Cognitive radios such as intelligent phones and Bluetooth devices have been considered essential goods in next-generation communication systems.Such devices will have to share the same frequency band owing to the limited bandwidth resource.To improve spectrum efciency,we formulate multi-channel power allocation as a market competitive equilibrium(CE)problem,and prove that its solution exists and is unique under the condition of weak interference.We then propose two distributed power allocation algorithms achieving CE,namely the fast convergent power allocation algorithm(FCPAA)and the social-fairness-aware FCPAA(SFAF).Theoretical analysis and simulation results demonstrate that the proposed algorithms lead to better system performance in terms of the guaranteed interference temperature constraint using the price mechanism instead of a strategy based on the Nash equilibrium.Moreover,it is shown that the FCPAA maximizes total utility,and converges more quickly than the method addressed in prior research with the help of improved round-robin rules.However,the FCPAA cannot ensure the same social fairness among secondary users as the SFAF scheme in both the non-fading channel and Rayleigh fading channel;the SFAF balances the individual utility by adjusting each user’s budget at the expense of a small quantity of system total throughput. Cognitive radios such as intelligent phones and Bluetooth devices have been considered essential goods in next-generation communication systems. Such devices will have to share the same frequency band due to the limited bandwidth resource. To improve spectrum efciency, we formulate multi-channel power allocation as a market competitive equilibrium (CE) problem, and prove that its solution exists and is unique under the condition of weak interference. We then propose two distributed power allocation algorithms achieve CE, namely the fast convergent power allocation algorithm (FCPAA) and the social -airair-aware FCPAA (SFAF). Theoretical analysis and simulation results demonstrate that the proposed algorithm lead to better system performance in terms of the guaranteed interference temperature constraint using the price mechanism instead of a strategy based on the Nash equilibrium. Moreover, it is shown that the FCPAA maximizes total utility, and converges more quickly than the method addressed in prior research with the help of improved round-robin rules. However, the FCPAA can not ensure the same social fairness among secondary users as the SFAF scheme in both the non-fading channel and the Rayleigh fading channel; the SFAF balances the individual utility by adjusting each user’s budget at the expense of a small quantity of system total throughput.