Ambiguity function and detection probability considerations for matched waveform design

Abstract

Abstract-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.

Integrated range-Doppler map and extended target identification with adaptive waveform for cognitive radar

“…where β now here is a constant that ensures the waveform weights sum up to one as dictated by (3). Now, it is clear in (8) that the biased terms where MAP is used in (6) would be removed.…”

“…Our interest, however, is extended target and matched illumination [1][2][3]. The SNR-based waveform matched to a known extended target is sometimes referred to as the eigenwaveform.…”

Comparison of ambiguity function of eigenwaveform to wideband and pulsed radar waveforms: a comprehensive tutorial

“…In [5], eigenwaveform design was considered in improving or mitigating the effects of moving extended targets in terms of detection probability. Both works in [5, 6] discussed the detection probability with the use of eigenwaveform for known extended target in Gaussian noise. The works in [7, 8] applied the notion of adaptive matched waveforms (e.g.…”

Adaptive waveform for integrated detection and identification of moving extended target

“…With the use of eigenwaveform, it can be shown that the probability of detection of each point in [3] is enhanced by the number of L pulses.…”

“…Our interest, however, is the extended target illuminated by eigenwaveform [1][2][3]. In target identification, some works are performed through spatial matched filter classifiers or using various radar signatures or range profile where plenty of papers exist but we list some examples [4][5].…”