信号检测的统计理论

D. Middleton
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引用次数: 15

摘要

提出了一种完备的检测理论,能够在任意统计特征的噪声中处理一般类型的信号(如周期、非周期、随机)。通过将检测问题适当地表述为统计假设的检验,可以指定最优检测器的精确结构,并唯一地确定最小可检测信号。对于阈值接收(主要感兴趣的问题),出现了两类操作:如果检测是相干的,就对输入信噪比的依赖而言,无论信号有多弱,都是线性系统;另一方面,对于非相干接收,总是对输入比(调制抑制)有二次依赖。在这两种情况下,阈值接收分别需要接收数据与先验已知信号的适当加权交叉相关,或接收数据与自身的适当加权自相关。最优检测器通常是一台计算机,涉及非线性操作并以决策操作结束,这取决于定义观察者的统计检验类型(例如Neyman-Pearson, Ideal, Sequential等)。决策的门槛必须由合适的投注或成本曲线决定。(考虑了数据的离散(数字)和连续(模拟)采样。)通过这种方式,与外部约束相一致的最佳性能被指定,并且实际系统偏离该极限最佳的程度可以计算出来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical theory of signal detection
A complete theory of detection is presented, which is capable of treating general types of signals (e.g. periodic, aperiodic, random) in noise of arbitrary statistical character. By proper formulation of the detection problem as a test of statistical hypotheses, the precise structure of the optimum detector can be specified and minimum detectable signals uniquely determined. For threshold reception (the problem of main interest) two classes of operation arise: if detection is coherent, as far as dependence on the input signal-to-noise ratio is concerned one has a linear system, no matter how weak the signal; on the other hand for incoherent reception one always has a quadratic dependence on this input ratio (modulation suppression). Threshold reception in these two instances requires respectively a suitably weighted cross-correlation of the received data with the a priori known signal, or a suitably weighted autocorrelation of the received data with itself. The optimum detector is in general a computer, involving non-linear operations and terminating in a decision operation, which depends on the type of statistical test (e.g. Neyman-Pearson, Ideal, Sequential, etc.) defining the observer. The threshold of decision is necessarily determined by a suitable betting or cost curve. (Both discrete (digital) and continuous (analog) sampling of the data are considered.) In this way optimum performance, consistent with the external constraints, is specified, and the extent by which actual systems depart from this limiting optimum can be calculated.
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