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摘要: 分辨率是雷达系统的重要性能指标之一，传统采用模糊函数(AF)来分析波形的距离和多普勒分辨能力。该文提出以下观点：第一，传统的模糊函数分析方法的基本出发点是首先采用匹配滤波来处理回波信号，而从机理上来说，匹配滤波是在白噪声和点目标前提下使得输出信噪比(SNR)最大，对检测来说最优，但不适用于多个目标的分辨问题；第二，模糊函数分析方法并不能反映出噪声、目标起伏等随机因素，以及近距多目标波形相互干扰等因素的影响；第三，模糊函数只适用于两相同信噪比目标分辨，不适用于实际中经常存在的不同信噪比的多个目标的分辨。该文基于原始回波数据，采用统计学中的假设检验理论来研究雷达近邻目标距离分辨的问题，在给出统计意义上的正确分辨概率和虚判概率定义基础上，推导近邻目标距离统计分辨限(SRL)的表达式。仿真表明，统计分辨限可以突破瑞利限。当设定虚判概率和分辨概率分别为0.001和0.5时，对两幅度相位差为90度的0 dB的线性调频信号，距离统计分辨下限可达0.3倍瑞利限。Abstract: Resolution performance is an important performance criteria of the radar systems. Typically, the Ambiguity Function (AF) of signals is used to define the range and Doppler limits. In this study Some new opinions are proposed—First, the AF is based on the signals processed with matched filter, which can guarantee the maximization of the output of the Signal-to-Noise Ratio (SNR). Thus, the AF is optimal for target detection. However, the AF is unsuitable for the resolution of multiple targets. Second, the AF cannot reflect the effect of random factors, such as noise, target fluctuation, and mutual interference of close targets. Third, the AF can only handle two equal-powered targets and provide the conclusion of the limits. However, the AF fails to distinguish multiple unequal-powered targets, which is often the case in reality. Therefore, the hypothesis testing theory is applied to resolve the range resolution of two closely spaced targets for radars, and our study is based on the original echoes of the signals. With the definition of the correct resolution and false alarm rates in the statistical standpoint, we derive the expression of the range Statistical Resolution Limit (SRL). The simulation results indicate that the SRL can exceed the Rayleigh limit. With the false alarm and correct resolution rates being 0.001 and 0.5, respectively, for the two phase-orthogonal linear-frequency-modulated signals, the range SRL can be as low as 0.3 times of the Rayleigh limit.
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图 1 两线性调频信号相关的单次蒙特卡洛仿真
Figure 1. Monte Carlo simulation of the correlation result of two LFM signals
图 2 假设检验和匹配滤波方法的分辨性能对比
Figure 2. Comparisons of the hypothesis test and matched filter
图 4 分辨概率与相关系数的关系
Figure 4. Relationship of the resolution rate and the correlation coefficient
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