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In this paper we consider the design of spectrally efficient time-limitedpulses for ultrawideband (UWB) systems using an overlapping pulse positionmodulation scheme. For this we investigate an orthogonalization method, whichwas developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set ofN orthogonal (L\"owdin) pulses, which remain time-limited and spectrallyefficient for UWB systems, from a set of N equidistant translates of atime-limited optimal spectral designed UWB pulse. We derive an approximateL\"owdin orthogonalization (ALO) by using circulant approximations for the Grammatrix to obtain a practical filter implementation. We show that the centeredALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tendsto infinity. The set of translates of the Nyquist pulse forms an orthonormalbasis or the shift-invariant space generated by the initial spectral optimalpulse. The ALO transform provides a closed-form approximation of the L\"owdintransform, which can be implemented in an analog fashion without the need ofanalog to digital conversions. Furthermore, we investigate the interplaybetween the optimization and the orthogonalization procedure by using methodsfrom the theory of shift-invariant spaces. Finally we develop a connectionbetween our results and wavelet and frame theory.

Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio