Effects of additional independent noise in binary composite hypothesis-testing problems

Performance of some suboptimal detectors can be improved by adding independent noise to their observations. In this paper, the effects of adding independent noise to observations of a detector are investigated for binary composite hypothesis-testing problems in a generalized Neyman-Pearson framework. Sufficient conditions are derived to determine when performance of a detector can or cannot be improved via additional independent noise. Also, upper and lower limits are derived on the performance of a detector in the presence of additional noise, and statistical characterization of optimal additional noise is provided. In addition, two optimization techniques are proposed to calculate the optimal additional noise. Finally, simulation results are presented to investigate the theoretical results.