In this paper, we consider requirement-driven selection of Costas arrays for the detection of closely spaced targets. We review existing order selection strategies in terms of the time–bandwidth product and treat selection of specific Costas arrays separably. Our computational analyses prioritize a clear central region in single-pulse discrete ambiguity functions (DAFs) and also address maximum frequency hops. Using finite field arithmetic, we significantly generalize results about 1s in the central square DAF regions for Welch and Lempel–Golomb arrays, and prove two general results about the nonexistence of such clear regions. We find that order 14 is very beneficial for target detection in which Costas arrays having an almost entirely clear $5 \times 5$ square central region in the single-pulse DAF exist and feature the corresponding time–bandwidth product of 196 within an example. We feature a first-principles system simulation with such an order-14 Costas array to obtain a 3-dB target detection improvement. Since radars commonly use burst waveforms, we also consider three different kinds of bursts and discuss their merits using ambiguity function analyses. We provide supporting computational database surveys on central rectangular $3 \times m$ regions.

中文翻译：

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用于近距离目标检测的 Costas 阵列波形

在本文中，我们考虑了需求驱动的 Costas 阵列选择，以检测间隔很近的目标。我们根据时间 - 带宽乘积审查现有的订单选择策略，并分别对待特定科斯塔斯阵列的选择。我们的计算分析优先考虑单脉冲离散模糊函数 (DAF) 中的清晰中心区域，并解决最大跳频问题。使用有限域算法，我们显着地概括了 Welch 和 Lempel-Golomb 阵列中心方形 DAF 区域中大约 1s 的结果，并证明了关于不存在此类清晰区域的两个一般结果。我们发现 14 阶对于目标检测非常有益，其中 Costas 阵列几乎完全清晰$5 \times 5$单脉冲 DAF 中存在方形中心区域，并且在示例中具有 196 的相应时间带宽积。我们采用具有此类 14 阶 Costas 阵列的第一性原理系统模拟，以获得 3-dB 的目标检测改进。由于雷达通常使用突发波形，我们还考虑了三种不同类型的突发，并使用模糊函数分析讨论了它们的优点。我们提供对中心矩形的支持计算数据库调查$3 \times m$ 地区。