Binary Sequences With Small Peak Sidelobe Level
Binary Sequences With Small Peak Sidelobe Level
复制标题
具有小峰值旁瓣电平的二进制序列
DOI：
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发表时间：
2012
影响因子：
2.5
通讯作者：
K. Schmidt
中科院分区：
文献类型：
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作者：
K. Schmidt
长度为n的二进制序列是具有{-1，1}中的元素的n元组，并且其峰值旁瓣电平是其非零移位处的非周期自相关的最大绝对值。一个经典的问题是找到二进制序列，其峰值旁瓣电平相比，序列的长度是小的。本文利用概率组合学中的已知技术，给出了一个长度为n的二进制序列的构造方法，该序列的峰值旁瓣电平至多为2nlog（2n），其中n > 1。这改善了显式构造的二进制序列族的峰值旁瓣电平的最佳已知界，该界是针对m序列族而产生的。通过数值分析，它认为，所构造的序列的峰值旁瓣电平的增长实际上是像顺序n log log n，因此，严格增长比一个典型的二进制序列的峰值旁瓣电平更慢。
A binary sequence of length n is an n-tuple with elements in {-1,1} and its peak sidelobe level is the largest absolute value of its aperiodic autocorrelations at nonzero shifts. A classical problem is to find binary sequences whose peak sidelobe level is small compared to the length of the sequence. Using known techniques from probabilistic combinatorics, this paper gives a construction for a binary sequence of length n with peak sidelobe level at most √2nlog(2n) for every n >; 1. This improves the best known bound for the peak sidelobe level of a family of explicitly constructed binary sequences, which arises for the family of m-sequences. By numerical analysis, it is argued that the peak sidelobe level of the constructed sequences grows in fact like order √n log log n and, therefore, grows strictly more slowly than the peak sidelobe level of a typical binary sequence.