Polyphase sequence design using a genetic algorithm

The performance of direct sequence code division multiple access (DS-CDMA) systems depends on the autocorrelation and cross-correlation properties of the deployed spreading sequences. Since good autocorrelation characteristics come at the expense of the cross-correlation properties and vice versa, a combination of these two measures needs to be optimized when designing a DS-CDMA system. In this paper, we consider the design of complex-valued spreading sequences with optimized correlation characteristics. In particular, the maximum nontrivial aperiodic correlation values are used to specify the cost or fitness function for the optimization problems. A genetic algorithm is presented for the design of polyphase sequences, namely, Oppermann sequences and modified Walsh-Hadamard sequences. It can be seen from these applications that the genetic algorithm is well suited to efficiently design polyphase sequences especially when the number of parameters for the optimization problem is large.