In the detection theory framework, it is customary to assign a bound to the false alarm probability and to attempt to maximize the detection probability subject to this constraint. In the problem of moving target detection in passive radar with a noisy reference channel, we formulate a detection problem as a composite hypothesis-testing problem and solve it with the likelihood ratio test (LRT) principle, which is known as generalized LRT in the electrical engineering works of literature. In such a problem, we show that any uncertainty in the value of the direct signal-to-noise ratio of the reference channel, abbreviated as $\text{DNR}_r$, can result in excessive false alarm probability of the proposed noisy-reference-channel-based detector in the low-$\text{DNR}_r$ regime. To facilitate efficient operation under uncertainty in $\text{DNR}_r$, we propose a new threshold-setting strategy to adjust the level of the proposed detector. Through extensive Monte–Carlo simulations, we examine the above problem and investigate the efficiency of the proposed threshold-setting strategy. Besides, we apply the framework of the kernel theory to the target detection problem of a noisy and ideal reference channel passive radar to propose two new detectors. As such, we replace the inner products of the proposed tests with appropriate polynomial kernel functions allowing for richer feature space to be deployed in the detection, achieving better detection performance. In this case, our detection performance results show that the kernelized detectors offer more that 1-dB signal-to-noise ratio gain as compared to their conventional counterparts.

中文翻译：

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噪声参考信道下无源雷达目标检测：一种新的阈值设置策略

在检测理论框架中，习惯上为虚警概率分配一个界限，并试图在此约束下最大化检测概率。针对具有噪声参考信道的无源雷达中的运动目标检测问题，我们将检测问题表述为复合假设检验问题，并用似然比检验（LRT）原理解决它，这在电学中被称为广义LRT。工程文学作品。在这样的问题中，我们表明参考通道的直接信噪比值的任何不确定性，缩写为$\text{DNR}_r$, 可能导致所提出的基于噪声参考通道的检测器在低$\text{DNR}_r$政权。促进在不确定性下的有效运作$\text{DNR}_r$，我们提出了一种新的阈值设置策略来调整所提出的检测器的级别。通过广泛的蒙特卡罗模拟，我们检查了上述问题并研究了所提出的阈值设置策略的效率。此外，我们将核理论的框架应用于噪声和理想参考信道无源雷达的目标检测问题，提出了两种新的检测器。因此，我们用适当的多项式核函数替换了建议测试的内积，允许在检测中部署更丰富的特征空间，从而实现更好的检测性能。在这种情况下，我们的检测性能结果表明，与传统检测器相比，核化检测器提供了超过 1-dB 的信噪比增益。