Nonlinear test statistic to improve signal detection in non-Gaussian noise

We compare two simple test statistics that a detector can compute from multiple noisy data in a binary decision problem based on a maximum a posteriori probability (MAP) criterion. One of these statistics is the standard sample mean of the data (linear detector), which allows one to minimize the probability of detection error when the noise is Gaussian. The other statistic is even simpler and consists of a sample mean of a two-state quantized version of the data (nonlinear detector). Although simpler to compute, we show that this nonlinear detector can achieve smaller probability of error compared to the linear detector. This especially occurs for non-Gaussian noises with heavy tails or a leptokurtic character.