Contributions to the theory of importance sampling for communication and detection systems
Importance Sampling (IS) has been widely used to reduce the simulation time of complex communication and detection systems. Although IS can potentially offer a reduction in simulation time of several orders of magnitude, the lack of theoretical results concerning the selection of the IS density prevents IS from achieving this goal in many practical instances. This work is centered around several enhancements to both the theory and practice of IS simulations. The results obtained fall into three categories: (i) Choice of the IS density for the random signal in noise problem; (ii) An asymptotic analysis of IS when the IS density is a shifted version of the noise density; and (iii) Derivation and analysis of an automated procedure for IS density selection for the known signal-in-noise problem. It is shown that using an IS density that is the same as the noise density but with a modified covariance structure provides a reduction in simulation time for systems that detect random signals in noise (HF communications, SONAR, RADAR). A second primary contribution concerns the use of IS with systems that detect a known signal in additive noise. In this case, an IS density that is a shifted version of the noise density is used. Asymptotic analysis techniques are used to show that a significant reduction in simulation time for a large class of systems (including non-linear/non-Gaussian) is achieved. The analysis identifies the asymptotically optimum shift vector and shows that the simulation time is minimized when the mode of the IS density is shifted to the mode of the unconstrained optimal IS density. In practice, the determination of the optimal shift vector is very difficult. This problem is overcome by the introduction of a class of Adaptive Importance Sampling (AIS) algorithms that iteratively optimize the shift vector. Three AIS algorithms that estimate the optimal shift vector are presented. It is shown that all of the algorithms converge to the asymptotically optimal shift and will provide a significant reduction in simulation time for a large class of systems. Empirical evidence is used to verify the theoretical results.
Stadler, John Scott, "Contributions to the theory of importance sampling for communication and detection systems" (1993). Dissertations available from ProQuest. AAI9331842.