Research On The Construction Method Of Punctured Binary Sequence Pairs

Spread spectrum communication has the advantages of strong resistance to blocking,good privacy,and can reduce electromagnetic interference.It has important applications in bluetooth,mobile broadband,ranging and positioning,civil digital hive and other fields.Therefore,the performance requirement of the signal is also gradually improved,and the signal with ideal correlation characteristics has gradually become the research focus of scholars.However,the current research results of ideal sequence pairs are far from meeting the engineering needs.Therefore,the purpose of this study is to obtain two kinds of ideal sequence pairs,namely the perfect punctured binary sequence pairs and the pseudorandom punctured binary sequence pairs.Firstly,a punctured binary sequence pair search algorithm based on classical cyclotomy and 2-2 order generalized cyclotomy with period pq is designed.The method of classical cyclotomy is to first construct the punctured difference set pair and then get the punctured binary sequence pair according to the definition of the feature sequence and the punctured sequence.In the 2-2 order generalized cyclotomy with pq period,the generalized cyclotomic classes is the combination of the cyclotomic classes and the chinese residual theorem.Compared with the classical cyclotomy,this method can search more punctured difference set pairs,so as to expand the search scope of the perfect and pseudorandom punctured binary sequence pairs and obtain more experimental results.Secondly,the experimental data of classical cyclotomy method are analyzed and summarized,and punctured difference set pairs of different parameter forms are found(2f+1,f,f+1,f,f/2),(5f+1,2f+1,4f+1,2f+1,f/2).Six perfect punctured binary sequence pairs and two pseudorandom punctured binary sequence pairs are proposed.Their main peaks can be expressed as f,3f and so on.Combining the knowledge of cyclotomic number and the necessary and sufficient conditions for the existence of perfect punctured binary sequence pairs and pseudorandom punctured binary sequence pairs,a detailed proof process is given and illustrated with examples.Finally,the data sets of the generalized cyclotomy method are sorted out,andpunctured difference set pairs of different parameter forms are concluded(pq,(pq+1)/2,(3pq+p-q+1)/4,(pq+p-q+3)/4,(p+1)(q-1)/8).Three general rules of the perfect punctured binary sequence pairs and a pseudorandom punctured binary sequence pair are proposed.Their main peaks can be expressed as(pq-p+q-1)/4,q and so on.The proofs and realities are given in combination with relevant theories.The two construction methods proposed in this paper can not only obtain the perfect and pseudorandom punctured binary sequence pairs,but also open up a new direction and provide a new scientific research idea for searching other types of punctured sequences.