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

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>