  The everlasting bandwidth limitations in wireless communication networks has
directed the researchers' thrust toward analyzing the prospect of overloaded
Code Division Multiple Access (CDMA). In this paper, we have proposed a Genetic
Algorithm in search of optimum signature matrices for binary-input synchronous
CDMA. The main measure of optimality considered in this paper, is the per-user
channel capacity of the overall multiple access system. Our resulting matrices
differ from the renowned Welch Bound Equality (WBE) codes, regarding the fact
that our attention is specifically aimed at binary, rather than Gaussian, input
distributions. Since design based on channel capacity is computationally
expensive, we have focused on introducing a set of alternative criteria that
not only speed up the matrix formation procedure, but also maintain optimality.
The Bit Error Rate (BER) and Constellation measures are our main criteria
propositions. Simulation results also verify our analytical justifications.
