Heterogeneous network(HetNet) as a promising technology to improve spectrum efficiency and system capacity has been concerned by many scholars, which brings huge challenges for power allocation and interference management in multicell network structures. Although some works have been done for power allocation in heterogeneous femtocell networks, most of them focus centralized schemes for single-cell network under interference constraint of macrocell user. In this paper, a sum-rate maximization based power allocation algorithm is proposed for a downlink cognitive Het Net with one macrocell network and multiple microcell networks. The original power allocation optimization problem with the consideration of cross-tier interference constraint, maximum transmit power constraint of microcell base station and inter-cell interference of microcell networks is converted into a geometric programming problem which can be solved by Lagrange dual method in a distributed way. Simulation results demonstrate the performance and effectiveness of the proposed algorithm by comparing with the equal power allocation scheme. Heterogeneous network (HetNet) as a promising technology to improve spectrum efficiency and system capacity has been concerned by many scholars, which brings huge challenges for power allocation and interference management in multicell network structures. Although some works have been done for power allocation in heterogeneous femtocell networks, most of them focus centralized schemes for single-cell network under interference constraint of macrocell user. In this paper, a sum-rate maximization based power allocation algorithm is proposed for a downlink cognitive Het Net with one macrocell network and multiple microcell networks. The original power allocation optimization problem with the consideration of cross-tier interference constraint, maximum transmit power constraint of microcell base station and inter-cell interference of microcell networks is converted into a geometric programming problem which can be solved by Lagrange dual method in a distributed way. Simulation results demon strate the performance and effectiveness of the proposed algorithm by comparing with the equal power allocation scheme.