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Interference from coexisting narrowband services is a critical factor affecting performance of ultra-wideband (UWB) radio communications. There is clearly a need to quantify interference and compare UWB systems on that basis. In this paper, we develop a general Rake reception model along with a unifying transmission framework for low duty-cycle UWB multiple access encompassing existing and novel spreading codes, including direct sequence, digital singleand multi-carrier, time-hopping, and combinations of them. Our unifying framework relies on a digital model, which leads to closed-form performance analysis expressions. Different from existing alternatives that require oversampling, our general model is developed directly from the samples of the Rake receiver output and allows for various Rake finger delay selections. Signal-to-interference-plus-noise ratio analysis and simulations are carried out to assess the relative merits of several UWB systems in the presence of narrowband interference, multipath and additive white Gaussian noise, for both matched-filter and minimum mean square error Rake receivers.