Universal Costas Matrices: Towards a General Framework for Costas Array Construction

2026-02-03

AI Summary

This work proposes a unified framework that jointly integrates universal Costas matrices (UCMs) and universal Costas frequency-domain matrices (UCFMs), addressing the longstanding absence of a cohesive approach in traditional Costas array construction methods, which has hindered the efficient discovery of novel structures. By systematically combining structural analysis, matrix reconstruction, and a systematic search algorithm within this framework, the authors achieve highly efficient generation of Costas arrays. The proposed approach not only substantially accelerates the search process but also provides deeper structural insights into the generative mechanisms underlying Costas arrays. This advancement establishes a solid theoretical foundation for AI-assisted discovery of new Costas array configurations, opening promising avenues for future research in radar, sonar, and communications applications.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Costas arrays
• Universal Costas Matrices
• array construction
• autocorrelation
• cross-correlation

Innovation

• Universal Costas Matrices
• Costas arrays
• reconstruction-based search
• autocorrelation
• AI-assisted discovery