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Ann. Geophys., 22, 1623-1632, 2004
www.ann-geophys.net/22/1623/2004/
© European Geosciences Union 2004
Optimal binary phase codes and sidelobe-free decoding filters with application to incoherent scatter radar
M. S. Lehtinen1, B. Damtie2, and T. Nygrén2
1Sodankylä Geophysical Observatory, FIN-99600, Sodankylä, Finland
2Department of Physical Sciences, University of Oulu , P.O.Box 3000, FIN-90014, Finland
Abstract. This paper presents binary phase codes and corresponding decoding filters
which are optimal in the sense that they produce no sidelobes and they
maximise the signal-to-noise ratio (SNR henceforth). The search is made
by investigating all possible binary phase codes with a given length.
After selecting the code, the first step is to find a filter which
produces no sidelobes. This is possible for all codes with no zeros in
the frequency domain, and it turns out that most codes satisfy this
requirement. An example of a code which cannot be decoded in this way is
a code with a single phase, i.e. a long pulse. The second step is to
investigate the SNR performance of the codes. Then the optimal code of a
given length is the one with the highest SNR at the filter output. All
codes with lengths of 3–25 bits were studied, which means investigating
33554428 binary phase codes. It turns out that all Barker codes except
the 11-bit code are optimal in the above sense. It is well known that the
performance of matched-filter decoding of Barker codes is better than
decoding without sidelobes. In the case of the 7-bit Barker code, it
is shown here that the SNR given by sidelobe-free decoding is nearly
30% worse than that of standard decoding, but for the 13-bit code
sidelobe-free decoding is only about 5% worse. The deterioration of SNR
should be evaluated against the benefits gained in disposing of the
sidelobes, which, even for the 13-bit code, contribute by 7.1% to the
total signal power from a homogeneous target. Thus, regions of weak
scattering can be contaminated by the sidelobes from neighbouring layers
of strong scattering, causing broadening of thin spatial structures and
giving a lower spatial resolution than implied by the bit length. A
practical example is shown where sidelobes mask a weak signal when the
standard matched filter is used in the analysis. An improvement is
achieved when sidelobe-free filtering is carried out.
Key words.
Radio science (ionospheric physics; signal processing;
instruments and techniques)
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