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An ultra-wideband (UWB) transmitted reference (TR) system transmits an un-modulated pulse and a delayed modulated pulse pair. Then, a correlation receiver uses the former to demodulate the latter. Because of the long spread of a typical UWB channel, time delay between the two pulses is preferable to be larger than the channel delay spread for reduced noise at the receiver. However, for bandwidth efficiency, that delay should be made small, resulting in inter-pulse interference at the receiver. In this paper, digital receivers are constructed for TR-UWB systems including inter-pulse interference. A typical mean matching technique, appropriate for both PPM and PAM schemes, is implemented digitally to obtain a good template for symbol detection. Joint estimation and detection performance of this family of digital receivers, using finite number of bits in analog-to-digital conversion and finite noisy observations, is analyzed. Closed form results are derived and verified by computer simulations. In addition, the effect of time offset between the reference pulse and information carrying pulse is studied. Overlap of the two pulses does not incur noticeable performance degradation. The proposed analytical framework can be applied to study detection performance of other related digital receivers not covered in this paper