  In this paper, a simple construction of interference-free zero correlation
zone (IF-ZCZ) sequence sets is proposed by well designed finite Zak transform
lattice 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 is
optimal with respect to the Tang-Fan-Matsufuji bound. Secondly, the
transformations that keep the properties of the optimal IF-ZCZ sequence set
unchanged are given, and the equivalent relation of the optimal IF-ZCZ sequence
set is defined based on these transformations. Then, it is proved that the
general construction of the optimal IF-ZCZ sequence set proposed by Popovic is
equivalent to the simple construction of the optimal IF-ZCZ sequence set, which
indicates that the generation of the optimal IF-ZCZ sequence set can be
simplified. Moreover, it is pointed out that the alphabet size for the special
case of the simple construction of the optimal IF-ZCZ sequence set can be a
factor of the period. Finally, both the simple construction of the optimal
IF-ZCZ sequence set and its special case have sparse and highly structured Zak
spectra, which can greatly reduce the computational complexity of implementing
matched filter banks.
