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首页> 外文期刊>Information Theory, IEEE Transactions on >New Sequences Design From Weil Representation With Low Two-Dimensional Correlation in Both Time and Phase Shifts
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New Sequences Design From Weil Representation With Low Two-Dimensional Correlation in Both Time and Phase Shifts

机译：在时间和相移方面具有低二维相关性的威尔表示新序列设计

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摘要

A new elementary expression of the construction first proposed by Gurevich, Hadani, and Sochen is given, which avoids the explicit use of the Weil representation. The sequences in this signal set are given by both multiplicative character and additive character of finite field $BBF_{p}$ . Such a signal set consists of $p^{2}(p-2)$ time-shift distinct sequences, the magnitude of the two-dimensional autocorrelation function (i.e., the ambiguity function) in both time and phase of each sequence is upper bounded by $2sqrt {p}$ at any shift not equal to (0, 0). Furthermore, the magnitude of their Fourier transform spectrum is less than or equal to 2. For a subset consisting of $p(p-2)$ phase-shift distinct sequences in this signal set, the magnitude of the ambiguity function of any pair is upper bounded by $4sqrt {p}$. A proof is given through finding a new expression of the sequences in the finite harmonic oscillator system. An open problem for directly establishing these assertions without involving the Weil representation is addressed.
机译：给出了由Gurevich，Hadani和Sochen首次提出的结构的新基本表达，它避免了对Weil表示的明确使用。该信号集中的序列由有限域 $ BBF_ {p} $ 的乘性和加性给出。这样的信号集由 $ p ^ {2}（p-2）$ 时移不同的序列，幅度每个序列在时间和相位上的二维自相关函数（即歧义函数）的上界由 $ 2sqrt {p} $ 在任何不等于（0，0）的移位处。此外，它们的傅立叶变换谱的幅度小于或等于2。对于由<公式一级的类型：inline“> $ p（p-2）$ 在此信号集中的相异序列不同，任何一对模糊函数的幅度都由 $ 4sqrt {p} $ < / tex> 。通过在有限谐波振荡器系统中找到序列的新表达式来给出证明。解决了直接建立这些断言而不涉及Weil表示的开放性问题。

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