L. Roininen, M. Lehtinen, P. Piiroinen and I. I. Virtanen, Perfect Radar Pulse Compression via Unimodular Fourier Multipliers, Inverse Problems and Imaging, 8 831-844 (2014).
This study is continuation of the perfect coding technique papers reported originally in the same journal:
M. Lehtinen, B. Damtie, P. Piiroinen and M. Orispää, Perfect and almost perfect pulse compression codes for range spread radar targets, Inverse Problems and Imaging, 3 465-486 (2009).
L. Roininen and M. S. Lehtinen, Perfect pulse-compression via ARMA algorithms and unimodular transfer functions, Inverse Problems and Imaging, 7 649-661 (2013).
The major new contribution in Roininen et al. 2014 paper is in extending the perfect coding technique to continuous waveforms.
Perfect Radar Pulse Compression via Unimodular Fourier Multipliers
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 first motivate the study with spreading and re-compression of a Gaussian radar pulse. 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.