存在阵列误差条件下波达方向估计算法研究
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摘要
波达方向(DOA)估计是阵列信号处理中的一个重要研究内容,在雷达、声纳、通信系统、智能家电以及智能会议系统中有着广泛的应用。现有的绝大多数DOA估计算法都是基于阵列流形精确已知的前提下得到的。但是在实际的工程应用中,真实的阵列流形往往会随着气候、环境以及器件本身的变化而出现一定程度的偏差。此时,这些算法的估计性能会严重恶化,甚至失效。因此,研究阵列误差条件下的DOA估计算法具有重要的理论意义和实用价值,也是近年来阵列信号处理领域的一个重要方向。本文主要针对三种典型阵列误差条件下的DOA估计问题展开研究,提出了几种有效的自校正算法,主要工作可以概括如下：
首先,对于通道幅相误差,我们提出了一种基于协方差矩阵幅值的估计算法。算法从参数去“耦合”的角度出发,通过对协方差矩阵的变换,依次对幅度误差、信号方向和相位误差进行估计。算法不需要迭代,且相位误差的大小不影响估计性能,即能获得独立于相位误差的性能。对于现代通信系统中的幅相误差自校正问题,所提算法能够很方便地推广到非圆信号的情况。进一步我们将算法推广到四阶累积量的情况,利用高阶累积量具有抑制高斯噪声和孔径扩展的能力,四阶算法在空间色噪情况下仍然能够有效地消除通道幅相误差的影响。
其次,对于阵元间的互耦,我们从信号的统计特性出发,提出了两种互耦自校正算法。现有的互耦自校正算法,利用阵列的结构特点,将互耦矩阵表示为特殊的矩阵形式,用维数较低的互耦系数表征互耦矩阵。为了提高互耦校正的性能,我们考虑利用信号的特殊统计特性来设计互耦自校正算法。我们提出了两种算法：第一种算法利用信号的不相关性,从协方差矩阵拟合出发,定义关于互耦系数、信号方向和信号功率的代价函数,利用轮换迭代方法进行求解,得到信号方向的估计。该算法可以适用于均匀线阵、均匀圆阵等特殊阵型,仿真实验表明该算法在低信噪比情况下能获得估计性能的改进。第二种算法针对均匀线阵,利用协方差矩阵和椭圆协方差矩阵定义代价函数,通过类似的迭代求解得到互耦系数的估计。仿真实验表明,利用信号的非圆特性能够有效地提高自校正算法的性能。
再次,对于阵元位置误差,我们针对代价函数最小化算法依赖于初始值的问题,提出了一种校正算法。鉴于位置误差可以表示为方向依赖的相位误差,我们基于MUSIC算法定义一种对于相位误差具有稳健性的空间谱,通过谱峰位置搜索可以得到信号方向和各信号导向矢量的估计,再利用导向矢量跟阵元位置的关系可以求得位置误差的最小二乘估计。该算法在获得初始方向估计的时候考虑了位置误差的影响,在一些传统算法不能有效分辨信号的情况下可以对阵列进行一定程度的校正,从而保证迭代算法的有效性。
最后,针对非均匀线阵的DOA估计和互耦自校正问题,从低秩矩阵重构的角度出发,我们提出了一种新的增广协方差矩阵构造算法。现有的基于协方差矩阵结构的自校正算法,都只利用了协方差的托普利兹性。我们考虑利用协方差矩阵秩的特性来提高重构精度,从而获得更好的误差校正性能。借鉴近几年低秩矩阵恢复的研究成果,我们将增广协方差矩阵构造问题表示为一个确定秩的半正定托普利兹矩阵恢复问题,再利用截断核范数规则化思想对问题进行简化,并通过轮换迭代的方法进行求解。利用构造的增广协方差矩阵,再应用传统的DOA估计算法即可以得到信号方向的估计。
As an important research branch of array signal processing, direction of arrival (DOA) estimation has been widely used in radar, sonar, communication systems, smart appliances and smart meeting systems. The vast majority of existing DOA estimation algorithms are based on the assumption that the array manifold is known precisely. However, in practical engineering applications, affected by the climate, environment and changes in the device itself, the uncertainties of the array manifold are unavoidable. Then the performance of these algorithms will deteriorate seriously, or even fail. Therefore, with important theoretical and practical value, DOA estimation in the presence of array error has become an important research area. In this paper, we focus on the problem of DOA estimation in the presence of three type of typical array errors. Several self-calibration algorithms are proposed, and the main contributions can be summarized as follows:
Firstly, for channel gain and phase errors, we propose an algorithm which is based on the amplitude of the covariance matrix. From perspective of "decoupling", the gain errors, source directions and phase errors are estimated sequentially. The proposed algorithm needs no iteration and has the advantage that the performance is independent of the phase errors. For applications in the modern communication systems, the proposed algorithm can be easily extended to exploit the noncircularity of the signals. As the high-order cumulant can be used to suppress the Gaussian noise, we proposed a similar fourth-order cumulants based algorithm, which can effectively eliminate the influence of channel gain and phase errors in colored noise environment.
