Detection of a determinate signal after random reflections

A mathematical model of a known signal reflected randomly from an object (as in active-detection techniques such as radar and sonar or in geophysics) is developed. Probability distributions for the random signal are obtained, and the likelihood ratio is calculated for the case of Gaussian white noise. An optimum receiver comprising a matched filter, a series of filters are representing a nonlinear device, and a time integrator is described. It is shown that for the case of low signal-to-noise ratio, the nonlinear device is well approximated by a linear and a quadratic filter.