基于Xampling的Gabor框架条件下的窄脉冲信号采集方法研究

项目名称： 基于Xampling的Gabor框架条件下的窄脉冲信号采集方法研究

项目编号： No.61501493

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 无线电电子学、电信技术

项目作者： 王成

作者单位： 中国人民解放军陆军工程大学

项目金额： 19万元

中文摘要： 采用基于Xampling的欠Nyquist采样理论对窄脉冲信号进行采样可以大大降低模数转换的采样率，但是目前利用Gabor框架进行采样的方法仅具有理论意义，在实际应用中面临通道滤波器设计复杂、采样通道数多、高冗余框架下重构效果差等问题。经过傅里叶矩阵加权的指数再生窗序列可以使得滤波器通过简单的指数滤波器实现，为基于Xampling的欠Nyquist采样理论具体实现提供了可能。本项目针对目标跟踪雷达中常用的窄脉冲信号，利用指数再生窗构建Gabor框架，建立了采样通道的滤波器理论模型；利用高度冗余字典对窄脉冲信号进行稀疏表示；改进了基于压缩感知的框架系数重构方法，并对最终恢复信号的唯一性、收敛性进行证明；根据目前现有的类似的采样系统搭建实验平台，对理论进行验证分析，对实际系统的鲁棒性进行验证。本项目的研究对于简化采样系统中滤波器设计、降低通道数、提高信号恢复精确度等方面具有重要意义。

中文关键词： Gabor框架；滤波器；压缩感知；欠Nyquist采样；窄脉冲

英文摘要： Adopting the Sub-Nyquist sampling theory based on Xampling could significantly decrease the sampling rate of the analogy to digital conversion (ADC), but it only has theoretical significance. In practical application, this method still has the problems such as complicated filter design, numerous sampling channels, huge recovery error, and etc. The exponential reproducing windows sequences weighted by Fourier matrix could construct simple exponential filters and make it possible to bridge theory to practice. Firstly, aiming at the general short pulses in target tracing radar, we studies the theoretical filter model with Gabor frames constructed by exponential reproducing windows. Then, the sparse representation for short pulses with Gabor frames is achieved. Under the condition of highly redundant dictionary, we propose new Gabor coefficients reconstruction method based on compressed sensing (CS), and analyze the uniqueness, convergence. At last, we will construct experience platform according to existing similar sampling system, verifying the theory proposed and analyze the robustness of practical system. This project holds important significance for simplifying filter realization, decreasing channel numbers and improving the signal recovery accuracy.

英文关键词： Gabor frames;filters;compressed sensing;sub-Nyquist sampling;short pulses