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This paper provides a new approach allocating resources between multimedia users in a multi-cell OFDMA system in order to maximize the number of users that can achieve their QoS requirements. It does this by formulating the problem as a non-cooperative game. We propose a distributed algorithm to get the Nash equilibrium (NE) as well as introducing a new performance indicator (the qualified throughput) to measure the actual throughput gained by those users whose QoS requirement is met. The proposed algorithm can achieve fast convergence and enhanced performance; it can also efficiently deal with an unbalanced user distribution as well as with a uniform one. In this paper we also validate the algorithm by using Iterative Water Filling (IWF) as a benchmark and compare it with an existing algorithm. It can offer significant advantages and successfully handle a mix of QoS requirements between users. The approach is generic but in the paper is applied to the uplink in a scenario based on IEEE802.22 Cognitive Radio.