非圆信号波达方向估计算法研究
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摘要
常用的BPSK和AM等信号,因其统计特性与其任意旋转的统计特性不同,被称为非圆信号。利用信号的非圆特性可以提高波达方向(DOA)估计算法的性能,是阵列信号处理领域一个新的研究热点。已有非圆信号DOA估计算法难以处理信源个数多于2(M-1)的情况(M为阵元数),均需进行特征分解或奇异值分解从而计算量较大,目前仅有的二维方向估计算法(2D-NC-UESPRIT)只适用于矩形阵列和规则六边形阵列,可处理的信号数及估计精度也有限。本文针对非圆信号DOA估计技术的这些问题展开研究,主要工作概括如下:
1.分析了模型误差对非圆信号测向MUSIC算法性能的影响,总结了谱峰搜索类算法性能分析的一般流程。
2.将信号的非圆特性与高阶累积量相结合,提出了基于任意偶数阶累积量的非圆信号方向估计MUSIC算法(NC-2_q-MUSIC),给出了基于均匀线阵的简化算法,并分析了模型误差对NC-2_q-MUSIC算法性能的影响。NC-2_q-MUSIC算法可对多于2(M-1)个信号进行DOA估计,其分辨力、估计精度以及对模型误差的稳健性均优于同阶的传统MUSIC算法,而且阶数越高性能越好,同时对模型误差也越不敏感。
3.针对已有非圆信号DOA估计算法计算量较大的问题,将信号非圆特性应用于传播算子方法,提出了非圆信号DOA估计的扩展传播算子算法(EPM),并分析了其渐近性能。EPM具有与NC-MUSIC算法相同的渐近性能,虽然在低信噪比和小快拍数下性能略逊于NC-MUSIC算法,但通过适当过估计信源个数可以提高算法性能,达到与NC-MUSIC算法相当的水平。给出了EPM算法的实值实现方法,其计算量只有复算法的四分之一。
4.基于双平行线阵提出了非圆信号二维方向估计RARE(2D-NC-RARE)算法,基于L形阵提出了非圆信号二维方向估计参数加权算法(NC-PWM),并分析了两种算法的渐近性能。这两种算法利用特殊的阵列结构,将多维搜索转换为一维搜索或求根,估计得到的二维方向自动配对。与目前仅有的非圆信号二维方向估计算法——2D-NC-UESPRIT算法相比,在可分辨信号数和估计精度等方面,这两种算法均具有较优的性能。
A signal is called to be noncircular if its statistics are rotationally variant. The BPSK and AM modulated signals, which are widely used in communication systems, are noncircular. Enhancing the performance of the direction-finding algorithms by utilising the noncircularity of the signals is a prosperous area in the array signal processing domain. The existent direction finding algorithms for noncircular signals, whose major computation comes from eigenvalue-decomposition or singular value decomposition of the covariance martix of the array outputs, can hardly handle large number of signals impinging on the array with limited sensors. And the 2D-NC-UESPRIT algorithm, which can be applied to rectangular arrays and regular-hexagonal shaped arrays, is the only 2-dimensional direction finding algorithms for noncircular signals. In this thesis, several algorithms for noncircular signals are proposed to overcome the above knots. The main research work and contributions are detailed as follows.
1. The performance of MUSIC algorithm for noncircular signals (NC-MUSIC) in the presence of modeling errors is analysed and the general flow of the performance analysis of the peak-searching algorithms is also presented.
2. The MUSIC algorithm for noncircular signals based on even-order (2q) cumulants (NC-2q-MUSIC) is presented for the case of a number of signals impinging on the array with limited sensors and its performance in the presense of modeling errors is also analysed. The estimation capacity, the resolution, the angle-estimation precision and the robustness to modeling errors of the proposed algorithms all exceed those of conventional MUSIC algorithms with the same order. And all the above four aspects of the performance increase with q, which is validated by theoretical analyses and simulation results.
3. The extended propagator method (EPM) for noncircular signals is proposed to alleviate the heavy computation of the eigenvalue-decomposition or singular value decomposition and its asymptotic performance is analysed. The EPM and NC-MUSIC share the same asymptotic performance. The performance of EPM in the case of low SNR and small number of snapshots is worse than that of NC-MUSIC. Fortunately, it can be overcome by over-estimating the number of signals properly. The real-valued version of EPM is proposed and its computational load is only a quarter of that of complex EPM.
