Research On Ternary Generalized Complementary Sequence And Perfect Sequence

The correlation functions of spreading sequences directly influence the performance and capacity ofthe CDMA communication system. In this paper, the mainly study focuses on aperiodic ternary generalized complementary sequence and perfect sequence. Aperiodic generalized complementary sequence in a multi-carrier CDMA system can completely eliminate multiple access interference(MAI), the multipath interference(MI) when the largest multi-path delay and delay falls within the zero correlation zones. Perfect sequence is widely applied in continuous wave radar systems and channel estimate, and so on. Pseudo-random sequences with good correlation are constructed by using perfect sequence and a quasi-synchronizing CDMA system can be designed. In this paper, aperiodic ternary generalized complementary sequence and perfect sequence are investigated concretely, that is,(1) the elementary transformations on ternary sequences and aperiodic ternary generalized complementary set,(2) constructions of aperiodic ternary generalized complementary set and their mates,(3) ternary perfect sequences with a few zero elements.(1)Elementary transformations on ternary sequences, elementary operations on aperiodic ternary generalized complementary pairs and the representatives of the equivalence class of them are proposed. The set of ternary generalized complementary pairs of some fixed lengths is determined by the set of inequivalent representatives. It is shown that aperiodic ternary Z-complementary pairs are better than aperiodic ternary complementary ones of the same length in terms of the number of them.(2)By modifying or improving the original methods of constructing complementary sets and their mates, constructions of aperiodic ternary generalized complementary sets and their mates are given. Generally speaking, the shorter ZCZ width, the more mates of an aperiodic ternary generalized complementary pair.(3)Ternary perfect sequences with a few zero elements are studied. An efficient search algorithm for ternary perfect sequences with 3、4、5、6 zero elements is given. Given the length of sequence less than 50, the result show that the non-existence of ternary perfect sequences of lengths less than 50 with three zero elements are obtained and there exist only one ternary perfect sequences of length 13 with 4 zero elements, only one ternary perfect sequences of length 21 with 5 zero elements, and only one ternary perfect sequences of length 31 with 6 zero elements. So it is conjectured that there exist no ternary perfect sequences of any lengths with three zero elements.