This paper deals with adaptive radar detection problems where several alternative hypotheses may be plausible. This kind of problems naturally extends the conventional binary tests that often occur in radar (as well as in other application fields) by including a further uncertainty degree related to the number of unknown signal parameters (model order). Such a modification consequently leads to multiple composite alternative hypotheses. In the companion paper (Addabbo et al., 2021), we have defined a new design framework which allows us to come up with decision schemes for these hypothesis testing problems by exploiting the Kullback-Leibler Information Criterion and without resorting to heuristic design criteria. The architectures devised within the proposed framework consist of the sum between the compressed log-likelihood ratio and a penalty term inherited from model order selection rules. Such a penalty term accounts for the number of unknown parameters to overcome the limitation of the generalized likelihood ratio test in the presence of nested hypotheses. In the present paper, we apply the new design framework to different detection problems related to both real aperture and (polarimetric) synthetic aperture radar. The analysis is carried out in comparison with suitable competitors (possibly based upon heuristic design criteria) and shows that the architectures devised within the proposed theoretically-founded design framework represent an effective means to deal with detection problems where the uncertainty on some parameters leads to multiple alternative hypotheses.

中文翻译：

---

使用 Kullback-Leibler 信息准则在存在多个替代假设的情况下进行自适应雷达检测 - 第二部分：应用

本文涉及自适应雷达检测问题，其中几种替代假设可能是合理的。这类问题通过包含与未知信号参数数量（模型阶数）相关的进一步不确定度，自然而然地扩展了在雷达（以及其他应用领域）中经常出现的常规二进制测试。因此，这种修改会导致多个复合替代假设。在配套论文（Addabbo 等人，2021 年）中，我们定义了一个新的设计框架，该框架允许我们通过利用 Kullback-Leibler 信息准则而不诉诸启发式设计标准来为这些假设检验问题提出决策方案。在所提出的框架内设计的架构包括压缩对数似然比和从模型顺序选择规则继承的惩罚项之间的总和。这样的惩罚项考虑了未知参数的数量，以克服存在嵌套假设的广义似然比检验的局限性。在本文中，我们将新的设计框架应用于与真实孔径和（极化）合成孔径雷达相关的不同检测问题。