Design of complementary sequence sets based on orthogonal matrixes

Based on any two orthogonal matrixes with the number of rows of one matrix equal to the number of columns of another matrix, a novel set of complementary sequences is proposed. The constructed complementary sequences with each sequence including a flock of element sequences have ideal auto-correlation and cross-correlation properties, where the correlation function of a complementary sequence is equal to the sum of correlation functions of its element sequences. Different from previous construction methods on the basis of orthogonal matrixes which limit the element sequence length and flock size, the presented method in this paper can obtain the element sequence length and flock size of any integer, which ensures a more flexible choice of sequence parameters for the systems employing complementary sequence sets.