Inverse Problems and Imaging (IPI)

Perfect and almost perfect pulse compression codes for range spread radar targets

Pages: 465 - 486, Volume 3, Issue 3, August 2009      doi:10.3934/ipi.2009.3.465

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Markku Lehtinen - University of Oulu, Sodankylä Geophysical Observatory, Sodankylä, Finland (email)
Baylie Damtie - Washera Geospace and Radar Science Laboratory, Bahir Dar University, P.O.Box, 79, Bahir Dar, Gojjam, Ethiopia (email)
Petteri Piiroinen - Department of Mathematics and Statistics, University of Helsinki, FI-00014, Helsinki, Finland (email)
Mikko Orispää - Sodankylä Geophysical Observatory, University of Oulu, Tähteläntie 62, FIN-99600 Sodankylä, Finland (email)

Abstract: It is well known that a matched filter gives the maximum possible output signal-to-noise ratio (SNR) when the input is a scattering signal from a point like radar target in the presence of white noise. However, a matched filter produces unwanted sidelobes that can mask vital information. Several researchers have presented various methods of dealing with this problem. They have employed different kinds of less optimal filters in terms of the output SNR from a point-like target than that of the matched filter. In this paper we present a method of designing codes, called perfect and almost perfect pulse compression codes, that do not create unwanted sidelobes when they are convolved with the corresponding matched filter. We present a method of deriving these types of codes from any binary phase radar codes that do not contain zeros in the frequency domain. Also, we introduce a heuristic algorithm that can be used to design almost perfect codes, which are more suitable for practical implementation in a radar system. The method is demonstrated by deriving some perfect and almost perfect pulse compression codes from some binary codes. A rigorous method of comparing the performance of almost perfect codes (truncated) with that of perfect codes is presented.

Keywords:  Radar waveform, comparison of experiments, Ambiguity function.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: October 2008;      Revised: February 2009;      Available Online: July 2009.