Constructions of Periodic Quasi-complementary Sequence Sets
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摘要: 该文基于2元序列支撑集和低相关序列集，提出一种新的周期准互补序列集构造框架。在此框架基础上，分别利用最优4元序列族A、族D和Luke序列集提出了3类渐近最优和渐近几乎最优周期准互补序列集，序列集参数由2元序列和低相关序列集共同决定。与传统的完备互补序列集相比，所构造的准互补序列集具有更多的序列数目，应用到多载波扩频通信系统中可以支持更多的用户。Abstract: Based on the support of binary sequences and low correlation sequence sets, a new framework for constructing periodic quasi-complementary sequence sets is proposed. Based on this framework, three classes of asymptotically optimal and asymptotically almost optimal periodic quasi-complementary sequence sets are proposed by using the optimal quaternary sequence family A, family D and Luke sequence set, respectively. In addition, the parameters of sequence set are determined by the binary sequence and the low correlation sequence set. Compared with the traditional complete complementary sequence set, the quasi-complementary sequence set includes more sequences, which can support more users in multi-carrier spread spectrum communication system.
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表 1 方法1周期准互补序列集参数
$n$ $M$ $K$ $N$ ${\delta _{\max }}$ $\rho $ 6 64 16 63 54.0 1.9486 7 128 32 127 104.5 1.8851 8 256 64 255 204.0 1.8403 9 512 128 511 400.9 1.8086 10 1024 256 1023 792.0 1.7862 
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表 2 方法2周期准互补序列集参数
$n$ $M$ $K$ $N$ ${\delta _{\max }}$ $\rho $ 7 128 32 254 152.7 1.9562 8 256 64 510 295.5 1.8888 9 512 128 1.22 577.0 1.8421 10 1024 256 2046 1134.0 1.8095 11 2048 512 4094 2240.0 1.7866
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表 3 方法3周期准互补序列集参数
$n$ $M$ $K$ $N$ ${\delta _{\max }}$ $\rho $ 2 8 4 8 6.0 1.4882 3 26 13 26 16.1 1.2374 4 80 40 80 45.0 1.1249 5 242 121 242 129.3 1.0685 6 728 364 728 378.0 1.0385
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表 4 准互补序列集参数比
方法 序列数目 子序列数目 序列长度 $\delta_{\max} $ $\rho $ 约束条件 文献[11]方法1 pn pn–1–1 pn–1 $\dfrac{1}{2}\left( p^{\frac{n}{2}+p^n}\right)$ 1 $p=2 $ 文献[11]方法2 pn pn–1–1 2(pn–1) $ p^{\frac{n}{2}}+ p^n$ $ \sqrt {\frac{3}{2}}$ $p=2 $ 文献[12]方法1 p $\dfrac{p-1}{2}$ p $\dfrac{p+\sqrt {p} }{2}$ 1 p是奇素数且p≥5 文献[12]方法2 p K p $\sqrt {\dfrac{pK(p-K)}{p-1} }$ 1 p是奇素数且p≥5 文献[13]方法A pn–1 K pn–1 $\sqrt {\dfrac{p^n K(p^n-K-1)}{p^n-2} }$ 1 p是素数 文献[13]方法B pn–1 $\dfrac{p^n}{4}$ pn–1 3·2n–2 $\sqrt {3} $ p=2 文献[13]方法C pn–1 $\dfrac{p^n-1}{2}$ pn–1 $\dfrac{1}{2}(p^n+p^{\frac{n}{2} })$ 1 p是奇素数 文献[13]方法D pn–1 pn–1 pn–1 $p^{n-\frac{1}{2}} $ 1 p是素数 文献[13]方法E p2n–1 pn p2n–1 $p^{\frac{3n}{2}} $ 1 p是素数 本文方法1 pn pn–2 pn–1 $3(p^{\frac{n}{2}-2}+p^{n-2}) $ $\sqrt {3} $ p=2 本文方法2 pn pn–2 2(pn–1) $3(p^{\frac{n}{2}-1}+p^{n-\frac{3}{2}}) $ $\sqrt {3} $ p=2 本文方法3 pn–1 $\dfrac{p^n-1}{2}$ pn–1 $\dfrac{1}{2}(p^n+p^{\frac{n}{2} })$ 1 p是奇素数
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