Nonlinear sum statistic to improve signal detection in Gaussian mixture noise

This paper discusses the binary decision problem in Gaussian mixture noise by the nonlinear sum statistic (nonlinear detector) based on a Maximum a posteriori probability (MAP) criterion. When the signal is suprathreshold, the nonlinear detector can obtain a smaller the probability of error Per compared to the standard linear detector which can minimize Per in Gaussian noise. When the signal is subthreshold, the nonlinear detector can also obtain a smaller Per compared to the standard linear detector for Gaussian mixture noise with stronger noise intensity. Noise can improve signal detection, i.e., Stochastic resonance (SR) exists. According to the variation of the Probability density function (PDF), we discuss how the noise parameters affect the detection performance, and why SR occurs for the subthreshold signal. These results confirm further that there are some simple nonlinear statistics that can improve signal detection in non-Gaussian noise, and also show the robustness of SR to noise.