极化敏感阵列信号处理的研究
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摘要
极化敏感阵列是指极化敏感阵元按一定方式在空间放置所构成的阵列系统，利用极化敏感阵元可获取空间电磁信号的极化信息，利用阵列几何结构进行空域采样可获取信号的空域信息。和普通阵列相比，极化敏感阵列具有优越的系统性能：较强的抗干扰能力、稳健的检测能力、较高的分辨能力以及极化多址能力，因此极化敏感阵列具有重要的军事和民事应用价值。论文以极化敏感阵列为研究对象，研究了信号滤波、检测及参量估计等一系列信号处理过程，从理论上定量地证明了极化敏感阵列的优势和潜能。研究将丰富阵列信号处理理论，指导极化敏感阵列系统设计，为现代战场信息感知与处理提供有力的技术支撑，为解决移动通信领域中的关键问题提供崭新的研究思路。
极化敏感阵列信号滤波主要研究利用干扰信号与期望信号空域和极化域的特征差异抑制干扰、增强信号的问题。首先，分析了已有滤波准则的性能并提出了一种新的滤波准则。然后，研究了完全极化、部分极化以及相关干扰条件下极化敏感阵列的滤波性能。证明了极化敏感阵列比普通阵列具有更强的抗干扰能力，干扰方要想获得有效的干扰效果，“最佳”干扰信号不仅到达角要和期望信号接近或相同，而且极化状态也要和期望信号接近或相同。在相同硬件设备量的前提下和普通阵列相比，在牺牲了部分空域滤波能力的条件下换取了极化域滤波能力。期望信号极化度越高，阵列滤波性能越好；干扰信号极化度越高，干扰越容易被抑制。期望信号和干扰信号相关性越强，阵列滤波性能差异越明显，且相关系数的相位影响着“最佳”干扰信号的空间到达角。最后，提出了一种双信息信号传输的方案并导出了无互扰传输的充要条件：两期望信号的信号矢量在以干扰噪声协方差矩阵的逆矩阵为加权矩阵的加权内积空间中正交，在给定的电磁环境下设计了双信息信号的极化状态。
极化敏感阵列信号检测主要研究待检测方向上广义噪声背景中未知极化信号的检测问题。首先，研究了匹配子空间检测理论和自适应子空间检测理论。归结起来，当噪声水平已知时，匹配子空间检测器属于“能量型”检测器；当噪声水平未知时，匹配子空间检测器属于“角度型”检测器。所有匹配子空间检测器都具有CFAR特性。在背景噪声协方差矩阵未知条件下，借鉴Kelly的研究思路，利用GURR思想导出了自适应子空间检测器。然后，利用匹配子空间检测理论研究了极化敏感阵列对完全极化信号的检测问题，极化状态未知的信号必定落入一个与到达方向有关的确定的二维子空间内。当附近存在干扰信号或信号到达角偏离波束方向时，信号的检测性能均下降。和普通阵列检测性能相比，极化敏感阵列对于任意极化信号具有恒定的检测特性，称为“恒极化”检测特性。最后，研究了极化敏感阵列对部分极化信号检测问题。
极化敏感阵列信号参量估计主要研究利用极化敏感阵列的一系列采样数据对信号空间到达角和极化状态角的联合估计问题。首先，利用典型的子空间类高分辨谱估计MUSIC
国防科学技术大学研究生院学位论文
算法构建了极化域一空域联合谱，根据谱峰位置估计信号的到达角和极化状态角。其次，
深入研究了联合谱的两项重要性能指标:谱估计精度和分辨力。用克拉美一劳限(CRB)来
衡量信号到达角和极化角的估计精度，利用Fisher信息矩阵求逆导出信号到达角和极化角
CRB的解析表达式，两信号特征参量接近时，它们的估计精度均下降。借助于MUsIC零
谱的统计特性研究了极化域一空域联合谱的分辨力，提出极化域一空域模糊图和极化敏感
阵列信号模糊函数的概念描述系统的分辨性能，当两信号到达角相同时信号不能被分辨开
来;当信号到达角不同时，极化状态的差别可以改善系统的分辨力;信号特征参量固定时
要将信号成功分辨需要的信噪比与采样点数总量是恒定的。然后，提出了“序贯”处理方
式下联合谱的自适应递推估计算法对信号参量进行实时测量。最后，将己获得的极化信息
应用到目标跟踪领域解决目标关联问题，提出广义“最近邻”数据关联算法。
最后总结了极化敏感阵列信号滤波、检测以及参量估计三部分的区别与联系，构建了
极化敏感阵列实验系统框架，归纳了论文的创新点，并指出了后续值得研究的方向。
关键词:极化敏感阵列;滤波;期望信号;干扰信号;完全极化;部分极化;相关;检测;
匹配子空间检测;自适应子空间检测;估计;极化域一空域联合谱;估计精度;克拉美一
劳限;分辨力;模糊图;模糊函数;“序贯”处理;广义“最近邻’，;
第n页
Polarization Sensitive Array (PSA) can acquire the polarization information besides the spatial information of the Electromagnetic signals, which consists of a group of polarization sensitive elements. PSA outperforms the common arrays due to the additional polarization information. PSA possesses strong anti-jamming ability, robust detecting performance, high resolving power and polarization multi-address capability. Therefore, PSA will play an important role in both military and civil areas due to these advantages. This dissertation focuses on the signal processing of PSA, including signal filtering, signal detection and signal parameter estimation to demonstrate the advantages of PSA over common arrays quantitatively, theoretically. The investigation will enrich the theory of array signal processing and guide the systemic design of PAS. In addition, it will avail to gather and process the information of modem war and provide novel ideas for the bottle-neck in the 3rd generation mobile communication.Signal filtering of PSA means suppressing interference and enhancing the desired signal, using the difference between desired signal and interference in spatial and polanzational domains. At first, the well-known filtering criterions are analyzed comparatively and a novel criterion is brought forth under multiple desired signals case. Then, the filtering performance is investigated under completely polarized case, partially polarized case and correlative case. It is showed that the PSA is more difficult to jam. To produce a poor SINR, the optimal interference signal must both arrive from the same direction and have the same polarization as the desired signal. With equal hardware equipment, PSA obtain the polarizational filtering ability at the cost of losing partial spatial filtering ability. The higher the polarization degree of desired signal being, the better filtering performance is. The higher the polarization degree of interference being, the interference can be