In this article, we define an ambiguity function (AF) for the generalized wideband multiple-input multiple-output (MIMO) radar, wherein the AF combines the signal processing in the fractional Fourier domain with all the functions of conventional AFs. We name it as the fractional AF for the wideband MIMO radar. In order to obtain the AF, we start from introducing the fractional order that relates to fractional signal processing into the matched-filter exploited by the AF, based on which we then derive the explicit expression of the AF. We provide explanations and implications of the fractional AF, and also derive its simplifications in terms of the case of slow-moving targets in far field. Moreover, we derive corresponding properties for the fractional AF, and meanwhile, we conduct analysis on the computational complexity of the AF. On the basis of the AF definition as well as its simplifications, we establish relationships of our proposed fractional AF to conventional AF forms. We show that our defined fractional AF can serve as a generalized AF form since conventional AFs are special cases of it. Our simulations show that the proper selection of fractional-orders can enable low sidelobe levels of the fractional AF for wideband MIMO radar.

中文翻译：

---

广义宽带 MIMO 雷达的分数模糊度函数


在本文中，我们为广义宽带多输入多输出（MIMO）雷达定义了模糊函数（AF），其中AF将分数傅里叶域中的信号处理与传统AF的所有功能结合起来。我们将其命名为宽带 MIMO 雷达的分数 AF。为了获得AF，我们首先将与分数信号处理相关的分数阶引入到AF所利用的匹配滤波器中，然后基于它推导出AF的显式表达式。我们提供了分数自动对焦的解释和含义，并根据远场缓慢移动目标的情况得出了其简化。此外，我们推导了分数AF的相应性质，同时，我们对AF的计算复杂度进行了分析。在 AF 定义及其简化的基础上，我们建立了我们提出的分数 AF 与传统 AF 形式的关系。我们证明，我们定义的分数 AF 可以作为广义 AF 形式，因为传统 AF 是它的特例。我们的仿真表明，正确选择分数阶可以实现宽带 MIMO 雷达分数 AF 的低旁瓣电平。