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This paper proposes a symbol-level synchronization technique for ultra-wideband (UWB) communications in networks without power control. The near-far problem dramatically degrades the performance of synchronization for UWB communications. The technique is based on an easy-to-implement procedure to suppress the interfering waveforms from high-power users without requiring knowledge of their spreading codes. The technique includes two operations, a "suppression" operation, and a subsequent dimension detection operation that determines the desired user's code phase during acquisition in the receiver. Simulation results are provided that show the improved performance of the near-far resistant synchronization procedure proposed in this paper for up to two high-power and four equal-power interfering users when compared to the best alternative from the literature.