The optimal power law for the detection of a Gaussian burst in a background of Gaussian noise

摘要

The optimal power law is analyzed using characteristic function techniques. For a signal occupying more than about lambda =0.5 of the integration time, the standard square-law energy detector is close to optimal (among the class of power-law detectors). The optimal power is nu *=3 for lambda approximately=0.3, increasing rapidly as lambda decreases below this value. The SNR advantage of the optimal processor is not significant for lambda <0.5, but exceeds 1 dB for lambda >0.1. It is further shown that a cube-law processor yields close-to-optimal results over a wide range of lambda . For the representative values of probability of false alarm (P/sub fa/) and probability of detection (P/sub d/) chosen in the performance analysis, the results do not depend strongly on the number of points N that are integrated. Calculations performed for other values of P/sub d/ and P/sub fa/ also show that the results do not depend strongly on the value of these two parameters.