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In this paper a range of reduced-rank adaptive multiuser detectors (MUDs) are proposed and investigated for the hybrid direct-sequence time-hopping ultrawide bandwidth (DS-TH UWB) systems. The adaptive MUDs are operated based on the recursive least square (RLS) principles. Three types of reduced-rank techniques are investigated, which are the principal component (PC), cross-spectral metric (CSM) and Taylor polynomial approximation (TPA). These reduced-rank adaptive techniques are beneficial to achieving low-complexity, high spectral-efficiency and robust detection in hybrid DSTH UWB systems. In this contribution bit error rate (BER) performance of the hybrid DS-TH UWB systems using proposed reduced-rank adaptive MUDs is investigated by simulations, when communicating over UWB channels modelled by the Saleh-Valenzuela (S-V) channel model. Our simulation results show that, given a sufficiently high rank of the detection subspace, the reduced-rank adaptive MUDs are capable of achieving a similar BER performance as that of the full-rank ideal minimum mean-square error MUD (MMSE-MUD) but with significantly lower detection complexity. Furthermore, the TPA-based reduced-rank adaptive MUD is capable of yielding a better BER performance than the PC- or CSM-based reduced-rank adaptive MUD, when the same but relatively low rank detection subspace is assumed.