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The inherent near-far effect in wireless networks causes nodes that are further away from the receiver to suffer from throughput degradation, as packets from nodes that are nearer are typically received with greater signal strengths. This unfair situation is traditionally overcome by power control. However, when power control is not feasible, for example in tiny sensor nodes with power-limited batteries, alternative solutions have to be utilized to achieve fairness in the network. In this paper, we propose U-LiBRA - an UWB Location Based Resource Allocation scheme to alleviate the contention between near and far nodes in a TH-UWB sensor network. U-LiBRA allocates different time slots to nodes that are at varying distances from the receiver, so that nodes that are further away from the receiver can achieve higher throughput than what they would typically obtain under the influence of the near-far effect. Simulation results show that U-LiBRA can effectively mitigate the near-far effect and improve fairness in the absence of power control.