Research On Array Pair And Its Search Algorithm

The perfect signal theory and its design have widely application and play an important role in optimizing design in the system of modern communication, radar, sonar, navigation, space ranging and controlling. It is of important academic value and practical meaning to study perfect signal.This paper aims at a new form signal-array pair, the theory of array pairs, perfect binary pairs and quasi-perfect binary array pairs is discussed synthetically. Based on this theory, a new searching algorithm is designed.In order to realize fast searching, the algorithm makes full use of the transform properties and necessary conditions of the perfect binary array pairs and quasi-perfect binary array pairs, exclude the array pairs of transform equivalence, so that reduced the searching space and amount, and improved the searching speed. Furthermore, using binary integer to express array, the shift transform and full sampling transform of array pairs is achieved by the Boolean calculation of binary integer. When calculate the correlation function of binary array pairs, using the Boolean calculation instead of the decimal multiplication, using the method of count the number of 1 in binary integer to calculate the correlation function of binary array pairs, the speed of searching is obviously improved by these methods.By the algorithm introduced in this paper, the constant weight and normative perfect binary array pairs whose volume from 4 to 28 and quasi-perfect binary array pairs whose volume from 2 to 24 were searched and gived the new result. Compared with exhausitive search algorithm,the search amout is remarkable reduced by this algorithm and the algorithm is very efficiency.With the searched perfect binary array pairs and quasi-perfect binary array pairs, new perfect binary array pairs of high dimension and volume can be constructed by all kinds of construct methods.The method in this paper provides a new approach to search perfect binary array pairs and quasi-perfect binary array pairs of big volume. It also can be used in the fast searching program for the sequences and arrays of other forms.