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In this paper we study the distributed multi-channel power allocation for spectrum sharing cognitive radio networks with QoS guarantee. We formulate this problem as a non- cooperative game G _MCPA-C with coupled strategy space to address both the co-channel interference among secondary users and the interference temperature regulation imposed by primary systems. We investigate the properties of Nash equilibrium (N.E.) for our G _MCPA-C , including the existence and QoS provisioning. Furthermore, we derive a layered structure by applying the Lagrangian dual decomposition to G _MCPA-C and design a distributed algorithm to find the N.E. via this structure. Simulation results are presented to show both the validity of our game theoretic model and the performance of our proposed algorithm. Finally, we incorporate the Pigouvian taxation into our algorithm to improve the efficiency of N.E. when social …