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

TL;DR

This paper introduces a new class of permutation polynomials for interleaving Zadoff-Chu sequences to generate novel CAZAC sequences, extending the understanding of their correlation properties and confirming a recent conjecture.

Contribution

It proposes high-degree permutation polynomials for interleaving ZC sequences, demonstrating the generated CAZAC sequences are distinct from existing classes and confirming a key conjecture.

Findings

New class of high-degree permutation polynomials over Z N.

Constructed CAZAC sequences not covered by existing equivalence classes.

Validated the conjecture by Berggren and Popović regarding CAZAC sequence properties.

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.