Importance sampling for detection of scale problems

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.