稀疏阵列测角算法研究

论文总字数：29477字

摘 要

阵列DOA(Direction-of-Arrival)估计是一个重要的研究课题，实际问题中，很多情况下都需要准确获得信号的方向。例如，雷达，声呐，麦克风阵列系统等。几十年来该学科的发展产生了许多经典的信号处理理论与算法，例如，高分辨率子空间方法窄带DOA估计^[2]，以及使用频域信号子空间处理的宽带扩展方法。在DOA估计中，目标角度分辨性能由阵列长度和快拍数等因素决定。在某些特定应用中，阵列尺寸和观测快拍数会极大的受到限制，传统谱估计算法的目标角度分辨性能低下。现在研究表明：(1)通过设计特定阵列结构，采用稀疏阵（Sparse Array）可以明显地提高阵列的空间自由度;(2)借鉴先进稀疏信号处理方法，如压缩感知，利用有限样本能够极大提升信号分辨性能。本文通过构造两级嵌套阵，研究压缩感知以及联合空间平滑的DOA估计算法，然后结合嵌套阵与压缩感知进一步提升DOA估计性能，主要工作包括如下：

1. 本文首先给出了均匀阵列和稀疏阵列的接收模型，介绍传统的均匀阵列的两种测角算法以及介绍两种基于协方差矩阵向量化的测角算法，并分析了稀疏阵列的角度分辨率和自由度，然后再比较稀疏阵列测角算法和均匀阵列测角算法的性能。
2. 目前在研究稀疏阵列的过程中，大多数情况下都是假设信号是不相干的，但是实际中受多径效应等影响的入射信号源往往是相干/相关的。本文对于非独立入射信号源，采用了前相空间平滑方法降低两级嵌套阵列中的旁瓣峰值，获得了较好的测角效果。
3. 对单快拍和多快拍情况下的压缩感知算法，本文采用了凸优化的手段使噪声最小化以及SVD奇异分解来使信号时间相干性降低，从而提高模型对噪声的抗干扰能力，并对单快拍和多快拍情况下的阵列DOA估计的相关性能做了对比。
4. 布置两级嵌套阵，接着对它进行压缩感知的阵列DOA估计，对非独立信号源入射进行DOA估计，并提出了对去冗余重排和未去冗余重排的协方差矩阵进行压缩感知处理的一系列方法，在单快拍和多快拍情况下对协方差矩阵进行了重构，解决了嵌套阵中互耦效应存在时未知互耦信息的情况下的DOA估计问题。

关键词：DOA（Direction-of-Arrival）嵌套阵列 压缩感知 联合空间平滑

ABSTRACT

The DOA (Direction-of-Arrival) estimation is an important research topic in array signal processing. In fact,we often need to know the arrival direction of the signal. For example, radar, sonar, microphone array systems, and etc. The development of this discipline in decades has produced many elegant signal processing concepts and techniques, such as high-resolution subspace methods for narrow-band DOA estimation ^[2], and broadband extension methods using frequency-domain signal subspace processing ^[33]. In general, the performance of angle resolution is very related to the length of the array and the number of snapshots. In some specific applications, the array size and the number of observed snapshots are greatly limited, and the traditional spectral estimation algorithm has a low target angle resolution performance. Based on the observation that: (1) Using a specific array design, the sparse array (Sparse Array) can significantly improve the spatial freedom of the array; (2) Benefitting from advanced sparse signal processing methods, such as compressed sensing, signal resolution performance can be effectively improved when only finite samples are available. In this thesis, a two-level nested array is used for DOA estimation , then it adopts the compressed sensing and joint space smoothing DOA estimation algorithm, and then combines nested array and compressed sensing to further improve the DOA estimation performance., mainly the work includes the following:

1. In many cases,the signal direction needs to be accurately obtained. Firstly, it gives the signal models of uniform array and sparse array. Two kinds of angle measuring algorithms using traditional uniform array are introduced and two kinds of vectorized matrix covariance are introduced. The angle measurement algorithm analyzes the angular resolution and degree of freedom of the sparse array, and then compares the performance using the sparse array and uniform array.
2. At present,many existing DOA estimation methods are based on the assumption that the signals are irrelevant. However, in reality, the signal sources are highly correlated,such as from multipath,which dramatically degrades the DOA estimation. For the non-independent incident signal source, the pre-phase spatial smoothing method is used to reduce the sidelobe peaks in the two-level nested array, and we can obtain a good angle measurement effect.
3. The DOA estimation using compressed sensing is studied in this section.In the case of single snapshot, this paper uses the convex optimization method to minimize the noise. And in the case of mutiple snapshot, this paper uses SVD singular decomposition to reduce the signal time coherence, thus improving the model's anti-interference ability to noise. The correlation performance of array DOA estimation in single snapshot and multi-fast snapshot is compared.
4. In this section,a joint approach using both nested array and compressed sensing is studied to improve the DOA estimation. DOA estimation for non-independent signal source incidence, and compression of covariance matrix for de-redundant rearrangement and non-redundant rearrangement is proposed. A series of methods of perceptual processing reconstructs the covariance matrix in the case of single snapshot and multiple snapshots, also, when we do not known the mutual coupling information, it make the DOA estimation problem done which is in the presence of mutual coupling effects in nested arrays.

Keywords:DOA（Direction-of-Arrival）, nested array, compressed sensing, joint spatial smoothing

目 录

摘 要 II

ABSTRACT III

第一章 绪论 1

1.1稀疏阵列测角算法研究背景和意义 1

1.2国内外发展现状 2

1.3本文主要工作安排 3

第二章 阵列DOA估计基本原理 5

2.1经典线性阵列模型 5

2.2常见DOA估计算法 7

2.2.1 DBF算法 7

2.2.2 MUSIC算法 8

2.2.3联合空间平滑方法 9

第三章 两级嵌套阵DOA估计算法研究 11

3.1两级嵌套阵的结构 11

3.2基于两级嵌套阵结构的信号DOA估计 12

3.3实验及算法验证 13

第四章 基于压缩感知DOA估计算法研究 17

4.1理论 17

4.2基于压缩感知的DOA估计 18

第五章 本文工作总结和展望 26

5.1工作总结 26

5.2研究展望 26

参考文献 28

致 谢 29

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