A hierarchical wireless sensor network consists of multiple sensor nodes sending their sensed data to multiple access points (APs) to relay the aggregated data to a system server. In the data collection scenarios, the access points can reuse the subcarriers used by the sensors in the data relaying phase to improve spectral efficiency. The data rate requirements of sensors are heterogeneous, and energy consumption is the primary concern in any sensor-based application. This work aims to minimize the total power consumption of the whole device while satisfying each device’s minimum data rate requirements. The paper formulates the problem as a joint optimization of power allocation, AP selection, and subcarrier assignment. The deployment of a two-phase communication and the application of the Lagrangian method in each phase to allocate power and subcarriers for sensor nodes and APs bring the optimal solution. Numerical results show that the proposed algorithm achieves significant power savings compared to the existing methods.