Löwdin's approach for orthogonal pulses for UWB impulse radio

Abstract

In this contribution we present a novel orthogonalization method for ultra-wideband (UWB) impulse radio transmission. Contrary to other work we utilize Löwdin's orthogonalization method which delivers a shift-orthogonal basis optimally close (in energy) to the initial pulse generating the shift-invariant space. We show that the shift-orthogonal basis can be well approximated using the Zak transform whenever the initial pulse fulfils certain conditions. This method can be efficiently implemented with the discrete Fourier transform. Furthermore we discuss the existence of compactly supported shift-orthogonal pulses, which are desirable for pulse position modulation.