A novel zero-correlation zone sequence set with sequence subsets
Takafumi Hayashi, Takao Maeda, Satoshi Okawa · 2010
The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone. The proposed sequences can be constructed from a pair of Hadamard matrices of the orders n0and n1. The constructed sequence set consists of n0n1ternary sequences, each of length n0(m+2)(n1+2), for a non-negative integer m. The zero-correlation zone of the proposed sequences is |τ| ≤ n0m+1- 1, where τ is the phase shift. The sequence member size of the proposed sequence set is equal to n1/n1+2 times that of the theoretical upper bound on the member size of a sequence set with a zero-correlation zone. The proposed sequence set consists of n0subsets, each of member size n1. The correlation function of the sequences of a pair of different subsets, refereed to as the inter-subset correlation function, has a zero-correlation zone with a width that is almost twice that of the correlation function of sequences of the same subset (intra-subset correlation function). This wider inter-subset zero-correlation contributes to the performance improvement of applications of the proposed sequence set. The proposed sequence set has a zero-correlation zone for both periodic and aperiodic correlation functions.