Concept of Complex-Valued Parametric Pulse Models
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Concept of Complex-Valued Parametric Pulse Models Klaus Pourvoyeur,1 Andreas Stelzer,2 and Gerald Oßberger1 1 Linz
Center of Mechatronics GmbH, Altenberger Straße 69, 4040 Linz, Austria for Communications and Information Engineering, Johannes Kepler University, Altenberger Straße 69, 4040 Linz, Austria
2 Institute
Received 4 February 2005; Revised 7 November 2005; Accepted 8 November 2005 Recommended for Publication by Geert Leus In pulse-based radar systems, the knowledge of certain parameters of the received radar pulse is of great importance. We introduce a complex-valued parametric pulse model by extending a real-valued pulse signal into the complex plane. A modulation angle parameter unique to the complex representation gives an additional degree of freedom and can be used to model the basic shape of the pulse, thus lifting the conventional restriction to fixed pulse shapes in real-valued correlation techniques. As physical signals are real valued, the imaginary part of the complex signal is calculated by using the Hilbert transformation. Parameter estimation is based on the complex-valued continuous wavelet transform. The main advantages of this concept are demonstrated on synthetic data and verified on ultrawideband pulse radar measurements. Copyright © 2006 Klaus Pourvoyeur et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
For the detection and characterization of a pulse covered in noise, conventional correlation methods like matched filtering with real-valued signal shapes suffer one major drawback in analyzing the sampled signal: the requirement of the exact knowledge of the pulse shape. Since this information is generally not available in pulse-based radar systems, the employed signal analysis method must provide enough flexibility to deal with this uncertainty. The wavelet transform (WT) that is based on correlation with translated and dilated versions of a basic template waveform, or wavelet, is a means of overcoming some of the restrictions of the matched filtering approach, yet the analysis wavelet has to be chosen properly to match the specific shape of the searched pulse. In this contribution, we discuss the concept of complexvalued parametric pulse (CVPP) models in combination with the WT that gives us the ability to deal with different pulse shapes with a priori knowledge of only the approximate characteristic of the pulse. Since signals in nature are always real valued, the imaginary part of a CVPP has to be estimated from its real part. This paper is organized as follows. Section 2 describes the basic idea of complex-valued pulse models. Section 3 discusses the basic ideas of CVPPs, Section 4 explains how parameter estimation is accomplished, Section 5 deals with the main advantages of CVPPs on synthetic signals, and
Section 6 verifies the potential of CVPPs on measured data. A summary of the paper is give
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