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

Abstract

SUMMARYIn 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.

A novel construction method of zero-correlation zone sequences based on complete complementary codes

“…Difference with (13), (15) includes auto-correlaiton restriction. Therefore, we choose (M, Q, Q Z ) − ZCZ sequence set B as a p,n and allocate these as following,…”

“…In [4]- [8], the authors constructed ZCZ sequences based on complete complementary code (CCC) and, in [9]- [12], a perfect sequence is used. Moreover, mismatched filtering [13], m-sequence [14], and chip-like sequence [15] are also applied to construct ZCZ sequences.…”