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Golay complementary sets with large zero odd-periodic correlation zones

  • Corresponding author: Yang Yang

    Corresponding author: Yang Yang 

This work was supported in part by the National Science Foundation of China under Grants 61771016, 61661146003 and 11571285

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  • Golay complementary sets (GCSs) are widely used in different communication systems, i.e., GCSs could be used in OFDM systems to control peak-to-mean envelope power ratio (PMEPR). In this paper, inspired by the work on GCSs with large zero correlation zone given by Chen et al in 2018, we investigate the relationship between GCSs and zero odd-periodic correlation zone (ZOCZ) sequence sets, and present GCSs with flexible sequence set sizes, sequence lengths, large ZOCZ and low PMEPR. Those proposed sequences could be applied in OFDM system for synchronization.

    Mathematics Subject Classification: Primary: 94A05; Secondary: 60G35.


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  • Table 1.  Comparison of GCSs/GCPs with Large ZCZ/ZOCZ Property

    Parameters Constraints Ref.
    $ (2,2^m,2^{m-2}) $ Golay-ZCZ $ g_m\in \{\frac{H}{2},0\} $, $ H\equiv0\; \mathrm{mod}\; 2 $ [10,11]
    $ (2,2^m,2^{\pi(2)-1}) $ Golay-ZCZ $ \begin{array}{l} g_m\in \{0,\frac{H}{2}\},H\equiv 0\; \mathrm{mod}\; 2\pi(1)=m \end{array} $ [2]
    $ (2^k,2^m,2^{\pi_1(2)-1}) $ Golay-ZCZ $ \begin{array}{l}g_m\in \{0,\frac{H}{2}\}, H\equiv0\; \mathrm{mod}\; 2, \pi_\alpha(1)=m-\alpha+1, \;\mbox{ for }\; 1\le\alpha\le k\end{array} $ [2]
    $ (2,2^m,2^{\pi(2)-1}) $ Golay-ZOCZ $ \begin{array}{l} c_m\in \{\frac{H}{4},\frac{3H}{4}\},H\equiv0\; \mathrm{mod}\; 4, \pi(1)=m \end{array} $ Thm. 1
    $ (2^k,2^m,2^{\pi_1(2)-1}) $ Golay-ZOCZ $ \begin{array}{l}g_m\in \{\frac{H}{4},\frac{3H}{4}\}, H\equiv0\; \mathrm{mod}\; 4, \pi_\alpha(1)=m-\alpha+1, \;\mbox{ for }\; 1\le\alpha\le k\end{array} $ Thm. 2
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