Michael D. Zoltowski1, Tariq R. Qureshi1, Robert Calderbank2, and Bill Moran3
1 Purdue University
2 Princeton University
3 University of Melbourne
In active sensing systems, the objective is to design a communication system that allows one to learn the environment, which could be one or more moving targets in the case of a radar. In a radar system, the transmitted waveforms are reflected by the target, and the reflected returns are then processed at the receiving end to determine the location and speed of the target. The delay in the received waveforms corresponds to the distance of the target from the radar, and the Doppler shift determines the speed at which the target is moving . Therefore, it is desired to transmit a waveform that provides good resolution in terms of the delay–Doppler properties of the radar returns. This is characterized by the use of ambiguity functions, which measure the delay–Doppler correlation of the received waveforms with the actual transmitted waveform. The ambiguity function  of a waveform s(t) is given by
where τ and υ are the delay and the Doppler shift, respectively. A perfect radar waveform would have the ambiguity function of the form
which means that the spike in ...