Optimum Detection and Signal Design for Channels With Non- but Near-Gaussian Additive Noise

Abstract

Absrract -The Gram-Charlier series representation of the noiseprobability density function is used to determine an optimum detector for signals in norr-Gauaaian but near-Gaussian (NGNG) noise. Solutions are obtained for coherent and incoherent detection.Optimal detectors for several typical transmitting systems are determined.Generally these detectors consist of the standard detector for Gaussian noise with the addition of a few, not too sophisticated, nonlinear elements. The performance of a detector, specified by the upper bound on the probability of error, is assessed and is seen to depend on the signal ahape, the time-bandwidth product, and the sigml-to-noise ratio. The optimal signal to minimize the probability of error is determined and is seen to result as a solution to Duffing's aecondarder nonlinear differential equation.

John Barratt Moore 1941–2013

“…Within the control systems area, there was for example work on linear-quadratic optimization problems, Lyapunov stability, circle and Popov criteria and positive real transfer functions; see for example [8], [24], [25], [10], [38], [6], [15], [7], [16], [11], [27]. In the area of signal processing, there was work on Kalman filtering and its derivatives, detection of frequency modulated (FM) signals, spectral factorization, and pulse frequency modulation; see for example [42], [45], [46], [54], [57], [64], [66], [67], [69]. [71], [72], [76].…”