Quantizer noise benefits in nonlinear signal detection with alpha-stable channel noise

Two new theorems show how deliberately adding quantizer noise can improve statistical signal detection in array-based nonlinear correlation detection even in the case of infinite-variance alpha-stable channel noise. The first theorem gives a necessary and sufficient condition for such quantizer noise to increase the detection probability for a fixed false-alarm probability. The second theorem shows that the array must contain more than one quantizer for a stochastic-resonance noise benefit and that the noise benefit improves in the small-quantizer noise limit as the number of array quantizers increases. It further shows that symmetric uniform quantizer noise gives the optimal noise benefit among all symmetric scale-family noise types.