A generic construction of complex codebooks meeting the welch bound

Codebooks (also called signal sets) meeting the Welch bound on the maximum correlation amplitude are called MWBE codebooks and are desirable in code-division multiple-access systems. Two different but related constructions of MWBE codebooks from difference sets were developed by Xia et al. and Ding recently. The objectives of this correspondence are to present a generic construction of MWBE codebooks that contains the previous two constructions as special cases and describe new MWBE codebooks that cannot be produced by the earlier two constructions.