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 研究人员为非线性信号处理和无线通信信道开发了一种新的数学框架。这里解决的非线性信号处理问题是根据冗余线性表示的幅度进行信号重建。 当线性冗余表示与群表示（例如Weyl-Heisenberg群）相关联时，相关的Hilbert-Schmidt算子继承了这种不变性。 因此，快速（非线性）重建算法似乎是可能的。 无线通信信道被建模为线性算子，描述传输信号如何传播到接收器。 对于超宽带 (UWB) 信号，多普勒效应不再可以建模为频移。 相反，它被捕获为时间膨胀算子。 使用时间尺度变化的连续叠加来模拟 UWB 通信信道，并分析了伪微分算子理论的结果。 研究人员研究了两个与信号处理相关的问题。 首先，他考虑如何以允许从有限信息更有效地重建信号的方式来表示信号。 在第二部分中，他分析了无线通信通道的特性，旨在改进传输。 这些问题的解决对信息技术的战略领域产生重大影响。第一个问题的解决方案影响了信号处理、X 射线晶体学和量子计算等重要应用。 与第二个问题相关的高影响力应用包括超宽带穿墙成像系统、更高吞吐量的 802.15 无线个域网和无线传感器网络。