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This paper addresses the application of the emerging Compressive Sensing (CS) technology to the detection of UltraWideBand (UWB) signals. Capitalizing on the sparseness of random UWB signals in the basis of eigen-functions, the authors develop a new CS dictionary called eigen-dictionary. Coupled with this eigen-dictionary, an enhanced Bayesian learning procedure is proposed to reconstruct the sparse UWB signal from a small collection of random projection measurements. Furthermore, by utilizing a common sparsity profile inherent in UWB signals, the proposed Bayesian algorithm naturally lends itself to multitask CS for simultaneously recovering multiple UWB signals. Since the statistical inter-relationships between different CS tasks are exploited, the multi-task (MT) Bayesian CS can efficiently improve the reconstruction accuracy and thus the performance of UWB communications.
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