Core Concepts
A new family of constant amplitude zero autocorrelation (CAZAC) sequences can be constructed by interleaving Zadoff-Chu sequences with permutation polynomials, particularly quadratic permutation polynomials (QPPs) or their inverse permutation polynomials. This construction can generate sets of orthogonal CAZAC sequences.
Abstract
The paper proposes a new method for constructing constant amplitude zero autocorrelation (CAZAC) sequences, which are widely used in radar and communication systems. The key idea is to interleave Zadoff-Chu sequences, a well-known family of CAZAC sequences, with permutation polynomials.
The authors first provide the necessary definitions and properties of CAZAC sequences and permutation polynomials. They then prove that interleaving a Zadoff-Chu sequence with a QPP, or with the inverse of a QPP, preserves the CAZAC property. This result is stated in Theorem 1 and Theorem 2.
The authors also discuss the uniqueness of the interleaved Zadoff-Chu sequences, showing that in some cases the interleaved sequences can be equivalent to non-interleaved Zadoff-Chu sequences obtained through basic mathematical operations. They provide an analysis of the number of unique interleaved sequences that can be generated for different sequence lengths N.
Furthermore, the authors demonstrate that by using different QPPs, it is possible to construct sets of orthogonal interleaved Zadoff-Chu sequences. However, they note that a full set of N orthogonal sequences (when the set size I = N) cannot always be obtained using only QPPs.
The paper concludes by highlighting the potential of this new construction method to enrich the set of available CAZAC sequences, which is an important problem in areas such as cellular communications.