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Preferred Z-complementary pairs and their application in doppler resilient waveform design

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Abstract

Z-complementary pairs (ZCPs) are well-known, but few work has dedicated to their aperiodic cross-correlation. One objective of this paper is to propose a novel class of sequence pairs, called “preferred Z-complementary pairs (PZCPs)”, where each sequence pair has Z-complementary property, and the aperiodic cross-correlation between the two sequences in each pair are zeros within a certain region. Some constructions of PZCPs from Golay complementary pairs (GCPs) are presented. Another objective of this paper is to apply PZCPs to design Doppler resilient waveforms combined with equal sums of powers (ESPs). Simulation results show that the proposed waveform has good Doppler tolerance.

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Notes

  1. The pulse trains transmitted on each antenna are not unique, as long as the order of transmission conforms to {P0, P1}, it is feasible.

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Acknowledgements

The authors address their thanks to Associate Editor for this Special Issue and the reviewers for their valuable comments and constructive suggestions that highly improved the quality of this paper. This work was supported in part by the NSFC Project No. 62171389 and 62020106001, and also by the Central Government Funds for Guiding Local Scientific and Technological Development under Grant 2022ZYD0004.

Funding

This work was supported in part by the NSFC Project No. 62171389 and 62020106001, and also by the Central Government Funds for Guiding Local Scientific and Technological Development under Grant 2022ZYD0004.

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Bingsheng Shen & Yang Yang

  2. Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu, China

    Pingzhi Fan

Authors
  1. Bingsheng Shen
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  2. Yang Yang
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  3. Pingzhi Fan
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Contributions

Bingsheng Shen proposed the main idea of paper and wrote the main manuscript text. Yang Yang polished the article and verified the computation. Pinzhi Fan and Yang Yang supplemented the details of the article and polished the article. All authors reviewed the manuscript.

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Correspondence to Yang Yang.

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Shen, B., Yang, Y. & Fan, P. Preferred Z-complementary pairs and their application in doppler resilient waveform design. Cryptogr. Commun. 16, 71–87 (2024). https://doi.org/10.1007/s12095-023-00636-4

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