in the solution of the model according to the actual need.In order to solve the new model, the minimization of false alarm probability is investigated under the constraint on detection probability, which is regarded as case ①in this paper. Besides, the maximization of detection probability without increasing false alarm probability is called case ②. The optimal additive noise probability density function(pdf) for the two cases are deduced, and the additive noise satisfied the model is solved as the randomization of the optimal noise of the two cases.The sufficient conditions which the detection performance can or cannot be improved in the case ①, ② and the model are deduced. In addition, the additive noise and the corresponding pdf which can minimize the Bayes risk based on the Bayesian and Minimax criteria in certain conditions according to the analysis of the noise enhanced model.The formulation of increasing the output SNR as well as increasing detection probability and decreasing the false alarm probability is proposed. Then the noise enhanced SNR of a L-Q detector and the corresponding conditions are derived. Further, the noise enhanced detection performance for the same detector is studied. Finally, combine with the two aspects, the conditions which can improve the output SNR and the detectability simultaneously...