Invariance property of Gaussian signals : A new interpretation, extension and applications

摘要: This paper addresses the invariance property of Gaussian signals, originally derived by Bussgang, which characterizes input/output moment relation a hybrid nonlinear (HNM) estimator based on zero-memory nonlinearity (ZMN) g(y). Some re-derivations this are reviewed, and an original, direct, simple proof is presented (Appendix 1). The then derives new interpretation (Theorem 1) that shows moment-sense equivalence between g(y) linear mappingh1(y) whose coefficients a0 a1 completely characterized in terms ofg(y) shown to be optimal mean square error (MSE) sense. A direct very interesting byproduct relationship input output HNM involved. generalized 2) signals other than Gaussian, resulting infinite cumulant series expansion output, all ofg(y). Applications Theorem 1 some ZMNs commonly used signal processing control theory clearly illustrate power elegance property. Finally, conclusions given.