摘要
接收波束形成作为阵列信号处理的重要组成部分,已广泛应用于雷达、声纳、无线通信等领域。它的主要任务是通过空域滤波尽可能地提取信号,同时最大限度地抑制干扰和噪声。本论文从传统的Capon波束形成出发,主要总结了一些稳健接收波束形成方法,提出并验证了基于知识的稳健Capon波束形成方法,本论文的主要内容如下:
第一章主要介绍有关凸优化的一些背景和接收波束形成的发展动态以及国外研究现状,最后是全文的主要内容。
第二章主要介绍有关凸优化的基础理论,回顾了凸集,凸函数和凸优化等基本概念,然后介绍了优化问题的等价变换方法,Lagrange对偶理论和凸优化的一些重要子类,这些理论都将作为本文的基础,在后续章节中反复被用到。
第三章主要介绍了Capon波束形成的三种描述形式:空域滤波,协方差拟合和广义旁瓣对消Capon波束形成,证明了它们之间的等价关系,并且在Pisarenko框架下,进一步研究了一些空间谱估计器。
第四章主要总结了失配模型下的稳健Capon波束形成。总结了模型失配和少观测数据下的稳健Capon波束形成方法。其中,总结了两类方法,一类是优化最不利情况下的信号与干扰加噪声比,重点在于信号波形的精确估计;另一类是协方差拟合框架下的信号方向向量估计,重点在于精确估计信号功率。这两类方法都属于对角加载方法,但是与传统的固定系数对角加载相比,它们克服了传统的固定系数对角加载中有关加载系数选择的困难,在一定的失配模型下,在相应准则下是最优的。
第五章首先介绍空时自适应处理中一种协方差矩阵的估计方法,该方法在最小均方意义下,融合先验协方差矩阵和样本协方差矩阵,通过该方法可以得到一个增强的协方差矩阵的估计,基于该估计,本章提出基于知识的稳健Capon波束形成方法,并且通过仿真验证它的性能。
Receive Beamforming, as an essential part of array signal processing, has been widely used in radar, sonar and wireless communication in the past three decades. The main objective of receive beamforming techniques is to extract signal of interest from interference and noise via spatial filtering. Our work begins with a general review of traditional Capon beamforming, and continues with a comprehensive study of robust methods applied to Capon beamforming. Based on the covariance estimation method, we propose knowledge-aided robust Capon beamforming. Our main work is as follows:
In chapter one, we briefly introduce some background on convex optimization and receive beamforming and give a brief introduction to the state-of-art development in this area.
In chapter two, we review some preliminaries of convex optimization, which encompass the concepts of convex set, convex function and the abstract form of convex optimization problem. We continue with the topic of equivalent problems, after that, we go through Lagrange duality and some common-used subclasses of convex optimization problems. We emphasize that almost all the fundamentals introduced in this chapter lay basis for the subsequent chapters.
The traditional Capon beamforming is introduced in chapter three, with the interest in three form of Capon beamforming, namely spatial filtering Capon, covariance fitting Capon and generalized sidelobe cancelling Capon. We reveal the equivalence of such forms, after that we give some insight into some spatial spectral estimators under the Pisarenko framework.
In chapter four, we study robust Capon beamforming, especially cases in which there exists inherent model mismatch. Generally speaking, two main approaches are deduced for Capon beamforming, one is based on the worse-case SNIR optimization, aiming at estimation of waveforms and the other focuses on steering vector estimation, aiming at the accurate estimate of signal of interest. The two general methods fall into the class of diagonal-loading approach. To our knowledge, the loading factor in traditional approach is chosen in ad hoc manner which is not optimal in some sense, meanwhile we reveal the loading-factor of robust beamforming is scenario-dependent, and is optimal under the criterion chosen.
In chapter five, we study the knowledge-aided beamforming, by taking the priori of covariance into consideration, we can get an enhance estimation of covariance matrix under the mean square error criterion, and the enhance estimate can be applied in beamforming, we propose a method called knowledge-aided robust Capon beamforming, finally simulations are performed to demonstrate our propositions.
引文
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