We derive a detector function for quantum two-mode squeezing (QTMS) radar and noise radar that is based on the use of a generalized likelihood ratio (GLR) test for distinguishing between the presence and absence of a target. In addition to an explicit expression for the GLR detector, we derive a detector function which approximates the GLR detector in the limit where the target is small, far away, or otherwise difficult to detect. When the number of integrated samples is large, we derive a theoretical expression for the receiver operating characteristic (ROC) curve of the radar when the GLR detector is used. When the number of samples is small, we use simulations to understand the ROC curve behavior of the detector. One interesting finding is that there exists a parameter regime in which a previously-studied detector outperforms the GLR detector, contrary to the intuition that LR-based tests are optimal or nearly so. This is because neither the Neyman–Pearson lemma, nor the Karlin–Rubin theorem which generalizes the lemma to composite hypotheses, hold in this particular problem. However, the GLR detector remains a good choice for target detection in certain regimes.

中文翻译：

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QTMS雷达和噪声雷达的似然比检测器


我们推导了量子双模压缩（QTMS）雷达和噪声雷达的检测器函数，该函数基于使用广义似然比（GLR）测试来区分目标的存在和不存在。除了 GLR 检测器的显式表达式之外，我们还推导了一个检测器函数，该函数在目标较小、较远或难以检测的情况下近似 GLR 检测器。当集成样本数量较大时，我们推导了使用GLR探测器时雷达的接收机工作特性（ROC）曲线的理论表达式。当样本数量较少时，我们使用模拟来了解探测器的 ROC 曲线行为。一个有趣的发现是，存在一种参数机制，其中先前研究的检测器优于 GLR 检测器，这与基于 LR 的测试是最佳或接近最佳的直觉相反。这是因为内曼-皮尔逊引理和将引理推广到复合假设的卡林-鲁宾定理在这个特定问题中都不成立。然而，GLR 探测器仍然是某些情况下目标检测的不错选择。