The application of importance sampling (E)to the problem of detecting random signals is considered. It is well known that conventional importance sampling (CIS) which uses a scaled IS density suffers from a dimensionality effect when it is used to simulate systems that detect a known signal in additive noise. Our fundamental result shows that CIS is guaranteed to give an IS gain when used to simulate the detection-of-scale problem. Further, a numerical example for the generalized Gaussian family is provided where the IS gain from CIS actually increases with the dimensionality of the problem.

Parametric adaptive importance sampling (IS) algorithms that adapt the IS density to the system of interest during the course of the simulation are discussed. This approach removes the burden of selecting the IS density from the system designer. The performance of two such algorithms is investigated for both linear and nonlinear systems operating in Gaussian noise. In addition, the algorithms are shown to converge to the optimum improved importance sampling density for the special case of a linear system with Gaussian noise.>