Theoretical Research On Perfect Binary Complementary Sequence Pairs

Sequences and sequence pairs with good correlation,balance and high linear complexity are widely used in radar,navigation,sonar,satellite communication,electronic countermeasures,information encryption,positioning,coded aperture imaging and many other practical engineering fields.With the advent of 5g era,and the demand for ideal signals with good correlation characteristics is increasingHowever,due to the strict restrictions of ideal sequence,it is difficult to find a large number of sequences that meet the conditions,and can not meet the rapid growth of engineering needs.In order to break through the limitation of ideal sequence,scholars proposed complementary sequence and complementary sequence pair based on the idea of autocorrelation summation.These two kinds of discrete signals also have good autocorrelation characteristics.In this paper,complementary sequence pairs are studied from two aspects: one is to study the conversion between complementary sequence pairs and other optimal discrete signals;the other is to construct complementary sequence pairs directly based on the method of circle division.Firstly,the relationship between the complementary sequence pair and the punctured sequence is studied,and the equivalence between the punctured sequence and a special kind of complementary sequence pair is established by using Hall polynomials.All the punctured sequences can be used to construct the complementary sequence pair,and a large number of examples of complementary sequence pair are obtained.Secondly,the construction method of complementary sequence pairs based on difference set pairs is studied in depth.By studying the correlation characteristics of complementary sequence pairs,using the existing difference set pairs and difference sets to construct directly,combining with the difference set database,and based on the sequence polynomials for mathematical proof,several construction methods of complementary sequence pairs with universality are obtained.With the computer search algorithm,a large number of examples are obtained.The complementary sequence pairs constructed by this method have high energy efficiency.Finally,a search algorithm of complementary sequence pairs based on classical cyclotomic class is designed.Through the induction and analysis of experimental data,six theorems of constructing complementary sequence pairs are summarized and proved by cyclotomic number.It provides a new method for the construction of complementary sequence pairs.