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A computationally efficient subband adaptive chip-equalizer is investigated for downlink direct-sequence (DS) ultra-wideband (UWB) systems to cope with both the intersymbol interference (ISI) and the multiple-access interference (MAI) in multipath fading channels. This adaptive chip-equalization is developed based on the utilization of the reduced-rank (RR) multistage Wiener filter (MWF) in subbands. As a consequence, the proposed subband chip-equalizer achieves a substantial saving in complexity without compromising system performance. Simulations are conducted to provide a comparative evaluation of the proposed subband chip-equalizer with other existing fullband chip equalizers.