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We propose a simple distributed radio resource allocation algorithm for an OFDMA cellular system, which aims at minimizing the overall transmitted power subject to a rate constraint for each user. In order to reduce the problem complexity we use a single modulation; simulations show that the resulting performance degradation is negligible when the number of users is high enough. Moreover, we propose a simple distributed heuristic that, by reducing the rate constraints, steers the multicell system towards an stable resource allocation. Results show that the proposed system exhibits a great robustness to the destructive effects of multiple access interference.