A scale cross-ambiguity function for radar applications

We consider a generalization of the cross-ambiguity function (CAF) commonly used to resolve range and velocity of radar targets. The conventional CAF paradigm assumes that the transmitted signal is a sinusoid having slowly varying complex modulation, and models the received signal as a Doppler shift of the carrier frequency, composed with a time delay. For transmitted signals having more general form, including wide-band signals, the CAF model is inadequate. We argue that for transmitted signals which are not essentially sinusoids, it is more accurate to model the received signal as a time-scaled version of the transmitted signal, composed with a time delay. The resulting scale CAF (SCAF) model accounts for Doppler shifts of all frequencies in the emitted signal's spectrum, not just a carrier, and agrees with the CAF model when the transmitted signal has a single dominant carrier frequency. We demonstrate through simulations that for wide-band emitted signals, SCAF provides significantly more accurate estimates of range and velocity of radar targets than CAF. The new method is also readily adapted to the problem of geolocating an emitter when a wide-band transmitted signal is collected by two or more receivers in motion relative to the transmitter.