suppressed more easily. The correlative coefficient between desired signal and interference affects the filtering performance strongly, which changes the direction of optimal interference. At last, the Double Message Signal is proposed and the non-interfere condition is presented that the steering vectors are orthogonal in the weighted inner product space, with the inverse matrix of background covariance as the weighting matrix. The optimal polarization states are designed, according to the EM background.Signal detection of PSA means detecting the signal at given direction with unknown polarization state under generalized noise background. At first, Matched Subspace Detector (MSD) and Adaptive Subspace Detector (ASD) are derived theoretically. With known noise level, the MSD is of "power type". With unknown noise level, the MSD is of "angle type". All the MSDs possess CFAR property. When the covariance of noise is unknown, the ASD is derived by using Kelly's thought for reference. Then, the signal detection of completely polarized is
investigated with exploiting the MSD theory. It is shown that the detection probability decreases when interference approaches signal in spatial domain and when the signal direction is misaligned with the look direction. Compared with the common arrays, the detection performance is independent of polarization state of signal, called "Constant Polarization Detection". At last, the signal detection of partially polarized is investigated thoroughly.Signal parameter estimation of PSA means estimating the angles of arrival and the polarization angles simultaneously according to the samples of PSA. Firstly, the joint spectrum is established in polarizational and spatial domains utilizing the MUSIC algorithm. The positions of spectrum peaks indicate the characteristic parameters of EM signals. Secondly, the estimation accuracy and resolving power of joint spectrum are investigated. The Cramer-Rao bound (CRB) is used to evaluate the estimation accuracy, obtained thought inversing the Fisher Information Matrix. The estimation accuracy of
极化敏感阵列信号滤波主要研究利用干扰信号与期望信号空域和极化域的特征差异抑制干扰、增强信号的问题。首先，分析了已有滤波准则的性能并提出了一种新的滤波准则。然后，研究了完全极化、部分极化以及相关干扰条件下极化敏感阵列的滤波性能。证明了极化敏感阵列比普通阵列具有更强的抗干扰能力，干扰方要想获得有效的干扰效果，“最佳”干扰信号不仅到达角要和期望信号接近或相同，而且极化状态也要和期望信号接近或相同。在相同硬件设备量的前提下和普通阵列相比，在牺牲了部分空域滤波能力的条件下换取了极化域滤波能力。期望信号极化度越高，阵列滤波性能越好；干扰信号极化度越高，干扰越容易被抑制。期望信号和干扰信号相关性越强，阵列滤波性能差异越明显，且相关系数的相位影响着“最佳”干扰信号的空间到达角。最后，提出了一种双信息信号传输的方案并导出了无互扰传输的充要条件：两期望信号的信号矢量在以干扰噪声协方差矩阵的逆矩阵为加权矩阵的加权内积空间中正交，在给定的电磁环境下设计了双信息信号的极化状态。
极化敏感阵列信号检测主要研究待检测方向上广义噪声背景中未知极化信号的检测问题。首先，研究了匹配子空间检测理论和自适应子空间检测理论。归结起来，当噪声水平已知时，匹配子空间检测器属于“能量型”检测器；当噪声水平未知时，匹配子空间检测器属于“角度型”检测器。所有匹配子空间检测器都具有CFAR特性。在背景噪声协方差矩阵未知条件下，借鉴Kelly的研究思路，利用GURR思想导出了自适应子空间检测器。然后，利用匹配子空间检测理论研究了极化敏感阵列对完全极化信号的检测问题，极化状态未知的信号必定落入一个与到达方向有关的确定的二维子空间内。当附近存在干扰信号或信号到达角偏离波束方向时，信号的检测性能均下降。和普通阵列检测性能相比，极化敏感阵列对于任意极化信号具有恒定的检测特性，称为“恒极化”检测特性。最后，研究了极化敏感阵列对部分极化信号检测问题。
极化敏感阵列信号参量估计主要研究利用极化敏感阵列的一系列采样数据对信号空间到达角和极化状态角的联合估计问题。首先，利用典型的子空间类高分辨谱估计MUSIC
国防科学技术大学研究生院学位论文
算法构建了极化域一空域联合谱，根据谱峰位置估计信号的到达角和极化状态角。其次，
深入研究了联合谱的两项重要性能指标:谱估计精度和分辨力。用克拉美一劳限(CRB)来
衡量信号到达角和极化角的估计精度，利用Fisher信息矩阵求逆导出信号到达角和极化角
CRB的解析表达式，两信号特征参量接近时，它们的估计精度均下降。借助于MUsIC零
谱的统计特性研究了极化域一空域联合谱的分辨力，提出极化域一空域模糊图和极化敏感
阵列信号模糊函数的概念描述系统的分辨性能，当两信号到达角相同时信号不能被分辨开
来;当信号到达角不同时，极化状态的差别可以改善系统的分辨力;信号特征参量固定时
要将信号成功分辨需要的信噪比与采样点数总量是恒定的。然后，提出了“序贯”处理方
式下联合谱的自适应递推估计算法对信号参量进行实时测量。最后，将己获得的极化信息
应用到目标跟踪领域解决目标关联问题，提出广义“最近邻”数据关联算法。
最后总结了极化敏感阵列信号滤波、检测以及参量估计三部分的区别与联系，构建了
极化敏感阵列实验系统框架，归纳了论文的创新点，并指出了后续值得研究的方向。
关键词:极化敏感阵列;滤波;期望信号;干扰信号;完全极化;部分极化;相关;检测;
匹配子空间检测;自适应子空间检测;估计;极化域一空域联合谱;估计精度;克拉美一
劳限;分辨力;模糊图;模糊函数;“序贯”处理;广义“最近邻’，;
第n页
