On the construction of the unit tight frames in code division multiple access systems under total squared correlation criterion

We focus on the application of unit norm tight frames to design code division multiple (CDMA) systems spreading sequences with constant chip magnitude. An algorithm for the design of the overloaded real-valued signature sets with minimum total-squared-correlation equal to the Welch bound equality (WBE) set is presented. By using this algorithm we solved the open problem of existence of complex-valued WBE sequence sets with constant chip magnitude in the case when K=N+1K=N+1, where K is the number of active users in the system and N   is the processing gain. The normalized cross-correlation between any pair of signatures in a set obtained by the proposed algorithm is either 1/(K-1)1/(K-1) or -1/(K-1)-1/(K-1) corresponding to equiangular sequences. The results are derived in the context of synchronous CDMA systems. Numerical examples for K=5K=5 users for real WBE sequences and for K=4,3K=4,3 users for complex WBE sequences with constant chip magnitude are provided.