Jitter-Robust Orthogonal Hermite Pulses for Ultra-Wideband Impulse Radio Communications
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Jitter-Robust Orthogonal Hermite Pulses for Ultra-Wideband Impulse Radio Communications Giuseppe Thadeu Freitas de Abreu Centre for Wireless Communications, University of Oulu, Tutkijantie 2E, 90570 Oulu, Finland Email: [email protected]
Craig John Mitchell Division of Physics, Electrical and Computer Engineering, Graduate School of Engineering, Yokohama National University, 79-5 Hodogaya, Yokohama 240-8501, Japan Email: [email protected]
Ryuji Kohno Division of Physics, Electrical and Computer Engineering, Graduate School of Engineering, Yokohama National University, 79-5 Hodogaya, Yokohama 240-8501, Japan Email: [email protected] Received 3 October 2003; Revised 23 April 2004 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 N-by-N 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 communications, impulse radio, Hermite pulses, orthogonal design, jitter robustness, pulse-shape modulation.
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INTRODUCTION
Hermite polynomial-based orthogonal pulses—also known as Hermite pulses or simply Hermites—were proposed in [1] for pulse-shape modulated (PSM-) ultra-wideband impulse radio (UWB-IR) communications, as an alternative to the pulse-position modulated (PPM) scheme first presented in [2]. Later, it was also shown that PSM and PPM can be combined into a pulse-shape and pulse-position modulation (PSPM) scheme [3]. A number of alternative orthogonal pulse-shape designs for UWB-IR communications based on different elementary functions have also been considered [4, 5, 6]. These works have, however, contributed to demonstrating the advantages of Hermite pulses which are smooth functions
(differentiable in R), well concentrated in both time and frequency domains, and easily derived through successive derivation and scaling of the G
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