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This paper presents a signal processing model for the delay-hopped transmit-reference ultra wideband communications system introduced by Hoctor and Tomlinson. In that paper, a single-user receiver based on a bank of correlators and a sliding window integrator was proposed. However, the radio propagation channel also introduces correlations, which have a significant effect not taken into account by the Hoctor-Tomlinson receiver. Here we propose an accurate signal processing model for the transmit-reference system, including the effect of the propagation channel, as well as an algorithm to estimate the resulting effective channel coefficients.