Circular synthetic aperture radar (CSAR) imaging based on compressive sensing with random step frequency (RSF) as transmitted signal is introduced. CSAR is capable of obtaining both two-dimensional high resolution image and three-dimensional image due to a circular collection trajectory. RSF signal shares good characteristics of noise signals including ``thumbtack-shape" ambiguity function, low probability of interception, and strong anti-jamming capability. As a result, CSAR adopting RSF signal can make use of advantages of both CSAR and RSF signal. Compressive sensing is a new data acquisition and reconstruction theorem for sparse or compressible signals, which needs fewer samples to reconstruct signals than traditional Nyquist theorem. Simulation results show that both two-dimensional and three-dimensional targets can be well reconstructed from few samples by applying compressive sensing to RSF CSAR imaging.
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