Low-peak factor optimal zero-correlation zone sequence set and its applications

The present paper introduces a novel method for the construction of sequences that have a zero-correlation zone. For the proposed sequence set, both the cross-correlation function and the side lobe of the auto-correlation function are zero for phase shifts within the zero-correlation zone. The proposed sequence set can be generated from an arbitrary Hadamard matrix of order n and a set of 2n trigonometric-like function sequences of length 4n. The proposed construction can generate an optimal sequence set that satisfies, for a given zero-correlation zone and sequence period, the theoretical bound on the number of members. The peak factor of the proposed sequence set is equal to √2.