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In this letter, matching pursuit (MP) based tap selection technique is proposed and applied to ultra wideband (UWB) indoor channel equalization in the presence of inter symbol interference (ISI) and multiple access interference (MAI). Given the limited training sample support, quadratic constraint is incorporated into MP algorithm to insure the robustness for tap selection. The proposed method is shown to outperform the conventional minimum mean square error (MMSE) equalizer significantly given the same amount of training symbols.