鲁棒自适应波束成形研究
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摘要
作为信号处理领域的一个重要分支,阵列信号处理被广泛的应用于雷达、声纳、射电天文学、地震学、定向/定位、无线通信以及医疗诊断等众多领域。自适应波束成形器能够根据阵列接收到的信号,选择适当的波束成形权值矢量,达到增强期望信号,抑制干扰和噪声的目的。虽然相比于经典的波束成形器而言,自适应波束成形器有着更好的分辨能力和更强的干扰抑制能力,但是自适应波束成形器对于模型的误差是非常敏感,即便是轻微的模型失配也可能导致自适应波束成形器严重的性能衰落,这给自适应波束成形算法应用于实际系统造成了困难。为此,在过去的三十多年中,众多研究者致力于自适应波束成形算法的鲁棒性研究,并取得了很多研究成果。本文将在现有工作的基础上,研究了几种新的鲁棒自适应波束成形算法,以便能适应更为复杂、更为恶劣的环境。
本文首先提出了一种基于二次采样的贝叶斯自适应波束成形算法。在该算法中,期望信号的波达方向被看作是一个定义在若干候选波达方向上的离散随机变量,由阵列接收信号计算出各候选波达方向的后验概率,并将后验概率的分布作为是否需要进行二次采样的判断标准;随后,对各波达方向上的波束成形权值线性加权,便可得到自适应波束成形器,权系数为各候选波达方向的后验概率值。研究表明,这种基于二次采样的贝叶斯自适应波束成形算法,能跟踪目标移动引起的波达方向变化。
接着,论文研究了一种基于等效波达角方法的自适应波束成形算法。本文首次提出了“等效波达角”的概念,将所有导致期望信号导引矢量不确定的因素都归结为波达方向一个因素的不确定。通过对导引矢量的元素作互不相关的假设,阵列中各个阵元的等效波达角可以被一一估计出来。根据已知的阵列结构,可以得到期望信号导引矢量的估计值及其对应的自适应波束成形器。研究表明,基于等效波达角方法的自适应波束成形算法能有效提高波束成形器的鲁棒性。
考虑到基于最坏情况性能优化的自适应波束成形算法的保守性,本文最后研究了一类基于概率约束的鲁棒自适应波束成形问题,其在设计上更为灵活。当期望信号导引矢量的误差量服从零均值复高斯分布时,本文在基于概率约束和基于最坏情况性能优化这两种鲁棒自适应波束成形算法之间建立起一种精确的联系。研究表明,本文建立的精确联系对于导引矢量较大的不确定具有更好的鲁棒性。
As an important branch of the signal processing domain, the array signal processing is widely applied for many areas such as radar, sonar, radio astronomy, seismology, direction finding (DF) / location finding, wireless communications, and tomography. Beamforming is a ubitiquitous task in array signal processing. The adaptive beamformers can select the weight vector as a function of the received data to optimize the performance subject to various constraints. Although the adaptive beamformers can have better resolution and much better interference rejection capability than the traditional data-independent beamformers, they are much more sensitive to errors, such as the array steering vector errors. The adaptive beamformers maybe suffer severe performance degradation even if there is a slight steering vector mismatch, which is difficult when they are applied to practical applications because these mismatches are unavoidable. As a result, much efforts have been devoted over the past three decades to devise robust adaptive beamformers. Based on the existing results, this dissertation proposed several new algorithms to improve the robustness of the adaptive beamformers, which make the adaptive beamformers more robust for the complicated scenarios.
In this dissertation, a Bayesian approach based on secondary sample to robust adaptive beamforming is proposed firstly. In this algorithm, the direction-of-arrival (DOA) is assumed to be a discrete random variable with a priori probability density function (pdf) defined on a set of candidate points. Whether or not the secondary sample is required is based on the a posteriori probability distribution of a set of candidate point's, which can be calculated from the array received signals. And then, the resulting beamformer is a weighted sum of the beamformers pointed at the latest set of point's, which are combined according to the value of the a posteriori probability for each pointing direction. The study shows that the proposed Bayesian approach based on secondary sample to robust adaptive beamforming can be used to track the DOA's variation of the moved object.
This dissertation proposes, for the first time, the concept of Equivalent DOAs. In the robust adaptive beamforming based on equivalent DOAs method, all factors causing the steering vector uncertainties are ascribed to the DOAs uncertainty only. The equivalent DOA of each sensor can be estimated out one by one with the assumption that the elements of the steering vector are uncorrelated with each other. In this way, based on the a priori known array structure, the: desired signal steering vector and the corresponding adaptive beamformer can be obtained from these equivalent DOAs. The simulation results demonstrate that the proposed algorithm can be used to improve the robustness of the adaptive beamformers.
