Many radar designs transmit trains of pulses to estimate the Doppler shift from moving targets, in order to distinguish them from the returns from stationary objects (clutter) at the same range. The design of these waveforms is a compromise, because when the radar's pulse repetition frequency (PRF) is high enough to sample the Doppler shift without excessive ambiguity, the range measurements often also become ambiguous. Low-PRF radars are designed to be unambiguous in range, but are highly ambiguous in Doppler. High-PRF radars are, conversely unambiguous in Doppler but highly ambiguous in range. Medium-PRF radars have a moderate degree of ambiguity (say five times) in both range and Doppler and give better overall performance.
The ambiguities mean that multiple PRFs must be used to resolve the ambiguities (using the principle of the Chinese Remainder Theorom). A more serious issue, however, is that each PRF is now 'blind' at certain ranges, where the received signal arrives at the same time as the next pulse is transmitted, and at certain Doppler shifts (target speeds), when the return is 'folded' in Doppler so that it is hidden under the much larger clutter signal.
A practical radar therefore transmits successive bursts of pulses at different PRFs to overcome the 'blindness' and to resolve the ambiguities. Analysing the performance, although quite complex if done in detail, is possible using modern computer models, but the inverse problems of synthesing waveforms with a given performance remains difficult. Even more difficult is the problem of gaining intuitive insights into the likely effect of altering the waveforms. Such insights would be extremely valuable for the design process.
This problem is well known within the radar industry, but it is hoped that by airing it to an audience with a wider range of skills, some new ways of looking at the problem might be found.