A comparison of ultra wideband signal functions for wireless ad hoc networks

This paper describes, simulates, evaluates and compares four time and band limited functions that can be used to create ultra wideband signals. Expressions and methods for generating the functions are presented followed with simulations using uniform sets of parameters. It is shown at the -10 dB points the Hermite, prolate spheroidal wave function (PSWF) and wavelets have suitable UWB properties. Using the Daubechies wavelets as examples, we demonstrate that both the scaling and wavelet functions provide suitable UWB band widths. Their -10 dB bands are 1.9739 GHz and 3.4644 GHz respectively. The -10 dB bandwidth of the Daubechies wavelet of order 1 is about 0.61 compared to the Hermite function of the same order, but higher than what can be achieved with PSWF.