Myths concerning Woodward's ambiguity function: analysis and resolution

Abstract

Woodward’s ambiguity function measures the ability of a radar signal to simultaneously measure the range of an object via time delay and its velocity using Doppler shift. The ambiguity function is a foundational staple in radar signal processing. Six myths concerning Woodward’s ambiguity function (AF) are addressed in this paper: 1) the AF is uniquely defined, 2) the magnitudes of the various definitions of the AF are the same, 3) the AFs of the baseband and corresponding radio frequency signal are the same, 4) the maximum of a correlation’s magnitude determines optimality, and 5) multiplying a signal by a complex linear chirp rotates the AF and 6) the AF is not invertible. Each myth is explained, analyzed, and resolved. In discussing myth 6, the formula for inversion of the ambiguity function to its spawning signal is derived.