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This paper deals with the analysis of the timing acquisition (synchronization) process in Impulse Radio (IR-) Ultra Wide Band (UWB) systems based on Differential Transmitted Reference (DTR) receiver architectures. The fundamental contribution includes a theoretical framework for timing acquisition analysis, which is not only able to describe the first moment (Mean Acquisition Time, MAT), and the second moment (standard deviation of the acquisition time) of the acquisition process, but which also provides a consistent and comprehensive analysis of the probability mass function of the acquisition time, i.e., Acquisition Time Mass Probability. In particular, the specific novelty insights of this paper are as follows: (i) the proposal of a new synchronization algorithm, which is based on a two-step approach and relies on the specific characteristics and peculiarities of DTR receivers, as well as the analysis of its performance via a framework based on the theory of Markov processes; (ii) the exploitation of the LATTICE- POISSON algorithm to accurately estimate the Acquisition Time Mass Probability and Overall Acquisition Probability PD (ov), i.e., the probability to get synchronized before a given time; (iii) the performance analysis and comparison of one-step and two-step solutions with respect to the acquisition threshold; and (iv) the analysis of two approaches to estimate MAT and PD (ov) in multipath fading channels, i.e., "Tacq Average" and "Pd Average', which are shown to lead to different results in different scenarios. We observe that restricting the analysis to the MAT may lead to hasty conclusions about the effect of the acquisition threshold on the design of DTR receivers, thus substantiating the need for a more general analysis using PD (ov), as well as the necessity of specifying the characteristics of the wireless channel (e.g., quasi-static, slowly- or fast-fading) for an accurate performa- - nce analysis.