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In this paper we focus on compressive sampling (CS) based ultra wideband (UWB) differential detection. We formulate an optimization problem to jointly recover the sparse received UWB signals as well as the differentially encoded data symbol. We utilize an alternating direction method of multipliers (ADMoM) to solve this joint optimization problem. Our proposed joint recovery method outperforms the straightforward separate recovery method, which recovers the sparse received UWB signals in a first step and then detects the differentially encoded symbol based on the recovered signals.