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A Novel Construction of TreeStructured ZeroCorrelation Zone Sequence Sets
Takafumi HAYASHI Yodai WATANABE Takao MAEDA Shinya MATSUFUJI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.10
pp.21872194 Publication Date: 2017/10/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E100.A.2187 Type of Manuscript: LETTER Category: Coding Theory Keyword: zerocorrelation zone, ternary sequence, binary tree, intersubset zerocorrelation zone,
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Summary:
The present paper introduces a novel construction of structured ternary sequences having a zerocorrelation zone (ZCZ) for both periodic and aperiodic correlation functions. The crosscorrelation function and the side lobe of the autocorrelation function of the proposed sequence set are zero for phase shifts within the ZCZ. The proposed ZCZ sequence set can be generated from an arbitrary Hadamard matrix of order n. The sequence set of order 0 is identical to the rth row of the Hadamard matrix. For m≥0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set of order m has 2^{m} subsets of size n. The length of the sequence is equal to n4^{m}+2^{m+1}(2^{m}1); The phase shift of the ZCZ for the whole sequence set is from (2^{m}1) to (2^{m}1). The sequence set of order 0 is coincident with the rows of the given Hadamard sequence with no ZCZ. The subsets can be associated with a perfect binary tree of height m with 2^{m} leaves. The rth sequence subset consists of from the nrth sequence to the ((n+1)r1)th sequence. The rth subset is assigned to the rth leaf of the perfect binary tree. For a longer distance between the corresponding leaves to the rth and sth sequences, the ZCZ of the rth and sth sequences is wider. This treestructured width of ZCZ of a pair of the proposed sequences enables flexible design in applications of the proposed sequence set. The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth generation of radio access networks.


