Power Allocation for Energy Efficient Multiple Antenna Systems with Joint Total and Per-Antenna Power Constraints

An energy efficiency (EE) maximization problem with multiple transmit antennas (multiple-input-single-output or distributed antennas setups) is considered in this paper. