An algorithm for obtaining Welch bound equality sequences for S-CDMA channels

In this paper we describe the properties of those sequences (matrix) that meet equality in the Welch's lower bound on total squared correlation. These sequences are called also Welch Bound Equality (WBE) sequences. The generalized WEE sequences (matrix) are defined. Same definitions on majorization are introduced in order to characterize the eigenvalues of a hermitian matrix. A new algorithm for generating WEE spreading sequence multisets is proposed. We apply the proposed algorithm when all users have different average-channel-input energy constraint in the case of synchronous CDMA channels. We obtain real optimum signature sequences that maximize the sum capacity of S-CDMA channels.