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

该项目的目标是开发高效的迭代算法，用于存在非高斯干扰的系统设计（特别是通信系统），并将这些算法扩展到有效适应非平稳环境的系统设计中。具有非高斯输入的系统设计的解析解通常是难以处理的，因此经常需要数值方法。随机逼近算法是一种有效的设计方案，它只需要在一组迭代的系统参数下估计系统误差。该项目将重要性抽样的概念与现有的随机近似算法相结合，大大减少了参数化系统和输入设计中所需的总计算量。在输入是非平稳的情况下，开发了一种自修改重要性采样策略，用于这些算法的自适应实现。这需要将估计理论中的技术与来自静态系统的重要性抽样策略相结合。特别有趣的例子是在平稳和非平稳非高斯背景噪声存在下运行的通信系统。初步结果表明，对于标量设计情况，设计错误率降低的检测系统所节省的计算量是无限的。

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.