Ambiguity function and detection probability considerations for matched waveform design

In this paper we investigate the range resolution of transmit waveform designs matched to extended targets. We specifically look at eigenwaveform design which is also known as SNR-based illumination waveform design. To that end, we evaluate some ambiguity functions of radar systems employing eigenwaveforms. We consider some example targets and plot the corresponding ambiguity functions. Unlike traditional waveforms whose responses totally dictate the shape of the ambiguity function, both matched illumination waveform and extended target response contribute to the shape of the ambiguity function. In other words, range and Doppler resolutions are not just functions of the transmit waveform but of the target response itself which makes for interesting ambiguity functions. Moreover, we also evaluate the detection probability of eigenwaveforms matched to extended targets and show the performance improvement over wideband pulsed waveform designs.