频谱稀疏信号的压缩采样与阵列处理方法研究

This project focuses on the research of theory and methods for wideband signals compressive sampling and array processing under compressing sensing framework, with the aim of exploring new ideas to solve practical problems facing the complicated electromagnetic environment.Specifically, for two kinds of typical spectrum-sparse signals including multi-band signals and wideband fast frequency-hopping signals, the structured compressed sensing models are established and stable blind reconstruction algorithms developed. The construction of low-dimensional measurement matrices are fulfilled for spectrum-sparse signals' efficient sampling and recovery, based on structurally random matrices and deterministic matrices. As a result, a theoretical basis for the wideband signals' compressive sampling is carried out, through in-depth study of the configuration characterstics of spectrum-sparse signals and measurement matrices.Furthermore, by building joint-sparsity model for broadband array, novel methods for multiple parameters' estimation are proposed with the restriction of multi-domain sparsity, and so a robust direction-of-arrival (DOA) estimation algorithm is suggested to alleviate the noise adverse impacts. New dimension-reduction methods for lager-scale array are discussed in the manner of random measurement matrices, and the realization of fast and rigorous patterns recovery of compressed array is successfully achieved. The error factors of the compressed array system model are analyzed, and a robust DOA estimation algorithm is derived. Adaptive beamforming methods of the compresed array are considered for improving their robustness under intricate jamming conditions. Consequently, an efffecive solution for array signal processing and its application is provided, via the studies of array processing methods based on compressive sensing theory.

本项目主要研究基于压缩感知的宽频带信号压缩采样与阵列处理理论和方法，旨在探索解决所面临的复杂电磁环境问题的新思路。针对多频带信号和宽带快跳频信号两种典型频谱稀疏信号，建立结构化压缩感知模型，研究稳定的盲重构算法；设计基于结构随机矩阵和确定性矩阵的低维测量矩阵，实现频谱稀疏信号的高效采样和重构。通过深入研究频谱稀疏信号及测量矩阵的结构特征，为实现宽频带信号的欠奈奎斯特采样提供理论依据。建立宽带阵列的多域联合稀疏模型，研究基于联合稀疏性约束的多参数估计方法，提出噪声背景下宽带阵列DOA估计的鲁棒算法；研究基于随机测量矩阵的大规模阵列降维方法，实现压缩阵列快速、高精度的波束重构；分析压缩阵列系统模型误差，提出鲁棒的DOA估计算法；研究压缩阵列的自适应波束形成方法，改善复杂干扰环境下算法的干扰抑制性能。通过压缩感知阵列处理方法研究，为阵列信号处理及应用提供一种新的有效解决方案。

压缩感知是一种全新的信号采集与处理的理论框架，本项目主要研究了基于压缩感知的频谱稀疏多带信号压缩采样与阵列处理理论和方法。主要研究成果总结如下：.1、针对宽带频谱稀疏信号采样与处理问题，以调制宽带转换器压缩采样结构为基础，重点研究欠Nyquist宽带压缩采样的原理方法、重构算法及系统实现。详细分析了m序列、Golay序列等确定性序列应用于调制宽带转换器（MWC）系统的性能，并给出了RIP界的理论证明；针对确定性序列构造的部分循环矩阵存在周期长度限制的问题，提出了一种结构化循环测量矩阵的构造方法；研究了一种基于改进贪婪算法的频谱支撑集恢复方法，提出了一种基于信号子空间的MUSIC谱支撑集恢复算法；研制了基于MWC的宽带压缩采样与处理原型系统，并进行系统性能的测试和验证。.2、构造确定性测量矩阵及设计相应的重构算法对压缩感知的推广与应用具有重要意义。研究本项目基于LDPC编码理论及PD译码算法，对确定性测量矩阵的构造、重构算法的设计及其应用展开。提出了一类基于LDPC码的确定性测量矩阵构造方法，从理论上分析了该类测量矩阵的相干性及可重构条件；针对PD重构算法在低信噪比下鲁棒性差的问题，提出了两种改进方案；研究了一种新的多速率互质采样（MRCS）方案。.3、对空间分辨率高、计算复杂度低的压缩感知DOA估计算法开展了深入研究。建立了基于加权信号子空间稀疏表示的DOA估计压缩感知模型，提出了基于贝叶斯压缩感知的窄带DOA估计算法BCS-WSF；提出了一种基于波束域预处理的窄带DOA估计算法，能够适应大型阵列的实际应用需求；在窄带BCS-WSF算法的基础上，引入贝叶斯压缩感知中的多任务学习思想，提出了一种无需角度预估和频域聚焦的宽带DOA估计算法JBCS-WSF；提出了L型平面阵列二维DOA估计算法MSBL-MP。.4、结合压缩感知理论和稀疏多带信号模型，分别研究了基于空时互质阵列的频率和DOA参数联合估计方法、空频二维谱稀疏恢复中栅格失配的校正与超分辨估计算法、多速率互质采样下的超分辨谱估计方法。针对当前宽频段窄带信号的空时域联合欠采样问题，提出一种基于互质阵和互质采样的稀疏空时二维谱估计方法。