Nonlinear statistics to improve signal detection in generalized Gaussian noise

This paper compares the nonlinear sum statistic with the standard linear statistic and with the nonlinear mean statistic that a detector can compute from multiple noisy data in a binary decision problem based on a maximum a posteriori probability (MAP) criterion. Like the nonlinear mean detector, the detection performance of the nonlinear sum detector comes close to that of the standard linear detector for Gaussian noise. For generalized Gaussian noise, it can also obtain a better detection performance compared to that of the standard linear detector, especially for those noises which concentrate their values heavily around the zero mean. This paper also gives a tentative explanation why the nonlinear detectors can improve signal detection better as the exponent parameter in the probability density function of generalized Gaussian noise becomes smaller.