多载波雷达系统的信息量及克拉美罗界

Multi‑carrier Radar System Information and Cramer‑Rao Bound

采用香农信息论的思想方法,以接收信号与被测目标的距离⁃幅相之间的互信息为测度,提出了目标距离信息和幅相信息的统一定义及描述方法,并推导出目标距离信息和幅相信息的闭合表达式,从而建立起多载波雷达系统的信息理论模型。研究表明,目标距离信息和幅相信息将产生相互影响,幅相信息通常依赖于距离信息。当目标的散射系数服从复高斯分布时,目标的幅相信息只与信噪比有关,而与距离信息无关。本文进一步研究了目标的距离信息量与最大似然估计之间的关系。理论分析与数值仿真结果表明,在高信噪比条件下,Cramer⁃Rao界就是距离信息量的渐近上界。然而,实际雷达系统通常工作于中等信噪比环境,长期以来,其理论上界并不清楚。现在,目标的距离信息量可作为最大似然估计的性能上界,为实际系统的性能提供了比较的依据。这一结论显示雷达信息理论对实际应用具有重要的指导作用。

In this paper,we adopt the thoughts and methodologies of Shannon’s information theory and use the distance⁃amplitude and phase mutual information between the received signal and the measured object as a measure to propose a unified definition and description method of the target distance information and amplitude⁃phase information and derive their closed expression.Thus,we establish an information theory model for multi⁃carrier radar systems.Studies have shown that target distance information and amplitude⁃phase information will interact with each other,and amplitude⁃phase information usually depends on distance information.Besides,the amplitude⁃phase information of the target is only related to the SNR but not to the distance information when the scattering coefficient of the target obeys the complex Gaussian distribution.This paper further studies the relationship between the distance information of the target and the maximum likelihood estimation.Theoretical analysis and numerical simulation results show that the Cramer⁃Rao bound is an asymptotic upper bound for distance information at high SNR.However,the actual radar system usually works in the medium SNR environment,and its theoretical boundary is not clear for a long time.Now,the distance information of the target can be used as the upper bound of the maximum likelihood estimation,which provides a basis for the performance of the actual system.This conclusion reveals that radar information theory has an important guiding role for practical applications.