A Nonlinear Optimum-Detection Problem: Theoretical Solution and Simulation

An approximate log-likelihood ratio is derived for detecting a deterministic signal in linear stationary and nonlinear Gaussian noise. The new aspect of this detection problem is the inclusion of the nonlinear Gaussian noise which takes a quadratic form in the linear (stationary) Gaussian noise and a certain interaction between the signal and the linear noise, such as modulation of the signal by the noise, in addition to the usual white background noise. Such a detection problem may arise in radar where the transmitted signal is reflected by clutter or random particles as well as by a target. The primary reflection by the clutter produces the linear Gaussian noise and the secondary reflection produces the nonlinear noise. It is assumed that the second is an order of magnitude smaller than the first, and the approximation used in the derivation is based on this assumption. The secondary reflection (by the clutter) of the target-reflected signal (i.e., the signal) produces the signal-noise interaction.