基于修正Hermite函数的UWB最优脉冲设计

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。

Design of optimal UWB pulse shapes based on modified Hermite functions

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.