The Density of Costas Arrays Decays Exponentially
The Density of Costas Arrays Decays Exponentially
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DOI：
10.1109/tit.2022.3202507
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发表时间：
2023-01-01
影响因子：
2.5
通讯作者：
Swanson, Christopher N.
中科院分区：
文献类型：
--
作者：
Warnke, Lutz;Correll, Bill;Swanson, Christopher N.
科斯塔斯阵列在雷达和声纳工程中很有用，以及许多其他需要最佳二维自相关的设置：它们是排列矩阵，其中连接不同对的向量都是不同的。证明了Costas阵列在置换矩阵中的密度是指数衰减的，解决了Costas阵列理论中的一个核心问题。这个证明结合了随机图论的思想和概率组合学的工具。
Costas arrays are useful in radar and sonar engineering, and many other settings in which optimal 2-D autocorrelation is needed: they are permutation matrices in which the vectors joining different pairs of ones are all distinct. We prove that the density of Costas arrays among permutation matrices decays exponentially, solving a core problem in the theory of Costas arrays. The proof combines ideas from random graph theory with tools from probabilistic combinatorics.