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However, the phase\u2010array\u2010based DOA estimations usually require complicated system architecture and signal processing. Digital programmable metasurfaces (DPMs) can realize flexible spatial modulations of electromagnetic (EM) waves without using massive transceivers, and hence can be used for DOA estimations with much simplified architectures. Here, a mechanism of DPM\u2010based DOA estimations at Ka band is proposed. A reflective DPM is designed to produce a series of dual beams in random, so as to establish a sensing matrix and sample the incident wave. Orthogonal matched pursuit algorithm is used to estimate DOA from the sparsely sampled datasets. The performances of the DPM\u2010based DOA estimations are demonstrated by simulations and experiments for the cases of single source and double sources. 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