CAREER: A Unified Approach to Iterative and Universal Methods for Signal Processing and Communications

摘要：将理论方法应用于实际系统中最困难的一个方面是如何将现实问题转化为可管理的理论模型。通常，问题的许多方面要么难以简洁地建模，要么是完全未知的。例如，在许多商业和军事应用中，需要能够在广泛的可能环境中工作的紧凑、高效的设备。这项研究正在开发一个框架，用于明确处理无线和水声通信、信号估计和检测以及预测等许多重要领域的这种不确定性。特别是，这项研究利用了一些新的和令人兴奋的方法来处理信息理论文献中的不确定性和复杂性。不确定性和可变性的问题正在通过开发健壮的信号处理方法来解决，这些方法是由无损源编码和竞争性在线算法的当代应用所驱动的。这种通用算法可以为处理各种自适应估计问题中的不确定性提供一种特别有效的方法。这些包括通用估计和均衡策略，这些策略不需要信号或信道的先验知识，就可以渐近地实现调谐到所用信号或信道的最佳滤波器的性能。通过使用图形模型和迭代处理技术来研究涡轮码和低密度奇偶校验码，这些算法可以实际实现并集成到复杂性相对较低的大型系统中。诸如因子图之类的迭代算法为通常单独处理的各种任务的联合优化提供了一个自然框架。由于迭代译码和涡轮码的近容量实现性能，本研究正在开发实用、高效的迭代算法，用于具有码间干扰的单用户和多用户信道数字通信的联合检测、估计和译码。该研究项目的教育部分包括在本科和研究生阶段的重要课程开发，以及对研究生指导的大力投资。这项研究的一个关键方面包括本科生积极参与正在进行的研究。Singer努力水平声明：在推荐的支持水平下，Andrew Singer将尽一切努力满足本项目的原始范围和努力水平。

Singer ABSTRACT:One of the most difficult aspects of the application of theoretical methods to practical systems lies in the translation of a real-world problem into a manageable theoretical model. Often there are a number of aspects of the problem that are either difficult to model concisely, or that are completely unknown. For example, in many commercial and military applications, compact, efficient devices are desired that can operate in a wide range of possible environments. This research is developing a framework for explicitly dealing with such uncertainties in a number of important areas such as wireless and underwater acoustic communications, signal estimation and detection, and forecasting.In particular, this research leverages some of the new and exciting methods for dealing with uncertainty and complexity from the information theory literature. Problems of uncertainty and variability are being addressed through the development of robust signal processing methods motivated by contemporary applications in lossless source coding and competitive on-line algorithms. Such universal algorithms can provide a particularly effective means for handling uncertainty in a variety of adaptive estimation problems. These include universal estimation and equalization strategies which without prior knowledge of the signal or channel can asymptotically achieve the performance of the optimal filter tuned to the signal or channel in use. These algorithms can be practically implemented and integrated into larger systems with relatively low complexity through the use of graphical models and iterative processing techniques used in the study of turbo codes and low-density parity check codes. Iterative algorithms such as factor graphs provide a natural framework for the joint optimization of a variety of tasks typically treated separately. Motivated by the near-capacity achieving performance of iterative decoding and turbo-codes, this research is developing practical, efficient iterative algorithms for joint detection, estimation and decoding of digital communications over single and multi-user channels with inter-symbol interference. The educational component of this research program includes significant curriculum development at both the undergraduate and graduate levels, and a strong investment in the mentoring of graduate students. A key aspect of this research includes the active involvement of undergraduates in ongoing research.Singer LEVEL OF EFFORT STATEMENT:At the recommended level of support, Andrew Singer will make every attempt to meet the original scope and level of effort of this project.