Radar and communication waveform: Wideband ambiguity function and narrowband approximation

Aiming for a system combining radar and communications, along with high performance requirements, imposes a waveform characterized by a large time-bandwidth product. The assumption of a wideband signal model for the radar problem and wideband ambiguity function seem then a forced solution, but it is then relevant to identify the exact conditions and the sustainable degradation of performance that allow instead the use of the narrowband approximation. The need to use wideband representation depends on the waveform parameters bandwidth and duration. Certain types of future state-of-the art radar should take into account this representation.