The role of the ambiguity function in compressed sensing radar

As is clear from the ambiguity function (AF) uncertainty principle and the underlying matched filtering operation, pulse compression (PC) radars cannot accurately and simultaneously measure both the time delay and Doppler shift of moving targets. On the other hand, compressed sensing (CS) radar would seem to be emerging as a means to do just that, jointly to estimate the delay and Doppler shift, through convex optimization instead of matched filtering, such that PC resolution limits no longer apply. However, it turns out that the AF is closely related to the CS “dictionary coherence coefficient,” which affects the optimization recoverability. In this paper we formalize this relationship.