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

The Gram-Charlier series representation of the noiseprobability density function is used to determine an optimum detector for signals in non-Gaussian 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 shape, the time-bandwidth product, and the signal-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 second-order nonlinear differential equation.