A Generalized Construction of Zero-Correlation Zone Sequence Set with Sequence Subsets

Takafumi HAYASHI  Takao MAEDA  Satoshi OKAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.7   pp.1597-1602
Publication Date: 2011/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1597
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Spread Spectrum Technologies and Applications
finite-length sequence,  sequence subsets,  inter-subset zero-correlation,  zero-correlation zone,  aperiodic correlation function,  periodic correlation function,  

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The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of orders n0 and n1. The constructed sequence set consists of n0 n1 ternary sequences, each of length n0(m+2)(n1+Δ), for a non-negative integer m and Δ ≥ 2. The zero-correlation zone of the proposed sequences is |τ| ≤ n0m+1-1, where τ is the phase shift. The proposed sequence set consists of n0 subsets, each with a member size n1. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a zero-correlation zone with a width that is approximately Δ times that of the correlation function of sequences of the same subset (intra-subset correlation function). The inter-subset zero-correlation zone of the proposed sequences is |τ| ≤ Δn0m+1, where τ is the phase shift. The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set.