Non Trivial Orthogonal Matrix Pair Theory And Complementray Sequence Design

The famous Hadamard matrix due to the orthogonality of its own,widely used in communication systems,image analysis and signal processing and other fields,but the Hadamard of the matrix is limited and in some order case does not exist,in order to improve and remedy the situation,this paper studies the search method consists of two mutually orthogonal the square of the non trivial orthogonal matrix pair and construction method,and non trivial orthogonal pairs in complementary sequence design in application.First of all,we give two kinds of search methods of non trivial orthogonal matrix pairs of the two elements,namely the cyclic matrix search method and the complementary search method.Through these two kinds of search methods are presented in this paper based on the order of some non trivial element two orthogonal matrix pair examples,combined with the Kronecker product,in order to expand the number and the number of existing non trivial two element orthogonal matrix pair.In addition,the paper constructs a non trivial two element orthogonal matrix pair by using the cyclic matrix of the binary valued sequence of two values,which complements the search method and the order of the existence of the non trivial orthogonal matrix pairs in the product expansion method(Kronecker).Compared with the existence of Hadamard matrix,it is found that there exists a great advantage in the number and order of non trivial two element orthogonal matrix pairs.Secondly,studied the relationship between the non trivial orthogonal matrix pairs with complementary sequences,show that under certain conditions the non trivial orthogonal matrix pair can be constructed of non periodic complementary sequence,sequence length matrix pairs order number complementary sequence number is 2 times of the order of the matrix pair.In this paper,the two element matrix pair is mapped into a Hardamard matrix of four elements by Gray mapping,and the complementary sequence of the four elements is generated.In addition,constructed by mapping the complex non trivial orthogonal matrix pair,nontrivial complex orthogonal matrix pair expanded the existence of nontrivial orthogonal matrix pair field,no longer limited to two yuan,for the future engineering application foundation.Thirdly,this paper gives a new method to construct the non periodic complementary sequence set.In this paper,the periodic complementary sequence is shifted to form a square matrix,and a plurality of matrix rows are extracted and sorted to form a non periodic complementary sequence.