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
Satu set jujukan polifasa dengan ortogonal yang terdiri daripada unsur kompleks dengan magnitud unit, boleh dinyatakan dengan matriks unitari yang sepadan dengan matriks Hadamard kompleks atau matriks transformasi Fourier diskret (DFT), yang barisnya adalah ortogon antara satu sama lain. Bank penapis yang dipadankan (MFB), yang secara serentak boleh mengeluarkan korelasi antara simbol yang diterima dan sebarang jujukan dalam set, berkesan untuk membina sistem komunikasi secara fleksibel. Kertas kerja ini membincangkan reka bentuk padat MFB bagi set jujukan polifasa, yang boleh digunakan pada mana-mana set jujukan yang dijana oleh fungsi logik yang diberikan. Ia tertumpu terutamanya pada kod ZCZ dengan q-fasa atau lebih elemen dinyatakan sebagai A(N=qn+s, M=qn-1, Zcz=qs(q-1)), di mana q, N, M and Zcz masing-masing menunjukkan, integer positif, tempoh jujukan, saiz keluarga dan zon korelasi sifar, kerana reka bentuk padat MFB menjadi sukar apabila Zcz adalah besar. Ia ditunjukkan bahawa fungsi logik yang diberikan pada gelang integer modulo q menjana kod ZCZ memberikan perwakilan matriks MFB yang M-vektor keluaran dimensi boleh diwakili oleh hasil darab matriks kesatuan tertib M dan M-vektor input berdimensi yang unsurnya ditulis sebagai hasil tambah unsur an N-vektor input dimensi. Oleh kerana matriks unitari (matriks Hadamard kompleks) boleh difaktorkan ke dalam n-1 matriks kesatuan tertib M bersama qM elemen bukan sifar sepadan dengan transformasi unitari yang pantas, MFB padat dengan bilangan elemen litar minimum boleh direka bentuk. Kerumitan perkakasannya dikurangkan daripada O(MN) Untuk O(qM log 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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Salinan
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
Salinan
@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},}
Salinan
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 -