1. A generation method of orthogonal periodic complex number sequence sets with lowest peak of cross-correlation for any period based on chirp sequences.
- Author
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Ohue, Kenji
- Subjects
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SET theory , *ORTHOGONALIZATION , *FOURIER transforms , *FOURIER analysis , *ELECTRONIC systems , *TELECOMMUNICATION systems , *ELECTRONICS , *INFORMATION science - Abstract
In this paper, we propose a new generation method of orthogonal periodic complex number sequence sets based on chirp sequences that can derive the orthogonal periodic complex number sequence set having the minimum cross-correlation peak for any period. First, we use the Ohue–Okahisa Conjecture that is proven in a practical range related to the orthogonal periodic polyphase sequence obtained by taking the inverse discrete Fourier transform of a chirp sequence to derive the relationship between the period N having the minimum peak of the cross-correlation and the chirp sequence parameter R, and clearly explain a generation method of an orthogonal periodic complex number sequence pair having the minimum cross-correlation peak for any period. Next, we present a generation method of the orthogonal periodic complex number sequence set having the minimum cross-correlation peak for any two sequences in the set. The dimension of this set is clearly equal to the minimum prime factor of the period N. Furthermore, we present a generation method of the orthogonal periodic polyphase sequence set having the minimum cross-correlation peak for any period and show that the dimension of this set becomes a value 1 less than the minimum prime factor of period N. We show that this generation method can derive the orthogonal periodic complex number sequence set having the minimum cross-correlation peak for periods that could not be generated by conventional techniques and can derive the orthogonal periodic polyphase sequence set demonstrated previously. Finally, we present a generation example of the orthogonal periodic sequence set having the minimum cross-correlation peak and clearly show that the orthogonal periodic complex number sequence set and orthogonal periodic polyphase sequence set having the minimum cross-correlation peak can be generated. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(5): 1–11, 2004; Published online in Wiley InterScience (
www.interscience.wiley.com ). DOI 10.1002/ecjc.10129 [ABSTRACT FROM AUTHOR]- Published
- 2004
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