The radar ambiguity function plays a central role in the theory of radar signals. Its absolute value ($\abs{A(u)}$) measures the correlation between the signal $u$ emitted by the radar transmitter and its echo after reaching a moving target. It is important to know signals that give rise to ambiguity functions of given shapes. Therefore, it is also important to know to what extent $\abs{A(u)}$ determines the signal. This problem is called the "radar ambiguity problem" by Bueckner \cite{Bu}. Using methods developed for phase retrieval problems, we give here a partial answer for some classes of time limited (compactly supported) signals. In doing so, we also obtain results for Pauli's problem, in particular, we build functions that have infinitely many Pauli partners.