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In this paper, we analyze the performance of a particular class of Transmitted-Reference (TR) receiver for Impulse Radio (IR) Ultra Wide Band (UWB) communication systems, which is called Chip-Time Differential Transmitted- Reference (TC-DTR). The analysis aims at investigating the performance of this receiver in the presence of faded narrow- band interference, and at comparing it with other TR receiver schemes proposed in the literature. It is shown that Tc-DTR receivers can offer a substantial performance gain with respect to other non-coherent receiver architectures, provided that some optimization conditions on code design are satisfied. Guidelines for optimal code and system optimization to reject narrow-band interference are provided in the present manuscript, as well as their effect on system performance. Numerical simulations are also shown to substantiate findings and analytical derivations.