One of the most attractive features of time-hopping ultra-wide-band (UWB) transmission, largely ignored in the literature so far, is the possibility to operate in full-duplex mode, thanks to its very low duty-cycle. This allows a terminal to transmit and receive within the same time frame and frequency band, yielding a considerable saving of time and band resources at the radio-resource-management layer. In this paper, we propose a methodology to design channel estimation/synchronization and demodulation/decoding algorithms for a low-complexity receiver operating in full-duplex mode. The leading idea is simply to avoid, at reception, time intervals that correspond to pulse transmission. We also evaluate the performances of such a system through simulations over realistic propagation channels.