Minimization of the sum power of secondary users (SUs) equipped with multi-antenna is considered in the context of OFDM cognitive radio (CR) networks with coexisting primary users (PUs). The aggregated interference generated by SUs is constrained under a tolerable level so as to maintain reliable communication for PUs. Meanwhile, the quality of service (QoS) in terms of sum rate for SUs should be guaranteed as well. Sufficient conditions for the feasibility of this problem are provided for the facilitation of admission control. A novel on-line implementation algorithm is developed based on network duality and geometric programs (GPs) power control. This algorithm is proved to be convergent and the converged solution is locally optimal. Simulations results show that this algorithm is converged within several iterations and significant power savings can be achieved by the proposed algorithm compared with other relevant schemes.
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