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Ultra-wideband random noise radar theoretically has a thumbtack ambiguity function, which cannot be realized due to hardware, processing, and environmental limitations. Velocity estimation using traditional Doppler processing is not practicable for ultra-wideband random noise radar because of the large fractional bandwidth. Through analysis, this paper explores moving target detection using digital correlation processing of random noise signals in the time domain with a single receive channel. Additionally, simulated and measured results are presented.