On the Construction and Correlation Properties of Permutation-Interleaved Zadoff-Chu Sequences

2026-01-17

AI Summary

This work addresses the limited variety of existing constant-amplitude zero-autocorrelation (CAZAC) sequences by proposing a novel construction method based on higher-order permutation polynomials and their inverses to interleave Zadoff-Chu (ZC) sequences. Defined over the ring of integers, the resulting CAZAC sequences belong to equivalence classes distinct from those of conventional ZC sequences and their quadratic-permutation interleaved variants, thereby confirming the sufficiency of the Berggren–Popović conjecture. Leveraging permutation polynomial theory, sequence interleaving techniques, and equivalence class analysis, this study not only constructs new CAZAC sequences but also evaluates their aperiodic autocorrelation properties, thereby expanding their potential applications in radar and communication systems.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Constant amplitude zero auto-correlation (CAZAC) sequences are widely applied in waveforms for radar and communication systems. Motivated by a recent work [Berggren and Popovi\'c, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)], this paper further investigates the approach to generating CAZAC sequences by interleaving Zadoff-Chu (ZC) sequences with permutation polynomials (PPs). We propose one class of high-degree PPs over the integer ring Z N , and utilize them and their inverses to interleave ZC sequences for constructing CAZAC sequences. It is known that a CAZAC sequence can be extended to an equivalence class by five basic opertations. We further show that the obtained CAZAC sequences are not covered by the equivalence classes of ZC sequences and interleaved ZC sequences by quadratic PPs and their inverses, and prove the sufficiency of the conjecture by Berggren and Popovi\'c in the aforementioned work. In addition, we also evaluate the aperiodic auto-correlation of certain ZC sequences from quadratic PPs.

Problem

• CAZAC sequences
• Zadoff-Chu sequences
• permutation polynomials
• equivalence classes
• auto-correlation

Innovation

• Permutation Polynomials
• Zadoff-Chu Sequences
• CAZAC Sequences
• Interleaving
• Auto-correlation