Ideal Ambiguity Function
An ambiguity function of interest is a 2-dimensional Dirac delta function or "thumbtack" function; that is, a function which is infinite at (0,0) and zero elsewhere.
An ambiguity function of this kind would be somewhat of a misnomer; it would have no ambiguities at all, and both the zero-delay and zero-Doppler cuts would be an impulse. However, any Doppler shift would make the target disappear. This is not desirable if a target has unknown velocity it will disappear from the radar picture, but if Doppler processing is independently performed, knowledge of the precise Doppler frequency allows ranging without interference from any other targets which are not also moving at exactly the same velocity.
This type of ambiguity function is not physically realizable; that is, there is no pulse that will produce from the definition of the ambiguity function. Approximations exist, however, and binary phase-shift keyed waveforms using maximal-length sequences are the best known performers in this regard .
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