A Novel Class of Zero-Correlation Zone Sequence Sets Constructed from a Perfect Sequence

The present paper describes a method for the construction of a zero-correlation zone sequence set from a perfect sequence. Both the cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence sets are zero for phase shifts within the zero-correlation zone. These sets can be generated from an arbitrary perfect sequence, the length of which is the product of a pair of odd integers ((2n + 1)(2k + 1) for k ≥ 1 and n ≥ 0). The proposed sequence construction method can generate an optimal zero-correlation zone sequence set that achieves the theoretical bounds of the sequence member size given the size of the zero-correlation zone and the sequence period. The peak in the out-of-phase correlation function of the constructed sequences is restricted to be lower than the half of the power of the sequence itself. The proposed sequence sets could successfully provide CDMA communication without co-channel interference, or, in an ultrasonic synthetic aperture imaging system, improve the signal-to-noise ratio of the acquired image.