On optimizing importance sampling simulations

The importance sampling technique can result in large savings in simulation time for simulation of tail probabilities, but only when performed optimally. In this paper, we derive criteria for optimal importance sampling simulation of an arbitrarily weighted sum of independent exponential variates. We illustrate the use of importance sampling for false alarm threshold settings in square law integrators and MTI delay line cancelers in the presence of gaussian spectrum correlated clutter. For these systems, importance sampling simulation can not be optimally performed. Hence, we apply a linear transformation to decorrelate the clutter and perform importance sampling simulation optimally on the transformed system.