The best approximations of optimum combinations of ultra wideband waveform with differential Gaussian pulses were given.The satisfactory transmitting distance in the line of sight(LOS) multi-path channel and the minimum bit error rate(BER) in the Time-Hopping Multiple Access systems were analyzed.Multi user interference(MUI) with the hypothesis of Standard Gaussian Approximation

the inherent relations among bit error rate and σ2M and coefficient of differential Gaussian pulse were investigated and some useful conclusions were drawn.These analyses and conclusions provide important based on the waveform design with differential Gaussian pulses.It show that the proposed Ultra Wide Band signals not only reach the best approach but also have the best BER performance.Therefore

it can be extended as a perfect transmitting pulse in the wireless communication system for Ultra Wide Band.