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Jitter-Robust Orthogonal Hermite Pulses for Ultra-Wideband Impulse Radio Communications

Abstract

The design of a class of jitter-robust, Hermite polynomial-based, orthogonal pulses for ultra-wideband impulse radio (UWB-IR) communications systems is presented. A unified and exact closed-form expression of the auto- and cross-correlation functions of Hermite pulses is provided. Under the assumption that jitter values are sufficiently smaller than pulse widths, this formula is used to decompose jitter-shifted pulses over an orthonormal basis of the Hermite space. For any given jitter probability density function (pdf), the decomposition yields an equivalent distribution of -by- matrices which simplifies the convolutional jitter channel model onto a multiplicative matrix model. The design of jitter-robust orthogonal pulses is then transformed into a generalized eigendecomposition problem whose solution is obtained with a Jacobi-like simultaneous diagonalization algorithm applied over a subset of samples of the channel matrix distribution. Examples of the waveforms obtained with the proposed design and their improved auto- and cross-correlation functions are given. Simulation results are presented, which demonstrate the superior performance of a pulse-shape modulated (PSM-) UWB-IR system using the proposed pulses, over the same system using conventional orthogonal Hermite pulses, in jitter channels with additive white Gaussian noise (AWGN).

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Correspondence to Giuseppe Thadeu Freitas de Abreu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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de Abreu, G.T.F., Mitchell, C.J. & Kohno, R. Jitter-Robust Orthogonal Hermite Pulses for Ultra-Wideband Impulse Radio Communications. EURASIP J. Adv. Signal Process. 2005, 642192 (2005). https://doi.org/10.1155/ASP.2005.369

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  • DOI: https://doi.org/10.1155/ASP.2005.369

Keywords and phrases

  • ultra-wideband communications
  • impulse radio
  • Hermite pulses
  • orthogonal design
  • jitter robustness
  • pulse-shape modulation