周期為2p的低相關(guān)四進(jìn)制序列的構(gòu)造方法

李恒智 趙偉 王東 賈彥國 沈秀敏

摘 要：

具有理想自相關(guān)性、平衡性和易于實(shí)現(xiàn)特性的四進(jìn)制序列，廣泛應(yīng)用于通信等領(lǐng)域中。雖然已被發(fā)現(xiàn)的平衡理想自相關(guān)四進(jìn)制序列有很多，但低相關(guān)四進(jìn)制序列還有很大的研究空間。本文基于廣義四階分圓類和中國剩余定理對(duì)周期為2p（p=4f+1奇素?cái)?shù)）的低相關(guān)四進(jìn)制序列進(jìn)行研究，當(dāng)四進(jìn)制序列的第0位和第p位元素值分別同時(shí)為1和i時(shí)，得到了旁瓣值為{2，-2，-6}、{2，-2，-4，4}的平衡低相關(guān)四進(jìn)制序列，當(dāng)?shù)?位和第p位元素值分別同時(shí)為-1和-i時(shí)，得到了旁瓣值同為{2，2i，-2i，-2+2i，-2-2i}的平衡低相關(guān)四進(jìn)制序列。

關(guān)鍵詞：

低相關(guān)四進(jìn)制序列；廣義分圓類；中國剩余定理；平衡

中圖分類號(hào)：TN911.2? 文獻(xiàn)標(biāo)識(shí)碼： A? DOI：10.3969/j.issn.1007-791X.2023.01.010

3 結(jié)論

本文通過利用廣義四階分圓類和中國剩余定理得到了偶周期為2p（p=4f+1奇素?cái)?shù)）的平衡低相關(guān)四進(jìn)制序列。通過本文的研究總結(jié)，進(jìn)一步擴(kuò)大了四進(jìn)制序列的范圍，對(duì)于推進(jìn)研究基于四進(jìn)制序列的最佳離散信號(hào)有重要意義。

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Construction on low-correlation quaternary sequences with period 2p

LI Hengzhi1，ZHAO Wei2，3，WANG Dong2，JIA Yanguo2，SHEN Xiumin2

（1.Hebei Institute of International Business and Economics，Qinhuangdao，Hebei 066311，China;

2.School of Information Science and Engineering，Yanshan University，Qinhuangdao，Hebei 066004，China;

3.Liren College，Yanshan University，Qinhuangdao，Hebei 066004，China）

Abstract：

The quaternary sequence with the characteristics of ideal autocorrelation，balance and easy realization is widely used in the field of communication.Although many balanced ideal autocorrelation quaternary sequences have been found，there is still much room for research on low-correlation quaternary sequences.Based on the generalized cyclotomic class and the Chinese remainder theorem，a quaternary sequence with a period of 2p （p=4f+1 is odd prime number） is studied.When the 0th and pth element values of the sequence are 1 and i，a balanced low-correlation quaternary sequence with side-lobe values of {2，-2，-6}、{2，-2，-4，4}are obtained.When the 0th and pth element values of the sequence are -1 and -i，a balanced low-correlation quaternary sequence with side-lobe values of{2，2i，-2i，-2+2i，-2-2i} are obtained.

Keywords：

low-correlation quaternary sequence;generalized cyclotomic classes;Chinese remainder theorem;balance