一类非线性扩频序列的构造及其性能分析

Constuction and Analyysis of a Class Non-linear Spread Spectrum Sequence

基于本原三项式线性函数,构造了一类非线性序列.首先根据非线性序列生成规律,借助逻辑代数理论,推导并提取了非线性序列特征函数,利用特征函数筛分作用,合成了非线性反馈函数,据此实现了非线性序列生成.最后,对该类非线性序列特性进行了分析和计算,并将其应用于直接序列码分多址通信系统(DS-CDMA)仿真实验中,结果表明该类非线性序列不仅具有理想的伪随机特性、良好的线性复杂度,还具有优于m序列、gold序列的误码率.

In this thesis, we proposed a method to construct the feedback functions of the nonlinear shift registers based on three items＇ primary polynomial. First of all, we proved the characteristic state sets of the linear feedback shift registers with the feedback functions of three items＇ primary polynomial, we extracted its eigenfunction and synthesized the feedback function for the nonlinear shift register. Secondly, we implemented the non-linear feedback shift register on FPGA. Finally, we conducted analyses and calculations for new sequences generated by the nonlinear shift registers and simulated the sequences in direct sequence spread specmarn code division multiple access communication system（DS-CDMA）. The results show unanimously that the new sequences dose not only possess ideal pseudorandom property and better linear complexity, but also get lower bit error rate（BER） than m se- quence or gold sequence in the same communication system.