Polyphase related-prime sequences
Polyphase related-prime sequences
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DOI：
10.1049/ip-cdt:20010209
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发表时间：
2001-03
期刊：
影响因子：
--
通讯作者：
D. Green;P. Green
中科院分区：
文献类型：
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作者：
D. Green;P. Green
众所周知的家庭的二进制孪生素数序列一般的多值的情况下，通过采用多相表示的序列元素。这些多相版本表现出类似的周期性和非周期性的自相关特性，他们的二进制同行，并被称为q-相位相关素（RP）序列。这些序列的长度为L=r/spl middot/s，其中r和s都是素数，并且s=r+k。它们是通过组合两个长度为r和s的多相勒让德序列，并在某些点修改所得的复合序列来构造的。在构造和分析这些序列时采用了二维阵列结构，通过将长度为r和s的指数序列转换为模q形式，得到了原始的q相Legendre序列。当q为偶数时，根据L/spl equiv/q+1 mod 2 q还是L/spl equiv/1 mod 2 q，出现两类RP序列。对于奇数q，只有一个类是可用的，这里L/spl等于/1 mod 2 q。这些RP序列的异相周期相关值与序列长度无关，仅取决于相位数q和两个相关素数之间的差k。最大异相相关值由1-k给出。提供了可用序列表。
The well known family of binary twin-prime sequences is generalised to the multiple-valued case by employing a polyphase representation of the sequence elements. These polyphase versions exhibit similar periodic and aperiodic auto-correlation properties to their binary counterparts, and are referred to as q-phase related-prime (RP) sequences. These sequences have length L=r/spl middot/s, for r and s both prime, and with s=r+k. They are constructed by combining two polyphase Legendre sequences of lengths r and s, and modifying the resulting composite sequence at certain points. A two-dimensional array structure is employed in the construction and analysis of these sequences, The original q-phase Legendre sequences are derived by converting the index sequences of lengths r and s to modulo-q form. When q is even, two classes of RP sequence arise, depending on whether L/spl equiv/q+1 mod 2q or L/spl equiv/1 mod 2q. For odd q, only a single class is available, and here L/spl equiv/1 mod 2q. The out-of-phase periodic correlation values of these RP sequences are independent of the sequence length, and depend only on the number of phases q and the difference k between the two related primes. The maximum out-of-phase correlation values is given by 1-k. Tables of available sequences are presented.