Spectrally Efficient UWB Pulse Shaping Based on Sharpening of Polynomially Weighted Gaussian Pulses

Polynomially weighted Gaussian pulses such as Gaussian derivatives and recently developed flat-spectrum Gaussian pulses are well localized in time. Therefore, they are suitable for use in ultra-wideband (UWB) systems. However, their efficiency in filling UWB spectral masks is limited. In this paper, we propose polynomial sharpening of their amplitude spectra that significantly improves this efficiency. To obtain a high efficiency, we introduce polynomials that enforce flatness at the spectrum's peak and provide controllable steepness in its transition regions. The proposed approach is illustrated with the design of UWB pulses that effectively fill the FCC spectral masks.