A generation method of orthogonal periodic complex number sequence sets with lowest peak of cross‐correlation for any period based on chirp sequences

Abstract

AbstractIn 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