Secondly, for mutual coupling between array elements, we proposed two self-calibration algorithms utilizing the statistical characteristics of the signals. In most existing algorithms, the mutual coupling matrix is expressed with a particular form, which can be characterized using a few of mutual coupling coefficients. In order to improve the performance, we can take advantage of the statistical properties of the signals. We proposed two algorithms:The first one assumes that all signals are uncorrelated. According to the principle of covariance matrix fitting, a cost function is defined with respect to the mutual coupling coefficients, signal directions and power. An iterative method can be used to get the minimizer of the cost function and estimate the DOAs. This algorithm can be applied to uniform linear arrays, uniform circular arrays and some other special arrays. Simulation results have shown that this algorithm can obtain performance improvements for low SNR condition. The second algorithm is designed for uniform linear arrays. A cost function is defined based on the covariance matrix and the ellipse covariance matrix. The mutual coupling coefficients can be estimated using a similar iterative method. Simulation results show that using the noncircularity of the signals can effectively improve the performance of mutual coupling self-calibration.
Thirdly, for sensor location errors, we proposed an algorithm to solve the problem that the existing iterative algorithms are dependent on the initial estimates. As location errors can be expressed as direction-dependent phase errors, we define an MUSIC based spatial spectrum which is robust to phase errors. The DOAs and the steering vectors can be estimated by searching the peaks of this spectrum. Then the least squares estimate of the location errors can be got from the estimated steering vectors. Since the effect of the location errors is considered, the proposed algorithm can calibrate the array to some extent even when traditional algorithms cannot distinguish all signals. Therefore, the proposed algorithm can be used to ensure the effectiveness of the iterative algorithms.
Finally, for the problem of DO A estimation and mutual coupling self-calibration for non-unifrom linear arrays, we propose a new algorithm for constructing augmented covariance matrix. The existing self-calibration algorithms just make use of the Toeplitz structure of the covariance matrix. We consider utilizing the property of the rank of the covariance matrix to improve reconstruction accuracy. Inspired by the research in the field of low-rank matrix reconstruction, we construct the augmented covariance matrix through a problem of constructing a positive semidefinite Toeplitz matrix with determined rank. This problem is simplified by the way of truncated nuclear norm regularization and a solution can be got using an iterative schema. Then the DOAs can be estimated using traditional algorithms based on the constructed augmented covariance matrix.
首先,对于通道幅相误差,我们提出了一种基于协方差矩阵幅值的估计算法。算法从参数去“耦合”的角度出发,通过对协方差矩阵的变换,依次对幅度误差、信号方向和相位误差进行估计。算法不需要迭代,且相位误差的大小不影响估计性能,即能获得独立于相位误差的性能。对于现代通信系统中的幅相误差自校正问题,所提算法能够很方便地推广到非圆信号的情况。进一步我们将算法推广到四阶累积量的情况,利用高阶累积量具有抑制高斯噪声和孔径扩展的能力,四阶算法在空间色噪情况下仍然能够有效地消除通道幅相误差的影响。
其次,对于阵元间的互耦,我们从信号的统计特性出发,提出了两种互耦自校正算法。现有的互耦自校正算法,利用阵列的结构特点,将互耦矩阵表示为特殊的矩阵形式,用维数较低的互耦系数表征互耦矩阵。为了提高互耦校正的性能,我们考虑利用信号的特殊统计特性来设计互耦自校正算法。我们提出了两种算法：第一种算法利用信号的不相关性,从协方差矩阵拟合出发,定义关于互耦系数、信号方向和信号功率的代价函数,利用轮换迭代方法进行求解,得到信号方向的估计。该算法可以适用于均匀线阵、均匀圆阵等特殊阵型,仿真实验表明该算法在低信噪比情况下能获得估计性能的改进。第二种算法针对均匀线阵,利用协方差矩阵和椭圆协方差矩阵定义代价函数,通过类似的迭代求解得到互耦系数的估计。仿真实验表明,利用信号的非圆特性能够有效地提高自校正算法的性能。
再次,对于阵元位置误差,我们针对代价函数最小化算法依赖于初始值的问题,提出了一种校正算法。鉴于位置误差可以表示为方向依赖的相位误差,我们基于MUSIC算法定义一种对于相位误差具有稳健性的空间谱,通过谱峰位置搜索可以得到信号方向和各信号导向矢量的估计,再利用导向矢量跟阵元位置的关系可以求得位置误差的最小二乘估计。该算法在获得初始方向估计的时候考虑了位置误差的影响,在一些传统算法不能有效分辨信号的情况下可以对阵列进行一定程度的校正,从而保证迭代算法的有效性。
最后,针对非均匀线阵的DOA估计和互耦自校正问题,从低秩矩阵重构的角度出发,我们提出了一种新的增广协方差矩阵构造算法。现有的基于协方差矩阵结构的自校正算法,都只利用了协方差的托普利兹性。我们考虑利用协方差矩阵秩的特性来提高重构精度,从而获得更好的误差校正性能。借鉴近几年低秩矩阵恢复的研究成果,我们将增广协方差矩阵构造问题表示为一个确定秩的半正定托普利兹矩阵恢复问题,再利用截断核范数规则化思想对问题进行简化,并通过轮换迭代的方法进行求解。利用构造的增广协方差矩阵,再应用传统的DOA估计算法即可以得到信号方向的估计。
