A class of ternary sequence sets with a zero-correlation zone for periodic, aperiodic, and odd correlation functions
The present paper introduces a new approach to the construction of a class of ternary sequences having a zero-correlation zone. The cross-correlation function of each pair of the proposed sequences is zero for phase shifts within the zero-correlation zone, and the auto-correlation function of each proposed sequence is zero for phase shifts within the zero-correlation zone, except for zero-shift. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions. As such, the proposed sequence can be used as a finite-length sequence with a zero-correlation zone. A set of the proposed sequences can be constructed for any set of Hadamard sequences of length n. The constructed sequence set consists of 2n ternary sequences, and the length of each sequence is (n+1)2(m+2) for a non-negative integer m. The periodic correlation function, the aperiodic correlation function, and the odd correlation function of the proposed sequences have a zero-correlation zone from -(2(m+1) - 1) to (2(m+1) - 1). The member size of the proposed sequence set is n/n+1 of the theoretical upper bound of the member size of a sequence having a zero-correlation zone. The ratio of the number of non-zero elements to the the sequence length of the proposed sequence is also n/n+1.
ternary sequence zero-correlation zone odd correlation function finite-length sequence aperiodic correlation function