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A communication system based on transmit-reference (TR) ultra-wideband (UWB) is studied and further developed. Introduced by Hoctor and Tomlinson, the aim of the TR-UWB transceiver is to provide a straightforward impulse radio system, feasible to implement with current technology, and to achieve either high data rate transmissions at short distances or low data rate transmissions in typical office or industrial environments. The main contribution in this paper is the derivation of a signal processing model that takes into account the effects of the radio propagation channel, in particular, for the case where the two pulses in a doublet are closely spaced. Several receivers based on the code-division multiple-access-like properties of the proposed model are derived, and the performance of the algorithms is tested in a simulation.