Abstract: The Internet of Things (IoT) has become an essential supporting platform for the present and future cyber-enabled services. Cellular networks is considered as the main channel of the data access for IoT terminals distributed in the region of interest, and they have an irreplaceable value, especially in wide-area coverage. Thus, it has a significant application value to reduce the downlink transmit power consumption of base stations under the restrictions of the coverage requirements for the green communication in heterogeneous cellular networks. A gradient descent algorithm was proposed based on smooth approximation and root mean square propagation. The algorithm could minimize the total downlink power consumption of base stations while satisfying the IoT service coverage. First, the penalty function method was used to simplify such an optimization problem with complicated constraints to a new one with simple constraints. Then, the non-derivative objective function was transformed by an approximation method into a derivable form. We also presented the close-form of the gradient of the objective function with respect to both the azimuths of the antennas installed in the base stations and the downlink transmit power levels related to these antennas. Finally, the gradient descent algorithm with root mean square propagation was used to execute the optimization of the newly approximated but smoothed version of the original objective function. Simulation experiments were conducted, and the results show that the proposed algorithm can significantly reduce the total power consumption of the downlink radio frequency transmit under the restrictions of the coverage ratio requirements in the region of interest. Furthermore, not only is the convergence speed of the proposed algorithm very fast, but also the oscillation phenomenon that occurs during the iterative procedure steps of the optimization is greatly suppressed by the proposed algorithm compared with the meta-heuristic algorithms and ordinary gradient descent method.