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The University of Nebraska has developed an ultrawideband (UWB) random noise radar system which transmits an ultrawideband random noise (Gaussian) waveform with uniform power spectral density (PSD) in the 1-2 GHz frequency range. We look at the range and range rate resolution issues by analysing the Woodward's (1955) ambiguity function. In general, the radar signal ambiguity function is defined as the normalized response of a filter matched to a return signal with range rate V/sub 0/, to a return signal with range rate V/sub l/. It describes the resolution properties of a given signal in range and range rate. However, for a random noise radar a correlator matched to the transmit process is required. Therefore, an analogous ambiguity function may be defined as the expected value of the response of the correlator matched to a target moving with range rate V/sub 0/1, to the return signal from the target with range rate V/sub 1/. Moreover, for a UWB transmit random process, the compression or stretch due to the range rate on the envelope of the return process cannot be ignored.