Multiple SNC-ZCZ Sequence Sets With Optimal Correlations Based on Zak Transforms

Spectrally-null-constrained (SNC) sequences, characterized by a good zero correlation zone (ZCZ) property, are applied in contemporary communication and radar systems that operate across a non-continuous spectrum. Although a large number of previous studies have been conducted, there has been no work on constructing optimal SNC sequence sets with all-zero inter-set cross-correlation (AZISCC). In this letter, we present a method for constructing SNC-ZCZ sequence sets utilizing the finite Zak transform (FZT). The obtained multiple SNC-ZCZ sequence sets are optimal, and they achieve the theoretical bound. The cross-correlation between sequence sets is 0, and the inter-cell interference can be eliminated. Furthermore, the sparse representation of the sequences is convenient for performing signal processing tasks in many radar, sonar, and communication applications.