Nonlinear Signal Processing and Wireless Communications using Frames and Operators Theory

使用框架和算子理论的非线性信号处理和无线通信

• 批准号: 0807896
• 负责人: Radu Balan
• 金额: $ 17.72万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-08-15 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0807896&HistoricalAwards=false
• 关键词: Nonlinear; Signal; Processing; Wireless; Communications

BalanDMS-0807896 The investigator develops a new mathematical framework fornonlinear signal processing and wireless communication channels. The nonlinear signal processing problem addressed here is signalreconstruction from the magnitude of a redundant linearrepresentation. When the linear redundant representation isassociated to a group representation (such as the Weyl-Heisenberggrgoup), the relevant Hilbert-Schmidt operators inherit thisinvariance property. Thus a fast (nonlinear) reconstructionalgorithm seems possible. A wireless communication channel ismodeled as a linear operator that describes how transmittedsignals propagate to a receiver. For ultrawide band (UWB)signals, the Doppler effect no longer can be modeled as afrequency shift. Instead it is captured as a time dilationoperator. A continuous superposition of time-scale shifts isused to model a UWB communication channel, and consequences topseudo-differential operator theory are analyzed. The investigator takes up two problems related to signalprocessing. In the first he considers how to represent signalsin ways that allow more effective reconstructon of them fromlimited information. In the second he analyzes properties ofwireless communication channels, aiming at improvements intransmission. The solutions to these problems have a strongimpact in the strategic area of information technology. Important applications such as signal processing, X-raycrystallography, and quantum computing are affected by solutionsto the first problem. High-impact applications related to thesecond problem include ultrawide-band through-wall imagingsystems, higher-throughput 802.15 Wireless Personal AreaNetworks, and wireless sensor networks.

BALANDMS-0807896研究人员开发了一个新的数学框架，前线信号处理和无线通信渠道。这里解决的非线性信号处理问题是冗余线性陈述的大小的信号构造。 当线性冗余表示与组表示（例如Weyl-Heisenberggrgoup）相关时，相关的Hilbert-Schmidt运算符继承了此invariance属性。 因此，似乎可以使用快速（非线性）重建gor。 无线通信通道被iSMODEL作为线性运算符，该线性操作员描述了传输标志如何传播到接收器。 对于超速频带（UWB）信号，多普勒效应不再可以建模为a频移。 相反，它被捕获为时间扩张器。 时间尺度转移的连续叠加属于对UWB通信通道进行建模，并分析了后果差异算子理论。 研究人员提出了两个与信号处理有关的问题。 在第一个中，他考虑了如何代表信号的方式，这些方式允许从限制信息中重新重建它们。 在第二次中，他分析了无线通信渠道的属性，旨在改进传递。 这些问题的解决方案在信息技术的战略领域具有很大的影响。诸如信号处理，X射线晶体学和量子计算之类的重要应用受到第一个问题的影响。 与第三次问题有关的高影响应用程序包括超级波段贯穿壁成像系统，高通量802.15无线个人Areanetworks和无线传感器网络。