Design of a Legendre-polynomial-based orthogonal pulse generator for ultra-wideband communications

We propose a novel circuit for the generation of Legendre-polynomial-based pulses for use in impulse radio ultra wideband (UWB) communications. Both parallel and serial generation of pulses of different order can be developed. Pulses are produced by applying Bonnet´s recursion formula which can generate the Legendre polynomial functions of successive orders. This class of functions yield orthogonal pulses and have a constant pulse width regardless of the pulse order. This nice property can eliminate intersymbol interference (ISI) such that these pulses are suitable for use in pulse position modulation (PPM) ultra wideband communication systems.