New bounds on the total squared correlation and optimum design of DS-CDMA binary signature sets. - Karystinos, G.N.
The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.
Keywords: DS-CDMA.; Hadamard matrices; Welch lower bound; Binary sequences; Binary signature sets; Communication channel; Direct-sequence code-division-multiple-access.; Signal design; Spreading codes; Total squared correlation