Orthogonal and ZCZ Sets of Real-Valued Periodic Orthogonal Sequences from Huffman Sequences


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.12   pp.2728-2736
Publication Date: 2011/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.2728
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Wideband Systems)
periodic sequence,  finite-length sequence,  Huffman sequence,  orthogonal set,  ZCZ set,  fast correlation algorithm,  

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This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν+1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.