Time Domain UWB Bistatic SAR Ambiguity Function

The generalized ambiguity function of an ultra wideband waveform can be defined from the correlation between the waveform and a time-scaled and delayed version of it, where the time scaling is related to the relative velocity of the target and the delay to the range. As a result of complexity of wideband and bistatic spatial configuration, the time-scale factor is very difficult to be formulized. In this paper, a time domain expression for the wideband bistatic ambiguity function is derived. It is constructed by the convolution of two factors: one depends on radar parameters, the other one depends on parameters of the radar working scenario. It can provide a con-venient way to inspect how these two factors impact on the performance of radar system respectively, and reveals the coupling nature of ambiguity function.