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This work presents a novel method to reconstruct ultra-wideband radar signals over their entire bands when only a portion of the spectrum is available. The inherent sparse configuration of sensing radars is exploited to develop a robust wideband synthesizing framework. The proposed approach consists of the following two steps: 1) A radar signal model is developed which allows for a sparse representation of the target’s signature over wide bandwidths. 2) A flexible statistical model is introduced to solve the sparse model of Step 1 in a Bayesian framework. By imposing Gamma-Gaussian sparsity promoting priors on the target’s signature, the model improves the sensing accuracy. In addition, by introducing a Gaussian mixture model of noise, any non-deterministic density of noise or jamming can be accurately approximated. This significantly increases robustness in complex environments. The proposed approach is verified through the development of an ultra-wideband (12–110 GHz) radar system consisting of canonical-spherical targets. Monte Carlo simulations are carried out to compare the performance of the proposed statistical method when the data missing rate is 25% with other methods in the literature. It is shown that the proposed model has closed-form solutions and is robust to complex environments with satisfying performance. As the noise distribution violates the single Gaussian assumption, other relevant methods in the literature fail to recover the model with a large RMS error (< 0.50). In contrast, our method has a maximum RMS of only 0.11.
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