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This paper studies the performance of dual-pulse transmitted-reference (TR) ultra wideband (UWB) systems in presence of multi-access interference (MAI). We derive an analytical expression of the channel-averaged signal-to-interference ratio (SIR) for a TR UWB receiver in two asynchronous scenarios, based on random time-hopping (TH) codes. The analytical results and numerical results are presented for illustration. We further show the impact of the chosen system parameters (e.g. symbol duration and delay hopping code) to better understand their influence on the multi-user performance.