A new construction of asymptotically optimal codebooks

Codebooks with small cross-correlation amplitude have extensive applications in many fields including code division multiple access (CDMA) communications systems, space-time codes, and compressed sensing. In this paper, a class of asymptotically optimal codebooks was constructed, and the maximum inner-product of these presented codebooks was determined by using properties of character sums over finite fields. Furthermore, these codebooks provided new parameters.