Optimal Uncorrelated Polyphase ZCZ Sequences over an Alphabet of Minimum size

In this paper, we derive a lower bound on the alphabet size of the optimal uncorrelated polyphase ZCZ sequence families, assuming that Mow’s Conjecture is true. We also propose some new optimal uncorrelated polyphase ZCZ sequence families for all the optimal ZCZ parameters. All our proposed families achieve our proposed alphabet size bound so that this bound is the minimum alphabet size (assuming Mow’s conjecture is true). We also derive some interesting facts regardless of the truth of Mow’s Conjecture: an optimal ZCZ family of normalized sequence (not necessarily uncorrelated) is always periodic complementary; therefore, a sequence generated by interleaving all the sequences in an optimal uncorrelated ZCZ family of normalized sequences is always a perfect sequence.