Sub-Nyquist sampling technology can ease the conflict between high resolution and wide swath in a synthetic aperture radar (SAR) system. However, the existing sub-Nyquist SAR imposes a constraint on the type of the observed scene and can only reconstruct the scene with small sparsity (i.e., number of significant coefficients). The information channel model of microwave imaging radar based on information theory, in which scene, echo, and the mapping relation between the two correspond to information source, sink, and channel, is built, and noisy-channel coding theorem explains the reason for the aforementioned under this model. To allow the wider application of sub-Nyquist SAR, this paper proposes sub-Nyquist SAR based on pseudo-random space-time modulation. This modulation is the spatial and temporal phase modulation to the traditional SAR raw data and can increase the mutual information of information source and sink so that the scenes with large sparsity can be reconstructed. Simulations of scenes with different sparsity, e.g., an ocean with several ships and urban scenes, were run to verify the validity of our proposed method, and the results show that the scenes with large sparsity can be successfully reconstructed.
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