Perfect radar pulse compression via unimodular fourier multipliers

Lassi Roininen; Markku S. Lehtinen; Petteri Piiroinen; Ilkka I. Virtanen

doi:10.3934/ipi.2014.8.831

Article Contents

2014, Volume 8, Issue 3: 831-844. Doi: 10.3934/ipi.2014.8.831

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Perfect radar pulse compression via unimodular fourier multipliers

1.
University of Oulu, Sodankylä Geophysical Observatory, Tähteläntie 62, FI-99600 Sodankylä
2.
University of Helsinki, Department of Mathematics and Statistics, Gustaf Hällströmin katu 2b, FI-00014 University of Helsinki
3.
University of Oulu, Department of Physics, P.O.Box 3000, FI-90014 University of Oulu

Received: February 28, 2014

Revised: March 31, 2014

Published: July 2014

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Abstract

We propose a novel framework for studying radar pulse compression with continuous waveforms. Our methodology is based on the recent developments of the mathematical theory of comparison of measurements. First we show that a radar measurement of a time-independent but spatially distributed radar target is rigorously more informative than another one if the modulus of the Fourier transform of the radar code is greater than or equal to the modulus of the Fourier transform of the second radar code. We then motivate the study by spreading a Gaussian pulse into a longer pulse with smaller peak power and re-compressing the spread pulse into its original form. We then review the basic concepts of the theory and pose the conditions for statistically equivalent radar experiments. We show that such experiments can be constructed by spreading the radar pulses via multiplication of their Fourier transforms by unimodular functions. Finally, we show by analytical and numerical methods some examples of the spreading and re-compression of certain simple pulses.

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Mathematics Subject Classification: Primary: 94A12, 62M99; Secondary: 86A22.

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