In this study, the application of information theory to describe radar measurement problems is investigated. In Shannon's information theory, mutual information is used to quantify the reduction in the a priori uncertainty of the transmitted message. Similarly, the authors define the spatial information in the phased-array radar as the mutual information between range, direction of arrival (DOA), scattering properties, and the received signal. Such information content is composed of two parts. The first part is range-DOA information. The theoretical expression and its asymptotic upper bound are presented in a single target scenario. It is concluded that the range information is independent of DOA information at high signal-to-noise ratio. The relationship between the upper bound and the Cramér-Rao bound is discussed. The second part is scattering information. The corresponding expression is formulated theoretically. Based on spatial information, the authors put forth a definition of entropy error (EE) to evaluate the estimation performance in the phased-array radar. Numerical simulation of the information content confirms their theoretical observations. The regularity of information change reflects the information acquisition efficiency of a radar system, providing guidance for system designers. Numerical results of EE are also presented to demonstrate its effectiveness as an evaluation index.

中文翻译：

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相控阵雷达中的空间信息

在这项研究中，研究了信息理论在描述雷达测量问题中的应用。在香农的信息理论中，互信息用于量化传输消息的先验不确定性的减少。同样，作者将相控阵雷达中的空间信息定义为距离，到达方向（DOA），散射特性和接收信号之间的互信息。此类信息内容由两部分组成。第一部分是范围DOA信息。理论表达式及其渐近上限在单个目标方案中给出。结论是，在高信噪比下，距离信息与DOA信息无关。讨论了上界与Cramér-Rao界之间的关系。第二部分是散射信息。相应的表达式在理论上是公式化的。基于空间信息，作者提出了熵误差（EE）的定义，以评估相控阵雷达的估计性能。信息内容的数值模拟证实了他们的理论观察。信息变化的规律性反映了雷达系统的信息采集效率，为系统设计人员提供了指导。还提供了EE的数值结果，以证明其作为评估指标的有效性。信息内容的数值模拟证实了他们的理论观察。信息变化的规律性反映了雷达系统的信息采集效率，为系统设计人员提供了指导。还提供了EE的数值结果，以证明其作为评估指标的有效性。信息内容的数值模拟证实了他们的理论观察。信息变化的规律性反映了雷达系统的信息采集效率，为系统设计人员提供了指导。还提出了EE的数值结果，以证明其作为评估指标的有效性。