Research On The Constructions Of Sequence Pair And Sequence Pairs Set With Low Correlation

Low (zero) correlation zone sequence pairs set can be used in radar, sonar, and Code Division Multiple Access communication system, which play an important role in the optimizing design of modern communication, spatial measurement, signal processing and electronic countermeasure systems etc. Low (zero) correlation zone sequence pair sets provide many good code sequences for the actual engineering’s application, which are significant from the view point of theoretical research and practical application.Based on the known results, we take a in-depth research on the construction of sequence pair with two level correlation and sequence pairs with low (zero) correla-tion zone. Our results are as follows:1. Based on the observation of the constructions of ideal two-level correlation bi-nary sequence pairs introduced by Peng et al., a new proof of the ideal two-level correlation binary sequence pairs is presented, which simplifies the original proof greatly. We also provide a new construction of ideal two-level correlation binary sequence pair. As a co-product, new classes of difference set pairs can be derived.2. In contrast to the orthogonal matrix, orthogonal matrix pair is not restricted by the fact that the order of matrix should be the power of2, so its existence domain is wider. Three kind of construction methods of orthogonal matrix pair are proposed. Using the orthogonal matrix pair, we further propose a new construction of sequence pairs set with low correlation zone. Finally, the parameters of the constructed sequences pairs set are analyzed theoretically.3. Based on the shift sequences and interleaved technique, orthogonal sequence pairs set is constructed by interleaving the perfect sequence pairs set. Then binary zero correlation zone sequence pairs set is constructed by interleaving or-thogonal matrix pair with the constructed orthogonal sequence pairs set. Lastly, we analyze them theoretically and compare them with the known results. The result shows that the parameters of the new construction are more flexible, and have a very high energy effect.4. Two methods of constructing quaternary low correlation zone sequence pairs set are proposed. The first one is constructing quaternary sequence based on perfect binary sequence pair and inverse Gray mapping firstly, then generating a longer LCZ sequence by interleaved technique. Finally, it can be extended as quaternary low correlation zone sequence pairs set by using the orthogonal matrix pairs. The second one is firstly constructing quaternary sequence pairs by the same way, and then multiplying the orthogonal matrix pairs to generate two new matrixes. Finally, quaternary low correlation zone sequence pairs set can be obtained by combining the above two matrixes together.