Open Access

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

  • Giuseppe Thadeu Freitas de Abreu1Email author,
  • Craig John Mitchell2 and
  • Ryuji Kohno2
EURASIP Journal on Advances in Signal Processing20052005:642192

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

Received: 3 October 2003

Published: 17 March 2005

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).

Keywords and phrases

ultra-wideband communicationsimpulse radioHermite pulsesorthogonal designjitter robustnesspulse-shape modulation

Authors’ Affiliations

(1)
Centre for Wireless Communications, University of Oulu, Oulu, Finland
(2)
Division of Physics, Electrical and Computer Engineering, Graduate School of Engineering, Yokohama National University, Yokohama, Japan

Copyright

© de Abreu et al. 2005

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