Code-search for optimal TSC binary sequences with low cross-correlation spectrum

It has been shown that signature (multi) sets that meet Welch´s lower bound on the total squared correlation (TSC), maximize the sum capacity of the synchronous code division multiple access (CDMA) channel with equal average input energy constraints. However, a signature set that is TSC-optimum (i.e. achieves the lower bound on TSC), doesn´t necessarily have a low cross-correlation spectrum. Hence, for various system loads there may be users that experience high probability of error due to high cross-correlation of their assigned signature to others in the set. In this paper we present a search method to obtain new optimum TSC binary signature sets with low cross-correlation spectrum. We also show, based on our search method, that if we relax the TSC optimality constraint, codes with better cross-correlation spectrum may be found. In addition, a catastrophic binary code (i.e. a code having complementary codewords) can be TSC-optimal. Therefore, practically speaking, it is important that the TSC-optimality be sought along with the minimization of the cross-correlation spectrum. Finally our codes are tested on fully-loaded and overloaded synchronous CDMA systems, and simulation results show that they are a promising alternative to the Hadamard-Walsh codes, since they offer higher capacity.