A study of a class of detection waveforms having nearly ideal range—Doppler ambiguity properties

A special class of permutation matrices is considered. It is shown that these matrices may be beneficially used to determine the frequency-time pattern of a uniform pulse train. Proper choice of burst waveform parameters is shown to result in a detection wave-form having range and Doppler resolution properties consistent with the overall signal duration and bandwidth. The range-Doppler sidelobe peaks are well-controlled so that the ideal "thumbtack" ambiguity function behavior is closely approximated by the synthesis procedure presented.