Polarization Sensitive Array (PSA) can acquire the polarization information besides the spatial information of the Electromagnetic signals, which consists of a group of polarization sensitive elements. PSA outperforms the common arrays due to the additional polarization information. PSA possesses strong anti-jamming ability, robust detecting performance, high resolving power and polarization multi-address capability. Therefore, PSA will play an important role in both military and civil areas due to these advantages. This dissertation focuses on the signal processing of PSA, including signal filtering, signal detection and signal parameter estimation to demonstrate the advantages of PSA over common arrays quantitatively, theoretically. The investigation will enrich the theory of array signal processing and guide the systemic design of PAS. In addition, it will avail to gather and process the information of modem war and provide novel ideas for the bottle-neck in the 3rd generation mobile communication.Signal filtering of PSA means suppressing interference and enhancing the desired signal, using the difference between desired signal and interference in spatial and polanzational domains. At first, the well-known filtering criterions are analyzed comparatively and a novel criterion is brought forth under multiple desired signals case. Then, the filtering performance is investigated under completely polarized case, partially polarized case and correlative case. It is showed that the PSA is more difficult to jam. To produce a poor SINR, the optimal interference signal must both arrive from the same direction and have the same polarization as the desired signal. With equal hardware equipment, PSA obtain the polarizational filtering ability at the cost of losing partial spatial filtering ability. The higher the polarization degree of desired signal being, the better filtering performance is. The higher the polarization degree of interference being, the interference can be suppressed more easily. The correlative coefficient between desired signal and interference affects the filtering performance strongly, which changes the direction of optimal interference. At last, the Double Message Signal is proposed and the non-interfere condition is presented that the steering vectors are orthogonal in the weighted inner product space, with the inverse matrix of background covariance as the weighting matrix. The optimal polarization states are designed, according to the EM background.Signal detection of PSA means detecting the signal at given direction with unknown polarization state under generalized noise background. At first, Matched Subspace Detector (MSD) and Adaptive Subspace Detector (ASD) are derived theoretically. With known noise level, the MSD is of "power type". With unknown noise level, the MSD is of "angle type". All the MSDs possess CFAR property. When the covariance of noise is unknown, the ASD is derived by using Kelly's thought for reference. Then, the signal detection of completely polarized is
investigated with exploiting the MSD theory. It is shown that the detection probability decreases when interference approaches signal in spatial domain and when the signal direction is misaligned with the look direction. Compared with the common arrays, the detection performance is independent of polarization state of signal, called "Constant Polarization Detection". At last, the signal detection of partially polarized is investigated thoroughly.Signal parameter estimation of PSA means estimating the angles of arrival and the polarization angles simultaneously according to the samples of PSA. Firstly, the joint spectrum is established in polarizational and spatial domains utilizing the MUSIC algorithm. The positions of spectrum peaks indicate the characteristic parameters of EM signals. Secondly, the estimation accuracy and resolving power of joint spectrum are investigated. The Cramer-Rao bound (CRB) is used to evaluate the estimation accuracy, obtained thought inversing the Fisher Information Matrix. The estimation accuracy of
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