As the evolution of cloud radio access networks (CRANs), heterogeneous cloud radio access networks (H- CRANs) are now recognized as promising paradigm to achieve high spectral and energy efficiency through taking advantages of both heterogeneous networks and C- RANs. In H-CRANs, the heterogeneous processing node (HPN) guarantees the basic quality of service (QoS) requirement for the user equipment, while remote radio heads (RRHs) are deployed to provide enhanced QoS performances. Inter-tier interference between HPNs and RRHs should be coordinated for achieving high throughput gains in H-CRANs. In this paper, the transmit power for both RRHs and HPNs are researched to mitigate this inter-tier interference. The throughput maximizing problem with and without interference coordination under the power and interference constraints are developed. Since this kind of optimization problem is not convex, these two non- convex optimization problems are transformed into the form of matrix. Through the Perron-Frobenius theory, the optimal power allocation solution is derived. Simulation results show that the proposed solution is converged, and it can achieve significant performance gains.