A Novel Class of Zero-Correlation Zone Sequence Set Having a Low Peak-Factor and a Flat Power Spectrum

Takafumi HAYASHI  Yodai WATANABE  Anh T. PHAM  Toshiaki MIYAZAKI  Shinya MATSUFUJI  Takao MAEDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.12   pp.2429-2438
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2429
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Sequence
optimal zero-correlation zone,  low peak-factor,  pseudo-white noise,  perfect sequence,  

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The present paper introduces a novel method for the construction of a class of sequences that have a zero-correlation zone. For the proposed sequence set, both the cross-correlation function and the side lobe of the auto-correlation function are zero for phase shifts within the zero-correlation zone. The proposed scheme can generate a set of sequences of length 8n2 from an arbitrary Hadamard matrix of order n and a set of 2n trigonometric-like function sequences of length 4n. The proposed sequence construction can generate an optimal zero-correlation zone sequence set that satisfies the theoretical bound on the number of members for the given zero-correlation zone and sequence period. The auto-correlation function of the proposed sequence is equal to zero for all nonzero phase shifts. The peak factor of the proposed sequence set is √2, and the peak factor of a single trigonometric function is equal to √2. Assigning the sequences of the proposed set to a synthetic aperture ultrasonic imaging system would improve the S/N of the obtained image. The proposed sequence set can also improve the performance of radar systems. The performance of the applications of the proposed sequence sets are evaluated.