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Inverse Problems and Imaging (IPI)
 

Perfect pulse-compression coding via ARMA algorithms and unimodular transfer functions

Pages: 649 - 661, Volume 7, Issue 2, May 2013      doi:10.3934/ipi.2013.7.649

 
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Lassi Roininen - University of Oulu, Sodankylä Geophysical Observatory, Tähteläntie 62, FI-99600 Sodankylä, Finland (email)
Markku S. Lehtinen - University of Oulu, Sodankylä Geophysical Observatory, Tähteläntie 62, FI-99600 Sodankylä, Finland (email)

Abstract: We propose a method to construct perfect pulse-compression codes with autoregressive moving average algorithms. We first show the relation between the study of coding and decoding techniques in radar engineering and the study of unimodular polynomials with constrained coefficients. Then we extend the study to unimodular Fourier series and unimodular rational functions. We use the Fourier series and rational functions as transfer functions in the autoregressive moving average algorithms. We show that by a suitable choice of the coefficients, the autoregressive moving average algorithms are realisable, stable and causal. We show examples of some almost perfect codes, i.e. numerically truncated perfect codes. We end by proposing perfect code design principles for practical radar engineering purposes.

Keywords:  Perfect codes, autoregressive moving average, unimodular polynomials, inverse filter.
Mathematics Subject Classification:  Primary: 68P30; Secondary: 94A12, 93E11, 93E03.

Received: December 2011;      Revised: March 2013;      Available Online: May 2013.

 References