Private Mobile Radio (PMR) networks are cellular infrastructures dedicated to be used by professionals, such as public safety, military, industry and transportation organizations. The world PMR leader, Airbus Defence and Space (former Cassidian), intends to base the next generation of its products upon LTE-Advanced, enriched with a new sensing method which estimates interference probabilities between user entities (UEs) and neighboring base stations (eNodeBs). We work on a variant of the fractional coloring problem, which models an optimal Resource Blocks (RBs) allocation with spatially unrestrained frequency reuse, taking into account the new sensing. We propose a distributed allocation algorithm where eNodesBs allocate RBs to their UEs having at their disposal partial information concerning the possibility of interference between UEs, keeping in mind its possible implementation in PMR networks. We stress that exchanges of interference information are made between eNodeBs and not UEs. Overhead is thus transmitted over a wired network and its volume is very small. Because this problem is NP-hard without constant performance bounds, we perform an exhaustive procedure to evaluate the performance of our algorithm. Our distributed algorithm is confronted with the random one and two existing resource allocation schemes (Fractional/Soft Frequency Reuse). Our algorithm clearly outperforms the others even with incomplete interference information. Being little demanding in terms of execution time and overhead amount, it is an excellent candidate to be implemented in the new LTE-Advanced PMR networks.