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Sampling is the bottleneck for ultra-wideband (UWB) communication. Our major contribution is to exploit the channel itself as part of compressed sensing, through waveform-based pre-coding at the transmitter. We also have demonstrated a UWB system baseband bandwidth (5 GHz) that would, if with the conventional sampling technology, take decades for the industry to reach. The concept has been demonstrated, through simulations, using real-world measurements. Realistic channel estimation is also considered.