Constructing Orthogonal Constant Amplitude Zero Autocorrelation Sequences by Interleaving Zadoff-Chu Sequences with Permutation Polynomials

Keskeiset käsitteet

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.

Tiivistelmä

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.

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Tärkeimmät oivallukset

Permutation Polynomial Interleaved Zadoff-Chu Sequences

by Fredrik Berg... klo arxiv.org 04-29-2024

https://arxiv.org/pdf/2306.15945.pdf

Syvällisempiä Kysymyksiä

How can the construction of orthogonal interleaved Zadoff-Chu sequences be extended beyond the use of QPPs, to potentially achieve a full set of N orthogonal sequences for any N

To extend the construction of orthogonal interleaved Zadoff-Chu sequences beyond the use of QPPs and potentially achieve a full set of N orthogonal sequences for any N, one approach could involve exploring higher-order permutation polynomials. By considering permutation polynomials of higher degrees, such as quartic or quintic permutation polynomials, more intricate interleaving patterns can be created. These higher-order permutation polynomials can introduce additional levels of complexity and diversity in the interleaved sequences, potentially leading to a larger set of orthogonal sequences. Additionally, combining multiple permutation polynomials in a systematic manner could also be explored to generate a wider range of orthogonal sequences. By carefully designing the coefficients and structures of these permutation polynomials, it may be possible to achieve a full set of N orthogonal sequences for any given N.

What are the practical implications and applications of this new family of CAZAC sequences in areas such as cellular communications, radar, and other signal processing domains

The new family of CAZAC sequences constructed from permutation polynomial interleaved Zadoff-Chu sequences has significant practical implications and applications in various signal processing domains. In cellular communications, these CAZAC sequences can be utilized for tasks such as generating reference signals, synchronization signals, and random access preambles. By leveraging the constant amplitude zero autocorrelation property of CAZAC sequences, cellular communication systems can enhance signal detection, synchronization, and interference mitigation capabilities. These sequences can improve the overall performance and reliability of communication systems, especially in scenarios with high interference or fading channels. In radar applications, the use of CAZAC sequences can aid in target detection, tracking, and signal processing by providing sequences with ideal periodic autocorrelation properties. The unique properties of these sequences make them valuable in radar systems for enhancing signal detection and reducing false alarms. Overall, the new family of CAZAC sequences offers versatile and efficient solutions for a wide range of applications in cellular communications, radar systems, and other signal processing domains.

Are there other families of CAZAC sequences, beyond Zadoff-Chu, that could be explored for interleaving with permutation polynomials to further expand the available set of CAZAC sequences

Beyond Zadoff-Chu sequences, there are several other families of CAZAC sequences that could be explored for interleaving with permutation polynomials to expand the available set of CAZAC sequences. Some potential families of CAZAC sequences include Frank sequences, generalized chirp-like (GCL) sequences, Bj¨orck sequences, cubic polynomial phase sequences, biphase sequences, and modulatable CAZAC sequences. Each of these sequence families offers unique properties and characteristics that can be leveraged for different applications. By interleaving these sequences with permutation polynomials, it is possible to create new sets of CAZAC sequences with diverse correlation properties and spectral characteristics. Exploring the interleaving of these different families of CAZAC sequences with permutation polynomials can lead to the generation of a broader range of sequences with desirable properties for various signal processing tasks. This exploration can contribute to the advancement of sequence design techniques and the optimization of signal processing systems in different domains.