A Family of Codebooks with Nearly Optimal Set Size
Cuiling Fan, Rong LUO, Xiaoni Du · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2016
Codebooks with good parameters are preferred in many practical applications, such as direct spread CDMA communications and compressed sensing. In this letter, an upper bound on the set size of a codebook is introduced by modifying the Levenstein bound on the maximum amplitudes of such a codebook. Based on an estimate of a class of character sums over a finite field by Katz, a family of codebooks nearly meeting the modified bound is proposed.