Abstract
Codebooks (also called signal sets) meeting the Welch bounds are desirable in code-division multiple-access (CDMA) systems. In 2003, binary codebooks meeting Welch's bounds were constructed using difference sets by Ding, Golin, and Kloslashve. Recently, a generic construction of codebooks with cyclic difference sets meeting Welch's bound on the maximum cross-correlation amplitude was developed by Xia In this correspondence, the idea of Xia is extended, and related constructions of optimal codebooks with both cyclic and noncyclic difference sets are presented. These codebooks are optimal in the sense that they also meet this Welch bound. In addition, complex codebooks that almost meet Welch's bound on the maximum cross-correlation amplitude are also constructed with almost difference sets
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