频谱孔约束互补序列设计研究

因其完美的自相关特性和优异的峰均比特性，互补序列在红外线、通信、雷达等领域具有重要的应用，与布尔函数、Hadamard矩阵、Weighting矩阵、差族、Reed-Muller码等数学对象有深刻的联系。传统的互补序列设计没有考虑频谱孔的存在，不能满足频谱受限的现代无线通信系统的新需求。本项目拟对频谱孔约束新型互补序列进行深入研究：1）利用组合设计理论对频谱孔进行刻画，提炼出频谱孔约束互补序列的新型组合构型；2）基于有限域、（几乎）差族、分圆、布尔函数、交织等理论与技术，构造新型组合构型，得到具有灵活参数的频谱孔约束互补序列；3）研究频谱孔约束互补序列的互相关特性，构造准正交频谱孔约束序列。上述课题的研究具有重要的理论意义和实际应用价值。

Due to their perfect autocorrelation and low PAPR property, complementary sequences have important applictations in infrared ray, communications and radar. In addition, complementary sequences have close connection with some mathematical objects such as Boolean functions, Hadamard matrices, Weighting matrices, difference families, and Reed-Muller codes. However, traditional complementary sequences can not be directly used in the scenario of modern communications where the null constraints in frequency domain occur. The objective of this project is to give a well-rounded study of complementary sequences under null constraint: 1) we will first characterize the combinatorial features and structures of complementary sequences under null constraint; 2）and then construct such combinatorial structures to obtain complementary sequences under null constraint with flexible parameters using the mathematical tools including finite fields, (almost) difference families, cyclotomy and Boolean functions; 3) finally, we will study the cross-correlation property of the proposed sequences, and obtain quasi-synchronous complementary sequences under null constraints. The study of these subjects has both important theoretical significance and application value.