A Nonlinear Sum of Squares Search for CAZAC Sequences
Mark Magsino, Yixin Xu
TL;DR
This paper introduces a nonlinear sum of squares optimization method to search for CAZAC sequences, successfully identifying all length 7 sequences, providing evidence for finitely many length 10 sequences, and analyzing longer sequences' autocorrelation properties.
Contribution
It presents a novel optimization approach for CAZAC sequence search and provides comprehensive results for lengths 7 and 10, including the first exhaustive enumeration for length 7.
Findings
All length 7 CAZAC sequences identified
Finitely many length 10 CAZAC sequences estimated at 3040
Longer sequences analyzed for autocorrelation properties
Abstract
We report on a search for CAZAC sequences by using nonlinear sum of squares optimization. Up to equivalence, we found all length 7 CAZAC sequences. We obtained evidence suggesting there are finitely many length 10 CAZAC sequences with a total of 3040 sequences. Last, we compute longer sequences and compare their aperiodic autocorrelation properties to known sequences. The code and results of this search are publicly available through GitHub.
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Taxonomy
TopicsBiochemical and Structural Characterization · graph theory and CDMA systems · Evolutionary Algorithms and Applications