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This paper proposes a space-time selective RAKE (SRAKE) receiver with maximum signal-to-interference-plus-noise ratio (MSINR) for direct-sequence ultra-wideband (UWB) communications in the presence of narrowband interference (NBI) and multiple-access interference. For effectively extracting a fixed number of the UWB signal components (fingers) from numerous resolvable paths, four finger selection strategies (FSSs) are considered for the proposed space-time SRAKE receiver, including the optimum FSS (with MSINR), which is not very computationally feasible, and three feasible FSSs: an energy-based FSS (EB-FSS), a constrained energy-based FSS (CEB-FSS), and a hybrid energy-based FSS, which is also a combination of the EB-FSS and CEB-FSS. Through a performance analysis, we show that the performance of the proposed receiver in the presence of NBI not only depends on the power ratio, bandwidth ratio, and relative spectrum location of NBI with respect to the UWB signal, but also on the FSS used. Some simulation results are then presented to show that the proposed space-time MSINR-SRAKE receiver with the preceding FSSs used can provide a larger system capacity and better immunity to strong NBI than the existing time-only SRAKE receivers and space-time SRAKE receivers.