THE 2008 NSF-CBMS CONFERENCE ON INVERSE SCATTERING FOR RADAR IMAGING May 27-May 31, 2008 Speaker Schedule Lectures Outline Application Organizers Background Open problems Links Participants Pictures/Media Conference flyer 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 autocorrelation-side-lobe-preserving 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 Time-Frequency 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