Approximation of Gaussian derivatives for UWB communication

UWB is a new interesting technology for wireless communications. It can replace traditionally carrier-based radio transmission by pulse-based transmission using ultrawide band frequency but at a very low energy. An important aspect of research in this domain is to find a pulse with an optimal shape, whose power spectral density respects and best fits emission limitation mask imposed by FCC. In this paper we review common used Gaussian pulses and its derivatives and the influence of shape factor, finding an optimal specific value for each derivative. Next, we search to obtain possible better pulse shapes as linear combinations of Gaussian derivatives. Older studies refer in one case to the same shape factor for all derivatives and in other case to higher factor for first derivative and smaller shape factors for subsequent derivatives. Our new idea is to use Gaussian derivatives, each with its specific optimal shape factor and to use a "trial and error" algorithm to obtain a linear combination pulse with better performance.