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This study applies the expectation-maximisation (EM) algorithm to direct sequence ultra-wideband (DS-UWB) systems, combining channel estimation with data detection in iterative steps. UWB systems often suffer from multipath interference because of obstacles in indoor environments. This study employed a maximal-ratio combining (MRC) Rake receiver for its ability to exploit the gain in multipath diversity provided by multipath propagation when the channel coefficient is estimated correctly. Simulation results demonstrate that the channel coefficient captured by the MRC Rake receiver can be estimated efficiently using the proposed EM algorithm. The proposed system is capable of attaining practical convergence within a few iterations.