A nonlinear optimum-detection problem. II. Simple numerical examples

For pt.I see ibid., vol.36, no.2, p.347-57 (1990). Simple numerical examples are presented to illustrate the effect of the previously derived nonlinear filters for combating nonlinear Gaussian noise in detecting deterministic signals. The nonlinear Gaussian noise is expressed as a quadratic form in stationary Gaussian noise that is also present in the data, together with white Gaussian noise. Thus the nonlinear noise is referred to as the quadratic noise and the stationary noise as the linear noise. The former is assumed to be an order of magnitude smaller than the latter. When the signal overlaps with both the linear and the quadratic noise, use of both nonlinear filters for the small quadratic-noise region improves the detection performance well beyond the optimum level achievable in the absence of the quadratic noise. As the quadratic noise increases, this improvement diminishes and the performance eventually deteriorates below the level achievable by the linear and the first nonlinear filter combination