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The authors propose Maximum A Posteriori (MAP) based non-coherent differential detector for Ultra-WideBand (UWB) Impulse Radio (IR) signals, received at a sub-Nyquist sampling rate. They build their detector for a Laplacian distributed multipath channel, which models sparsity. Their MAP based detector outperforms differential detectors based on other state-of-the-art approaches from a practical point of view. Their work highlights the critical role of different measurement matrices for the compressed differential detectors in general and the MAP based compressed differential detectors in particular.
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