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It is well known that noise-like waveforms have the inherent property of suppressing ambiguities due to their nonrepetitive nature, as opposed to the more classical linear frequency modulated (LFM) pulsed waveforms. This aperiodicity also improves the robustness against jammers, making these waveforms harder to detect and classify by an enemy. However, noise waveforms are Doppler sensitive, requiring the use of Doppler-dependent matched filters for proper range compression. Also, when processed with classical matched filters, noise waveforms have sidelobes that spread out across the whole range-Doppler plane, potentially masking weak targets in the presence of strong ones. A possible solution to reduce the sidelobe interference is to use sparse signal processing (SSP). In this article, we demonstrate with simulated and experimental data how noise waveforms can be used in combination with SSP for unambiguous detection of strong as well as weak targets, improving upon the performance of more conventional LFM pulsed waveforms.