Signal Detection

M. S. Fadali
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引用次数: 24

Abstract

In Chapter 13 we considered hypothesis testing in the context of random variables. The detector resulting in the minimum probability of error corresponds to the MAP test as developed in section 13.2.1 or equivalently the likelihood ratio test in section 13.2.3. In this chapter we extend those results to a class of detection problems that are central in radar, sonar and communications, involving measurements of signals over time. The generic signal detection problem that we consider corresponds to receiv­ ing a signal r(t) over a noisy channel. r(t) either contains a known deterministic pulse s(t) or it does not contain the pulse. Thus our two hypotheses are H 1 : r(t) = s(t) + w(t) H 0 : r(t) = w(t), (14.1) where w(t) is a wide-sense stationary random process. One example of a scenario in which this problem arises is in binary communication using pulse amplitude modulation. In that context the presence or absence of the pulse s(t) represents the transmission of a " one " or a " zero ". As another example, radar and sonar systems are based on transmitting a pulse and detecting the presence or absence of an echo. In our treatment in this chapter we first consider the case in which the noise is white and carry out the formulation and analysis in discrete-time which avoids some of the subtler issues associated with continuous-time white noise. We also initially treat the case in which the noise is Gaussian. In Section 14.3.4 we extend the discussion to discrete-time Gaussian colored noise. In Section 14.3.2 we discuss the implications when the noise is not Gaussian and in Section 14.3.3 we discuss how the results generalize to the continuous-time case. In the signal detection task outlined above, our hypothesis test is no longer based on the measurement of a single (scalar) random variable R, but instead involves a collection of L
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信号检测
在第13章中,我们考虑了随机变量背景下的假设检验。产生最小误差概率的检测器对应于13.2.1节中开发的MAP测试或13.2.3节中等效的似然比测试。在本章中,我们将这些结果扩展到一类检测问题,这些问题是雷达,声纳和通信的中心,涉及信号随时间的测量。我们考虑的一般信号检测问题对应于在噪声信道上接收信号r(t)。R (t)要么包含已知的确定性脉冲s(t)要么不包含该脉冲。因此我们的两个假设是H 1: r(t) = s(t) + w(t) H 0: r(t) = w(t),(14.1)其中w(t)是一个广义平稳随机过程。出现此问题的一个场景示例是在使用脉冲幅度调制的二进制通信中。在这种情况下,脉冲s(t)的存在或不存在表示传输“1”或“0”。另一个例子,雷达和声纳系统是基于发射脉冲和探测回波的存在或不存在。在本章的处理中,我们首先考虑噪声为白的情况,并在离散时间内进行表述和分析,从而避免了与连续时间白噪声相关的一些微妙问题。我们也开始处理高斯噪声的情况。在第14.3.4节中,我们将讨论扩展到离散时间高斯彩色噪声。在第14.3.2节中,我们将讨论噪声不是高斯噪声时的含义,在第14.3.3节中,我们将讨论如何将结果推广到连续时间情况。在上面概述的信号检测任务中,我们的假设检验不再基于对单个(标量)随机变量R的测量,而是涉及到L的集合
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