2005 Fiscal Year Final Research Report Summary
Ternary Sequence Sets with a Zero-correlation Zone for Periodic, Aperiodic, and Odd Correlation Functions and their Applications
| Project/Area Number |
16560053
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | University of Aizu |
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Principal Investigator |
HAYASHI Takafumi University of Aizu, Dept.of Computer Software, Professor, コンピュータ理工学部, 教授 (20218580)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Zero Correlation Zone / Sequence Design / Ternary Sequence / Hadamard Sequence / Difference Set / Code Division Multiplexing / Ultrasonic Imaging |
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| Research Abstract |
Novel classes of ternary sequence having a zero-correlation zone (zcz), based on Hadamard matrices are developed. One of the proposed sequence construction can simultaneously generate a finite-length ternary ZCZ sequence set and a periodic ternary ZCZ sequence set. The generated finite-length ternary ZCZ sequence set has a zero-correlation zone for an aperiodic function. The generated periodic ternary ZCZ sequence set has a zero-correlation zone for even and odd correlation functions. One of the proposed ternary sequence sets have a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of size n_0×n_0 and a Hadamard matrix of size n_1×n_1. The constructed sequence set consists of n_0n_1 ternary sequences, and the length of each sequence is n^<(m+1)>_0(n_1+1) for a non-negative integer m. The zero-correlation zone of the proposed sequences is |τ|【less than or equal】n^m_0-1, where τ is the phase shift. The sequence member size of the proposed sequence set is equal to (n_1)/(n_1+1) times that of the theoretical upper bound of the member size of a sequence set with a zero-correlation zone.
Two kinds of ZCZ sequence sets, which can reach the upper bound on the code size are also developed. One is a ZCZ sequence sets of ternary sequences, which can be constructed by an orthogonal matrix including a Hadamard matrix and an orthogonal sequence. The other is a ZCZ sequence sets of pairs of ternary sequences and binary sequences, which can be constructed by an orthogonal matrix including a Hadamard matrix and an orthogonal sequence pair. These sequence sets can successfully provide CDMA communication without co-channel interference.
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Research Products
(14 results)