As an important research branch of array signal processing, direction of arrival (DOA) estimation has been widely used in radar, sonar, communication systems, smart appliances and smart meeting systems. The vast majority of existing DOA estimation algorithms are based on the assumption that the array manifold is known precisely. However, in practical engineering applications, affected by the climate, environment and changes in the device itself, the uncertainties of the array manifold are unavoidable. Then the performance of these algorithms will deteriorate seriously, or even fail. Therefore, with important theoretical and practical value, DOA estimation in the presence of array error has become an important research area. In this paper, we focus on the problem of DOA estimation in the presence of three type of typical array errors. Several self-calibration algorithms are proposed, and the main contributions can be summarized as follows:
Firstly, for channel gain and phase errors, we propose an algorithm which is based on the amplitude of the covariance matrix. From perspective of "decoupling", the gain errors, source directions and phase errors are estimated sequentially. The proposed algorithm needs no iteration and has the advantage that the performance is independent of the phase errors. For applications in the modern communication systems, the proposed algorithm can be easily extended to exploit the noncircularity of the signals. As the high-order cumulant can be used to suppress the Gaussian noise, we proposed a similar fourth-order cumulants based algorithm, which can effectively eliminate the influence of channel gain and phase errors in colored noise environment.
Secondly, for mutual coupling between array elements, we proposed two self-calibration algorithms utilizing the statistical characteristics of the signals. In most existing algorithms, the mutual coupling matrix is expressed with a particular form, which can be characterized using a few of mutual coupling coefficients. In order to improve the performance, we can take advantage of the statistical properties of the signals. We proposed two algorithms:The first one assumes that all signals are uncorrelated. According to the principle of covariance matrix fitting, a cost function is defined with respect to the mutual coupling coefficients, signal directions and power. An iterative method can be used to get the minimizer of the cost function and estimate the DOAs. This algorithm can be applied to uniform linear arrays, uniform circular arrays and some other special arrays. Simulation results have shown that this algorithm can obtain performance improvements for low SNR condition. The second algorithm is designed for uniform linear arrays. A cost function is defined based on the covariance matrix and the ellipse covariance matrix. The mutual coupling coefficients can be estimated using a similar iterative method. Simulation results show that using the noncircularity of the signals can effectively improve the performance of mutual coupling self-calibration.
Thirdly, for sensor location errors, we proposed an algorithm to solve the problem that the existing iterative algorithms are dependent on the initial estimates. As location errors can be expressed as direction-dependent phase errors, we define an MUSIC based spatial spectrum which is robust to phase errors. The DOAs and the steering vectors can be estimated by searching the peaks of this spectrum. Then the least squares estimate of the location errors can be got from the estimated steering vectors. Since the effect of the location errors is considered, the proposed algorithm can calibrate the array to some extent even when traditional algorithms cannot distinguish all signals. Therefore, the proposed algorithm can be used to ensure the effectiveness of the iterative algorithms.
Finally, for the problem of DO A estimation and mutual coupling self-calibration for non-unifrom linear arrays, we propose a new algorithm for constructing augmented covariance matrix. The existing self-calibration algorithms just make use of the Toeplitz structure of the covariance matrix. We consider utilizing the property of the rank of the covariance matrix to improve reconstruction accuracy. Inspired by the research in the field of low-rank matrix reconstruction, we construct the augmented covariance matrix through a problem of constructing a positive semidefinite Toeplitz matrix with determined rank. This problem is simplified by the way of truncated nuclear norm regularization and a solution can be got using an iterative schema. Then the DOAs can be estimated using traditional algorithms based on the constructed augmented covariance matrix.
引文
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