The Search Method Of Perfect Binary Complementary Sequence Pairs And Aperiodic Binary Sequence

Perfect signals are widely used in communication systems, for example, in frequency hopping communication system and CDMA communication system. Binary complementary sequence is one of perfect signals with good aperiodic autocorrelation feature. It was first studied by Golay. The binary complementary sequences known are only a little, which can't satisfy the need of engineering. So, binary complementary sequence pair was studied on the basis of binary complementary sequence.Time complexity and space complexity in searching binary complementary sequence pair are very huge because four sequences are involved in the calculation. And only sequence pairs with length below 10 can be got using exhaustive search method. To get even longer sequence pairs, a new searching method is used in this paper.In this new method, a data tree is produced. Each leaf of this data tree is a byte with 8 bits, the leaves of one layer are produced by the former layer. Each byte symbols 8 probabilities that sequence pair can be produced. That is, the data stored are not the sequence pairs themselves, but a symbol method. This largely decreased space complexity. Besides, 16 probabilities of producing sequence pairs are reduced to 8 considering their features, which decreased time complexity. The decrease of time complexity and space complexity make it possible to search longer sequence pairs, and we get sequence pairs with length up to 18.Genetic algorithm is an optimization algorithm simulating the evolution of creatures in the nature. Genetic algorithm was first studied by Holland. To different optimization problems it has different operations. Simple genetic algorithm is the base of all the genetic algorithms.Use simple genetic algorithm to optimize binary sequence and to improve it, we reserve the best individuals and search the individual locally. It can be seen from the experiments that better optimization performance can be got using the first method not the second method. Because the parameters can largely influence the genetic algorithm performance, we set its parameters through experiments. And a set of suitable parameters is obtained after comparing and studying the time consumed and the optimization results.