RIA: Efficient ALgorithms for the Design of Systems with non-Gaussian Inputs

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The objectives of this project are to develop highly efficient iterative algorithms for use in system design (especially communication systems) in the presence of non-Gaussian disturbances, and to extend these algorithms to the design of systems which efficiently adapt to nonstationary environments. Analytic solutions to the design of systems with non-Gaussian inputs are typically intractable, therefore numerical methods are frequently required. Stochastic approximation algorithms are effective design alternatives which require only estimates of the system error at an iterated set of system parameters. This project merges concepts from Importance Sampling with existing stochastic approximation algorithms to dramatically reduce the total required computations in the design of parameterized systems and inputs. In the situation where the inputs are non-stationary, a selfmodifying Importance Sampling strategy is developed for use with adaptive implementations of these algorithms. This requires the coupling of techniques in estimation theory with Importance Sampling strategies derived from static systems. Example of particular interest are communication systems operating in the presence of stationary and nonstationary non-Gaussian background noise. Preliminary results demonstrate that for the scalar design case, the computational savings are unbounded when designing detection systems whose error rates diminish.