Finding sub-optimum signature matrices for overloaded code division multiple access systems

The objective of this study is to design sub-optimal signature matrices for binary inputs for an overloaded code division multiple access (CDMA) system as developed by this author group. In this study, the authors propose to use the sum capacity, the bit error rate and distance criteria as objective functions for signature matrix optimisation. Three optimisation techniques, the genetic algorithm, the particle swarm optimisation and the conjugate gradient (CG) are exploited in this work. Since the optimisation computational complexity increases by matrix dimensions, it is practically impossible to directly optimise the large signature matrices. In order to address this problem, a method is proposed to enlarge small-scale signature matrices. It is also proved that the sum channel capacity of the enlarged matrix is scaled by its enlargement factor. The results indicate that this proposed signature matrices provide higher sum capacity than the commonly used signature matrices. The authors also address that this matrices are applicable for highly overloaded CDMA systems.