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A reduced-rank receiver based on the multi-stage Wiener filter (MSWF) is proposed for multiple-access interference suppression for ultra wideband time-hopping spread spectrum radio in multipath channels. The proposed reduced-rank MSWF receiver provides performance superior to that of the classical RAKE receiver with similar complexity, and comparable to that of the full rank minimum mean squared error receiver with much lower complexity. The reduced rank MWSF also offers improved tracking performance in the presence of time-varying channels. Simulation and theoretical results confirm that the reduced rank scheme achieves a comparable output SINR to that of the full-rank scheme employing only 1/50th of the full-rank dimension. The superior tracking behavior of the reduced rank MWSF is also demonstrated.