Considering the conservativity of the worst-case robust adaptive beamforming, the probability-constrained approach is investigated, which is a more flexible one to robust adaptive beamforming. In this dissertation, a precise relationship between the two approaches is built in the case of zero-mean Gaussian steering vector mismatch, which shows that the probability-constrained beamformer design can be interpreted in terms of the worst-case beamformer design. The study shows that the precise relationship built in this dissertation is more robust to the steering vector uncertainty with a wide range.
本文首先提出了一种基于二次采样的贝叶斯自适应波束成形算法。在该算法中,期望信号的波达方向被看作是一个定义在若干候选波达方向上的离散随机变量,由阵列接收信号计算出各候选波达方向的后验概率,并将后验概率的分布作为是否需要进行二次采样的判断标准;随后,对各波达方向上的波束成形权值线性加权,便可得到自适应波束成形器,权系数为各候选波达方向的后验概率值。研究表明,这种基于二次采样的贝叶斯自适应波束成形算法,能跟踪目标移动引起的波达方向变化。
接着,论文研究了一种基于等效波达角方法的自适应波束成形算法。本文首次提出了“等效波达角”的概念,将所有导致期望信号导引矢量不确定的因素都归结为波达方向一个因素的不确定。通过对导引矢量的元素作互不相关的假设,阵列中各个阵元的等效波达角可以被一一估计出来。根据已知的阵列结构,可以得到期望信号导引矢量的估计值及其对应的自适应波束成形器。研究表明,基于等效波达角方法的自适应波束成形算法能有效提高波束成形器的鲁棒性。
考虑到基于最坏情况性能优化的自适应波束成形算法的保守性,本文最后研究了一类基于概率约束的鲁棒自适应波束成形问题,其在设计上更为灵活。当期望信号导引矢量的误差量服从零均值复高斯分布时,本文在基于概率约束和基于最坏情况性能优化这两种鲁棒自适应波束成形算法之间建立起一种精确的联系。研究表明,本文建立的精确联系对于导引矢量较大的不确定具有更好的鲁棒性。
As an important branch of the signal processing domain, the array signal processing is widely applied for many areas such as radar, sonar, radio astronomy, seismology, direction finding (DF) / location finding, wireless communications, and tomography. Beamforming is a ubitiquitous task in array signal processing. The adaptive beamformers can select the weight vector as a function of the received data to optimize the performance subject to various constraints. Although the adaptive beamformers can have better resolution and much better interference rejection capability than the traditional data-independent beamformers, they are much more sensitive to errors, such as the array steering vector errors. The adaptive beamformers maybe suffer severe performance degradation even if there is a slight steering vector mismatch, which is difficult when they are applied to practical applications because these mismatches are unavoidable. As a result, much efforts have been devoted over the past three decades to devise robust adaptive beamformers. Based on the existing results, this dissertation proposed several new algorithms to improve the robustness of the adaptive beamformers, which make the adaptive beamformers more robust for the complicated scenarios.
In this dissertation, a Bayesian approach based on secondary sample to robust adaptive beamforming is proposed firstly. In this algorithm, the direction-of-arrival (DOA) is assumed to be a discrete random variable with a priori probability density function (pdf) defined on a set of candidate points. Whether or not the secondary sample is required is based on the a posteriori probability distribution of a set of candidate point's, which can be calculated from the array received signals. And then, the resulting beamformer is a weighted sum of the beamformers pointed at the latest set of point's, which are combined according to the value of the a posteriori probability for each pointing direction. The study shows that the proposed Bayesian approach based on secondary sample to robust adaptive beamforming can be used to track the DOA's variation of the moved object.
This dissertation proposes, for the first time, the concept of Equivalent DOAs. In the robust adaptive beamforming based on equivalent DOAs method, all factors causing the steering vector uncertainties are ascribed to the DOAs uncertainty only. The equivalent DOA of each sensor can be estimated out one by one with the assumption that the elements of the steering vector are uncorrelated with each other. In this way, based on the a priori known array structure, the: desired signal steering vector and the corresponding adaptive beamformer can be obtained from these equivalent DOAs. The simulation results demonstrate that the proposed algorithm can be used to improve the robustness of the adaptive beamformers.
Considering the conservativity of the worst-case robust adaptive beamforming, the probability-constrained approach is investigated, which is a more flexible one to robust adaptive beamforming. In this dissertation, a precise relationship between the two approaches is built in the case of zero-mean Gaussian steering vector mismatch, which shows that the probability-constrained beamformer design can be interpreted in terms of the worst-case beamformer design. The study shows that the precise relationship built in this dissertation is more robust to the steering vector uncertainty with a wide range.
引文
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