On the detection of impulsive stochastic transients over background noise

We develop a receiver which detects impulsive stochastic transients superimposed on Gaussian background noise and show that the new detector outperforms existing square- and ν^th-law detectors. To derive the receiver, we first study the structure of the probability density function (pdf) of random variables which are formed as the sum of two or more independent, symmetric stable random variables of different characteristic exponents