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Non-coherent detectors significantly contribute to the practical realization of the UltraWide-Band (UWB) Impulse-Radio (IR) concept, in that they allow avoiding channel estimation and provide highly efficient reception capabilities. Complexity can be reduced even further by resorting to an all-digital implementation, but Nyquist-rate sampling of the received signal is still required. The current paper addresses this issue by proposing a novel Differential Detection (DD) scheme, which exploits the Compressive Sampling (CS) framework to reduce the sampling rate much below the Nyquist-rate. The optimization problem is formulated to jointly recover the sparse received signal as well as the differentially encoded data symbols, and is compared with both the separate approach and the scheme using the compressed received signal directly, i.e., without reconstruction.
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