Costas arrays are a special type of permutation matrices with ideal autocorrelation and low cross-correlation properties, making them valuable for radar, wireless communication, and integrated sensing and communication applications. This paper presents a novel unified framework for analyzing and discovering new Costas arrays. We introduce Universal Costas Matrices (UCMs) and Universal Costas Frequency Matrices (UCFMs) and investigate their structural characteristics. A framework integrating UCMs and UCFMs is proposed to pave the way for future artificial intelligence-assisted Costas array discovery. Leveraging the structural properties of UCMs and UCFMs, a reconstruction-based search method is developed to generate UCMs from UCFMs. Numerical results demonstrate that the proposed approach significantly accelerates the search process and enhances structural insight into Costas array generation.

翻译：科斯塔斯阵列是一类特殊的置换矩阵，具有理想的自相关特性和低互相关性，因此在雷达、无线通信以及集成感知与通信应用中具有重要价值。本文提出了一种用于分析和发现新型科斯塔斯阵列的统一框架。我们引入了通用科斯塔斯矩阵和通用科斯塔斯频率矩阵，并研究了它们的结构特性。提出了一个整合UCM和UCFM的框架，为未来人工智能辅助的科斯塔斯阵列发现铺平道路。利用UCM和UCFM的结构特性，开发了一种基于重构的搜索方法，用于从UCFM生成UCM。数值结果表明，所提出的方法显著加速了搜索过程，并增强了对科斯塔斯阵列生成的结构性理解。