Construction of complex-valued simplex signature sets with constant chip magnitude

A new algorithm for the design of overloaded real-valued signature sets with total-squared-correlation equal to Welch bound equality (WBE) set is presented. It is proved that if K=N+1 the normalized cross correlation between any pair of signatures in a set obtained by the proposed algorithm is either -1/(K-1) or +1/(K-1) and the entire cross correlation matrix G is obtained analytically. Using this algorithm we solved the open problem of existence of complex valued WBE sequence sets with constant chip magnitude in the simplex case. The results are derived in the context of synchronous code division multiple access (CDMA) channels and a numerical example for K=3 and N=2 is given.