基于修正Hermite函数的UWB最优脉冲设计

Design of optimal UWB pulse shapes based on modified Hermite functions

首先对修正Hermite函数n阶导数的能量归一化与脉冲形状参数α、n的关系进行了研究,根据美国联邦通信委员会(FCC)对超宽带(UWB)脉冲的有关辐射掩蔽的标准提出了设计UWB脉冲的新方法,通过N个修正Hermite函数的线性组合来得到最优波形。仿真结果表明优化脉冲能够接近于辐射掩蔽,使得传输功率在低于FCC限定的条件下取得更大值。

Considering the various combinations of derivative for modified Hermite functions to get the optimal waveform,the relation between the normalized energy of the n-th derivative of the modified Hermite functions and the pulse shape parameter α as well as the order n of differentiation is studied.A novel method to design ultra-wideband（UWB） pulse is proposed in terms of the spectral mask standard that is set up by Federal Communications Commission（ FCC ）.The optimal waveform is gotten by the linear combination of the N modified Hermite functions.The simulation results indicate that the pulse obtained from this method can approach the spectral mask standard accurately,which makes the transmission power bigger under the condition of FCC.