4. To fill the lack of 2-dimensional (2-D) direction finding algorithms for noncircular signals, the extended rank reduction algorithm for 2-D direction finding of noncircular signals (2D-NC-RARE) is presented based on two parallel linear arrays and the parameter weighted method for noncircular signals (NC-PWM) is also presented based on the L-shaped array. The asymptotic performance of the two algorithms is analysed. Profiting from the configuration of the arrays, the two algorithms need only 1-D search for joint azimuth and elevation estimation. Comparing with the existent 2-D direction finding algorithm for noncircular signals, i.e., 2D-NC-UESPRIT, the proposed algorithms are superior in estimation capacity and angle-estimation precision.
1.分析了模型误差对非圆信号测向MUSIC算法性能的影响,总结了谱峰搜索类算法性能分析的一般流程。
2.将信号的非圆特性与高阶累积量相结合,提出了基于任意偶数阶累积量的非圆信号方向估计MUSIC算法(NC-2_q-MUSIC),给出了基于均匀线阵的简化算法,并分析了模型误差对NC-2_q-MUSIC算法性能的影响。NC-2_q-MUSIC算法可对多于2(M-1)个信号进行DOA估计,其分辨力、估计精度以及对模型误差的稳健性均优于同阶的传统MUSIC算法,而且阶数越高性能越好,同时对模型误差也越不敏感。
3.针对已有非圆信号DOA估计算法计算量较大的问题,将信号非圆特性应用于传播算子方法,提出了非圆信号DOA估计的扩展传播算子算法(EPM),并分析了其渐近性能。EPM具有与NC-MUSIC算法相同的渐近性能,虽然在低信噪比和小快拍数下性能略逊于NC-MUSIC算法,但通过适当过估计信源个数可以提高算法性能,达到与NC-MUSIC算法相当的水平。给出了EPM算法的实值实现方法,其计算量只有复算法的四分之一。
4.基于双平行线阵提出了非圆信号二维方向估计RARE(2D-NC-RARE)算法,基于L形阵提出了非圆信号二维方向估计参数加权算法(NC-PWM),并分析了两种算法的渐近性能。这两种算法利用特殊的阵列结构,将多维搜索转换为一维搜索或求根,估计得到的二维方向自动配对。与目前仅有的非圆信号二维方向估计算法——2D-NC-UESPRIT算法相比,在可分辨信号数和估计精度等方面,这两种算法均具有较优的性能。
A signal is called to be noncircular if its statistics are rotationally variant. The BPSK and AM modulated signals, which are widely used in communication systems, are noncircular. Enhancing the performance of the direction-finding algorithms by utilising the noncircularity of the signals is a prosperous area in the array signal processing domain. The existent direction finding algorithms for noncircular signals, whose major computation comes from eigenvalue-decomposition or singular value decomposition of the covariance martix of the array outputs, can hardly handle large number of signals impinging on the array with limited sensors. And the 2D-NC-UESPRIT algorithm, which can be applied to rectangular arrays and regular-hexagonal shaped arrays, is the only 2-dimensional direction finding algorithms for noncircular signals. In this thesis, several algorithms for noncircular signals are proposed to overcome the above knots. The main research work and contributions are detailed as follows.
1. The performance of MUSIC algorithm for noncircular signals (NC-MUSIC) in the presence of modeling errors is analysed and the general flow of the performance analysis of the peak-searching algorithms is also presented.
2. The MUSIC algorithm for noncircular signals based on even-order (2q) cumulants (NC-2q-MUSIC) is presented for the case of a number of signals impinging on the array with limited sensors and its performance in the presense of modeling errors is also analysed. The estimation capacity, the resolution, the angle-estimation precision and the robustness to modeling errors of the proposed algorithms all exceed those of conventional MUSIC algorithms with the same order. And all the above four aspects of the performance increase with q, which is validated by theoretical analyses and simulation results.
3. The extended propagator method (EPM) for noncircular signals is proposed to alleviate the heavy computation of the eigenvalue-decomposition or singular value decomposition and its asymptotic performance is analysed. The EPM and NC-MUSIC share the same asymptotic performance. The performance of EPM in the case of low SNR and small number of snapshots is worse than that of NC-MUSIC. Fortunately, it can be overcome by over-estimating the number of signals properly. The real-valued version of EPM is proposed and its computational load is only a quarter of that of complex EPM.
4. To fill the lack of 2-dimensional (2-D) direction finding algorithms for noncircular signals, the extended rank reduction algorithm for 2-D direction finding of noncircular signals (2D-NC-RARE) is presented based on two parallel linear arrays and the parameter weighted method for noncircular signals (NC-PWM) is also presented based on the L-shaped array. The asymptotic performance of the two algorithms is analysed. Profiting from the configuration of the arrays, the two algorithms need only 1-D search for joint azimuth and elevation estimation. Comparing with the existent 2-D direction finding algorithm for noncircular signals, i.e., 2D-NC-UESPRIT, the proposed algorithms are superior in estimation capacity and angle-estimation precision.
引文
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