A Novel Class of Structured Zero-Correlation Zone Sequence Sets

Takafumi HAYASHI; Takao MAEDA; Anh T. PHAM; Shinya MATSUFUJI

doi:10.1587/transfun.E101.A.2171

A Novel Class of Structured Zero-Correlation Zone Sequence Sets

Takafumi HAYASHI, Takao MAEDA, Anh T. PHAM, Shinya MATSUFUJI

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The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation 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 pair of an Hadamard matrix of order l_h and a binary/ternary perfect sequence of length l_p. The sequence set of order 0 is identical to the r-th 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 has l_p subsets of size 2l_h. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2^m+1-1) to 2^m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2^m+2-(l_h+1)((j-k) mod l_p) to -2^m+2-(l_h+1)((j-k) mod l_p). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2171-2183

Publication Date: 2018/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E101.A.2171

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Sequence

Authors

Takafumi HAYASHI
  Niigata University
Takao MAEDA
  University of Aizu
Anh T. PHAM
  University of Aizu
Shinya MATSUFUJI
  Yamaguchi University

Keyword

zero-correlation zone, ternary sequence, asymmetric zcz, inter-subset zcz

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Takafumi HAYASHI, Takao MAEDA, Anh T. PHAM, Shinya MATSUFUJI, "A Novel Class of Structured Zero-Correlation Zone Sequence Sets" in IEICE TRANSACTIONS on Fundamentals, vol. E101-A, no. 12, pp. 2171-2183, December 2018, doi: 10.1587/transfun.E101.A.2171.
Abstract: The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation 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 pair of an Hadamard matrix of order l_h and a binary/ternary perfect sequence of length l_p. The sequence set of order 0 is identical to the r-th 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 has l_p subsets of size 2l_h. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2^m+1-1) to 2^m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2^m+2-(l_h+1)((j-k) mod l_p) to -2^m+2-(l_h+1)((j-k) mod l_p). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2171/_p

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@ARTICLE{e101-a_12_2171,
author={Takafumi HAYASHI, Takao MAEDA, Anh T. PHAM, Shinya MATSUFUJI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Novel Class of Structured Zero-Correlation Zone Sequence Sets},
year={2018},
volume={E101-A},
number={12},
pages={2171-2183},
abstract={The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation 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 pair of an Hadamard matrix of order l_h and a binary/ternary perfect sequence of length l_p. The sequence set of order 0 is identical to the r-th 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 has l_p subsets of size 2l_h. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2^m+1-1) to 2^m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2^m+2-(l_h+1)((j-k) mod l_p) to -2^m+2-(l_h+1)((j-k) mod l_p). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.},
keywords={},
doi={10.1587/transfun.E101.A.2171},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - A Novel Class of Structured Zero-Correlation Zone Sequence Sets
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2171
EP - 2183
AU - Takafumi HAYASHI
AU - Takao MAEDA
AU - Anh T. PHAM
AU - Shinya MATSUFUJI
PY - 2018
DO - 10.1587/transfun.E101.A.2171
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation 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 pair of an Hadamard matrix of order l_h and a binary/ternary perfect sequence of length l_p. The sequence set of order 0 is identical to the r-th 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 has l_p subsets of size 2l_h. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2^m+1-1) to 2^m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2^m+2-(l_h+1)((j-k) mod l_p) to -2^m+2-(l_h+1)((j-k) mod l_p). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.
ER -