CIF:Small: Aspects of the Interplay Between Information Theory and Signal Processing: Extremal Problems and Applications

信号处理和无线通信中的许多关键问题都可以表述为极值优化问题，其解决方案需要仔细整合位于信息论、信号处理、统计学和优化等不同领域接口的结果。该项目解决了位于信息论和信号处理之间接口的极限优化问题。本项目主要研究两个主要问题：德布鲁因恒等式的推广和极值信息理论不等式的发展。该项目的成功完成有助于推进通信网络性能和通信信道安全性优化（评估窃听信道的保密能力，设计节能安全传输）、鲁棒通信系统设计（设计用于信道估计和同步的最小-最大最优训练序列）以及鲁棒信号估计和检测算法(用于智能电网、雷达、声纳和无线通信应用)。该项目由两个紧密交织的研究重点组成：开发De Bruijn恒等式的新扩展和应用，以及开发具有改进性能的无线通信系统设计中的新型极值信息理论不等式。在更广泛的范围内，该项目将通过开发更高效的通信网络、电网、无线传感和监测设备、生物医学设备、雷达和声纳系统等技术，对经济和社会产生积极影响。该项目还将与研究者所在大学的教育使命相结合，并将通过期刊论文、会议和讲习班演讲以及编辑期刊特刊等方式向社区广泛传播。

Many key problems in signal processing and wireless communications can be formulated as extremal optimization problems, whose solutions require a careful integration of results located at the interface of different fields such as information theory, signal processing, statistics, and optimization. This project addresses extremal optimization problems located at the interface between information theory and signal processing. This project focuses on two major research problems: extension of De Bruijn's identity and development of extremal information theoretic inequalities. Successful completion of this project helps to advance the state-of-the-art results in the optimization of communications networks performance and security of communication channels (evaluating the secrecy capacity of wiretap channels, designing of energy efficient secure transmissions), design of robust communications systems (designing min-max optimal training sequences for channel estimation and synchronization), and robust signal estimation and detection algorithms (for smart grid, radar, sonar, and wireless communications applications). This project consists of two closely intertwined research thrusts: developing new extensions and applications of De Bruijn's identity, and development of novel extremal information theoretic inequalities with applications in the design of wireless communications systems with improved performance. At a broader scale, this project will impact positively the economy and society through the development of more efficient technologies for communication networks, power grids, wireless sensing and monitoring devices, biomedical devices, and radar and sonar systems. This project will be also integrated with the educational mission of investigator's university and will be largely disseminated to the community through journal papers, conference and workshop presentations, and editing of journal special issues.