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Data acquisition speed is an inherent problem of stepped-frequency continuous-wave (SFCW) radars, which may discourage further usage and development of this technology. We propose an emerging paradigm called compressed sensing (CS) to overcome this problem. In CS, a signal can be reconstructed exactly based on only a few samples below the Nyquist rate. Accordingly, the data acquisition speed can be increased significantly. A novel design of an SFCW ground-penetrating radar (GPR) with high acquisition speed is proposed and evaluated. Simulation by a monocycle waveform and actual measurement by a vector network analyzer at a GPR test range indicate the applicability of the proposed system.