Lowdin Transform on FCC Optimized UWB Pulses

In this contribution we present a novel method for constructing orthogonal pulses for UWB impulse radio transmission under the FCC spectral mask constraint. In contrast to previous work we combine a convex formulation of the spectral design with Lowdin's orthogonalization method [1], which delivers a shift--orthogonal basis optimally close (in energy) to the initial pulse, which generates (in a stable way) the shift--invariant space. The convex formulation of the spectral design is achieved by approximating the FCC mask with a finite--order filter matched to Gaussian monocycles as input. The output pulse then has high energy concentration in the passband (NESP value). Using Lowdin's orthogonalization we compute the corresponding shift--orthogonal pulse. We show that our approach is able to generate for finitely many shifts, orthogonal equal energy pulses with nearly the same NESP value. Furthermore, we show that the orthogonalization procedure can be well approximated using the Zak transform allowing for an efficient implementation with the discrete Fourier transform. Surprisingly, we could observe, that for certain parameters, this approximation yields almost the same performance as the exact Lowdin method.