The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
단위 크기를 갖는 복소 요소로 구성된 직교성을 갖는 다상 시퀀스 세트는 행이 서로 직교하는 복소 하다마드 행렬 또는 이산 푸리에 변환(DFT) 행렬에 대응하는 유니터리 행렬로 표현될 수 있습니다. 수신된 기호와 집합의 모든 시퀀스 간의 상관 관계를 동시에 출력할 수 있는 MFB(Matched Filter Bank)는 통신 시스템을 유연하게 구성하는 데 효과적입니다. 본 논문에서는 주어진 논리 함수에 의해 생성된 모든 시퀀스 세트에 적용할 수 있는 다상 시퀀스 세트의 MFB의 컴팩트한 설계에 대해 논의합니다. 주로 ZCZ 코드에 중점을 둡니다. q- 다음과 같이 표현되는 위상 이상의 요소 A(N=qn+s, M=qn-1, Zcz=qs(q-1)), 여기서 q, N, M 및 Zcz 는 각각 양의 정수, 시퀀스 주기, 패밀리 크기, 제로 상관 영역을 나타냅니다. Zcz 크다. 정수 링에 주어진 논리 함수가 모듈로로 표시됩니다. q ZCZ 코드를 생성하면 다음과 같은 MFB의 행렬 표현이 제공됩니다. M-차원 출력 벡터는 단위 행렬의 곱으로 표현될 수 있습니다. M 및 M- 요소가 요소의 합으로 기록되는 차원 입력 벡터 N-차원 입력 벡터. 단위 행렬(복소 하다마르 행렬)은 다음과 같이 인수분해될 수 있습니다. n-1개의 단위 행렬 M 과 qM 빠른 단위 변환에 대응하는 0이 아닌 요소를 사용하여 최소한의 회로 요소 수로 컴팩트한 MFB를 설계할 수 있습니다. 하드웨어 복잡성이 다음과 같이 감소됩니다. O(MN)에 O(qM 기록 q M+N).
Sho KURODA
Yamaguchi University
Shinya MATSUFUJI
Yamaguchi University
Takahiro MATSUMOTO
Yamaguchi University
Yuta IDA
Yamaguchi University
Takafumi HAYASHI
Nihon University
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Sho KURODA, Shinya MATSUFUJI, Takahiro MATSUMOTO, Yuta IDA, Takafumi HAYASHI, "Design of Compact Matched Filter Banks of Polyphase ZCZ Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 9, pp. 1103-1110, September 2020, doi: 10.1587/transfun.2019EAP1138.
Abstract: A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAP1138/_p
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@ARTICLE{e103-a_9_1103,
author={Sho KURODA, Shinya MATSUFUJI, Takahiro MATSUMOTO, Yuta IDA, Takafumi HAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Design of Compact Matched Filter Banks of Polyphase ZCZ Codes},
year={2020},
volume={E103-A},
number={9},
pages={1103-1110},
abstract={A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).},
keywords={},
doi={10.1587/transfun.2019EAP1138},
ISSN={1745-1337},
month={September},}
부
TY - JOUR
TI - Design of Compact Matched Filter Banks of Polyphase ZCZ Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1103
EP - 1110
AU - Sho KURODA
AU - Shinya MATSUFUJI
AU - Takahiro MATSUMOTO
AU - Yuta IDA
AU - Takafumi HAYASHI
PY - 2020
DO - 10.1587/transfun.2019EAP1138
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2020
AB - A polyphase sequence set with orthogonality consisting complex elements with unit magnitude, can be expressed by a unitary matrix corresponding to the complex Hadamard matrix or the discrete Fourier transform (DFT) matrix, whose rows are orthogonal to each other. Its matched filter bank (MFB), which can simultaneously output the correlation between a received symbol and any sequence in the set, is effective for constructing communication systems flexibly. This paper discusses the compact design of the MFB of a polyphase sequence set, which can be applied to any sequence set generated by the given logic function. It is primarily focused on a ZCZ code with q-phase or more elements expressed as A(N=qn+s, M=qn-1, Zcz=qs(q-1)), where q, N, M and Zcz respectively denote, a positive integer, sequence period, family size, and a zero correlation zone, since the compact design of the MFB becomes difficult when Zcz is large. It is shown that the given logic function on the ring of integers modulo q generating the ZCZ code gives the matrix representation of the MFB that M-dimensional output vector can be represented by the product of the unitary matrix of order M and an M-dimensional input vector whose elements are written as the sum of elements of an N-dimensional input vector. Since the unitary matrix (complex Hadamard matrix) can be factorized into n-1 unitary matrices of order M with qM nonzero elements corresponding to fast unitary transform, a compact MFB with a minimum number of circuit elements can be designed. Its hardware complexity is reduced from O(MN) to O(qM log q M+N).
ER -