Research On The Constructions Of Sequences (Sets) With Good Correlations

In 5G wireless communication and radar systems,sequences(sets)with ideal autocorrelation properties are mostly used in identification,synchronization,ranging and resistance to inter-cell interference caused by users from different cells.The ultimate goal of designing the perfect sequences(sets)is to minimize the magnitudes of autocorrelation sidelobes and cross-correlation functions.In order to obtain the perfect sequences(sets)with good correlation properties,the constructions of the perfect integer sequences with low degree of freedom with a single variable are studied in this paper.At the same time,the construction methods of the optimal zero correlation zone sequence sets with good(low)correlation properties are studied.The research work are as follows:Firstly,in order to solve the problem of increasing the number of variables in the perfect Gaussian integer sequences,the perfect integer sequences construction methods are proposed based on the difference sets,trace function and generalized cyclotomic classes.The perfect two-valued integer sequences and the perfect three-valued(sparse)integer sequences of arbitrary period lengths are constructed by direct and indirect methods respectively.The generated perfect integer sequences with low degrees of freedom can save transmission bandwidth and reduce memory consumption,and provide more candidate signals for practical application systems.Secondly,the permutation matrices with specific properties are the basis for the constructions of the optimal zero correlation zone sequence sets.The existing permutation matrices can only rely on exhaustive computer search.In order to solve the problem,this paper takes the research background of circular Florentine matrices as the breakthrough point,summarizes and analyzes the definition,properties and necessary and sufficient conditions for the existence of circular Florentine matrices.There is an equivalent relationship between difference matrices and circular Florentine matrices.Then,based on the definition of the matrices and necessary and sufficient conditions,three construction methods of prime order circular Florentine matrices are proposed.The proposed general construction methods are more universal.Finally,in view of the limitations of the existing methods for constructing the optimal sequence sets with zero correlation zone mainly relying on the specific functions or matrices form currently known,we extend the required permutation matrices form for construction.This paper studies the general construction methods of three different Tuscan matrix types:circular Florentine matrices,Vatican matrices and Roman squares.Combined with the generation methods of perfect polyphase sequences,the optimal sequence sets with optimal correlation and multiple optimal zero correlation zone sequence sets with good(low)interset correlation are constructed,which expands the existence space of zero correlation zone sequence sets to a certain extent.