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In this paper, we investigate the problem of power allocation in a heterogeneous network that is composed of a pair of cognitive users (CUs) and an infrastructure-based primary network. Since CUs have only limited effective spectrum-sensing ability and primary users (PUs) are not active all the time in all locations and licensed bands, we set up a new multi-area model to characterize the heterogeneous network. A novel combined interference-avoidance policy corresponding to different PU-appearance situations is introduced to protect the primary network from unacceptable disturbance and to increase the spectrum secondary-reuse efficiency. We use dual decomposition to transform the original power allocation problem into a two-layer optimization problem. We propose a low-complexity joint power-optimizing method to maximize the transmission rate between CUs, taking into account both the individual power-transmission constraints and the combined interference power constraint of the PUs. Numerical results show that for various values of the system parameters, the proposed joint optimization method with combined PU protection is significantly better than the opportunistic spectrum access mode and other heuristic approaches.