A novel class of QPSK zero-correlation zone sequence sets

The present paper introduces the construction of Quadrature Phase Shift Keying (QPSK) modulation based sequences having a zero-correlation zone. For a zero-correlation zone sequence set of N sequences, each of length L, the cross-correlation function and the side lobe of the autocorrelation function of the proposed sequence set is zero for the phase shifts τ within the zero-correlation zone z, such that |τ| ≤ z (τ ≠ 0 for the autocorrelation function). The ratio N(z+1) over ℓ is theoretically limited to one. When the ratio of a sequence set is equal to one, the sequence set is called an optimal zero-correlation sequence set. The proposed zero-correlation zone sequence set can be generated from an arbitrary Hadamard matrix of order n. First, the proposed sequence set is generated as a set of 4n sequences of length 8n with the zero-correlation zone z = 1. The length of the proposed sequence set can be extended by sequence interleaving, where m times interleaving can generate the 4n sequences, each of length 2m+3n. The proposed sequence set is optimal for m = 0,1 and almost optimal for m > 1.