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Impulse radio is an ultrawideband system with attractive features for baseband asynchronous multiple-access, multimedia services, and tactical wireless communications. Implemented with analog components, the continuous-time impulse radio multiple-access model utilizes pulse-position modulation and random time-hopping codes to alleviate multipath effects and suppress multiuser interference. We introduce a novel continuous-time impulse radio transmitter model and deduce from it an approximate one with lower complexity. We also develop a time-division duplex access protocol along with orthogonal user codes to enable impulse radio as a radio link for wireless cellular systems. Relying on this protocol, we then derive a multiple-input/multiple-output equivalent model for full continuous-time model and a single-input/single-output model, for the approximate one. Based on these models, we finally develop design composite linear/nonlinear receivers for the downlink. The linear step eliminates multiuser interference deterministically and accounts for frequency-selective multipath while a maximum-likelihood receiver performs symbol detection. Simulations are provided to compare performance of the different receivers.