基于Householder变换的正交PSWF脉冲设计  

Design of Orthogonal Pulse for Prolate Spheroidal Wave Function Based on Householder Transformation

作　　者：张榛[1] 王红星[1] 赵志勇[1] 张磊[1] 刘锡国[1] 张晨亮[1] 

机构地区：[1]海军航空工程学院电子工程系,山东烟台264001

出　　处：《电讯技术》2013年第11期1452-1458,共7页Telecommunication Engineering

基　　金：国家自然科学基金资助项目(60772056);山东省"泰山学者"建设工程项目;海军航空工程学院研究生创新基金项目~~

摘　　要：传统的Schmidt方法对椭圆球面波函数(PSWF)脉冲组进行正交化时,脉冲组的最大互相关值受脉冲个数的影响,同时还存在计算复杂度高的问题。针对上述问题,提出了基于Householder变换的正交化方法,通过将PSWF脉冲离散化,再依次对各离散的PSWF脉冲进行Householder变换,实现了对PSWF脉冲组进行QR分解,并得到新的正交PSWF脉冲组。仿真结果表明,与传统Schmidt方法相比,基于Householder变换的正交化方法使得脉冲组的最大互相关值从10-4降低到10-11,改善了脉冲组的正交性能,突破了脉冲组在脉冲个数的限制,并降低了计算复杂度,同时能够保持PSWF脉冲带内能量集中度高的优势。In using traditional Schmidt method in the orthogonalization of the Prolate Spheroidal Wave Function （PSWF） pulses set, the maximum cross-correlation value of the pulses set is under the influence of pulse number, and this method has a high computational complexity. To solve the problems above, an orthogonalization method based on Householder transformation is presented. The QR decomposition is real-ized through discretizing the pulses set and Householder transformation for the discrete pulse, then the new PSWF orthogonalization pulses set is obtained. Simulation results show that comparing with Schmidt meth-od, the orthogonalization method based on Householder transformation makes the max correlation value re-duced from 10^-4 to 10^-11 and is not restricted to the pulse number, reduces the computational complexity, while maintaining the advantage of high energy concentration.

关 键 词：非正弦波通信 正交脉冲 椭圆球面波函数 Householder变换 

分 类 号：TN911.7[电子电信—通信与信息系统]