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Differential transmitted reference (DTR) ultra-wideband (UWB) impulse radio (IR) system is one of the most attractive solution for realizing non-coherent low data rate and low complexity UWB systems. In this paper, the bit error rate (BER) performance of DTR-UWB receivers conditioned on a channel realization is analyzed. The modeling of low complexity DTR-UWB systems using equivalent system models is presented. The average BER is verified through simulation for different signal-to-noise ratio (SNR) values. It is also compared to the average BER derived using the equivalent system model.