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The following are some open problems that were suggested by Greg Coxson
of Technology Service Corporation:
1) Prove that the longest Barker code is of length 13.
2) Do polyphase codes longer than length greater than 77 exist? (a length 77 code was found by Carol Nunn)
3) Conjecture: There exists a polyphase Barker code of length N if the sequence elements are the Nth roots of unity.
4) How many digits of precision are needed for polyphase codes using N roots of unity?
5) Classify autocorrelationsidelobepreserving groups for polyphase codes.
6) Develop (approximately) orthogonal code sets, particularly for MIMO radar.
7) Waveform optimization under frequency constraints (certain frequency bands may be unavailable or denied).
Some other open problems:
8) Ambiguity volume is not conserved for wideband waveforms, which suggests
that it may be possible to design waveforms that can measure both range and velocity
to arbitrary accuracy. Characterize such waveforms, and determine how to produce them.
Some background: the wideband ambiguity function was defined by D. Swick, and is discussed in
Leon Cohen's book on TimeFrequency Analysis. The study of ambiguity functions is closely
connected with group representation theory; see the work by Willard Miller, J. Bertrand and P. Bertrand,
J. P. Ovarlez, and Altes.
9) Inverse problem: given the ambiguity function, find the corresponding waveform (there is
some old work by Calvin Wilcox on this).
10) Optimize the waveform to identify certain targets (see the work by E. M. Kennaugh).
11) Find optimal waveforms for imaging and for suppressing clutter (see
the work by B. Yazici,
C.E. Yarman, M. Cheney, and T. Varslot).
12) Find optimal waveforms for propagation through complex media, including attenuating
media, dispersive media, and the ionosphere (see the work by S. Tsynkov).
Tuncay Aktosun
aktosun@uta.edu
Last modified: May 30, 2008
