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

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 advances 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 ZN, 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 operations. 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 interleaved by quadratic PPs.