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In this paper, a simple construction of interference-free zero correlationzone (IF-ZCZ) sequence sets is proposed by well designed finite Zak transformlattice tessellation. Each set is characterized by the period of sequences$KM$, the set size $K$ and the length of zero correlation zone $M-1$, which isoptimal with respect to the Tang-Fan-Matsufuji bound. Secondly, thetransformations that keep the properties of the optimal IF-ZCZ sequence setunchanged are given, and the equivalent relation of the optimal IF-ZCZ sequenceset is defined based on these transformations. Then, it is proved that thegeneral construction of the optimal IF-ZCZ sequence set proposed by Popovic isequivalent to the simple construction of the optimal IF-ZCZ sequence set, whichindicates that the generation of the optimal IF-ZCZ sequence set can besimplified. Moreover, it is pointed out that the alphabet size for the specialcase of the simple construction of the optimal IF-ZCZ sequence set can be afactor of the period. Finally, both the simple construction of the optimalIF-ZCZ sequence set and its special case have sparse and highly structured Zakspectra, which can greatly reduce the computational complexity of implementingmatched filter banks.

A Note on "Optimum Sets of Interference-Free Sequences With Zero Autocorrelation Zone"