On transformation noise as a model for correlated noise

The authors consider transformation noise processes, which are those that can be generated by passing an underlying noise process through a memoryless invertible nonlinearity. They point out the close relationship between the dependency structure of the transformation noise and that of the underlying noise. The use of the class of transformation noise generated from multivariate Gaussian background noise to approximate other noise processes is proposed. This class has tractable, closed-form joint densities. Some ad hoc ways to find the parameters in the model are suggested. It is shown that the nonlinearities in the optimal detector, in the case of transformation noise with a mixture marginal density are approximately the sum of the nominal term and a term proportional to the parameter ∈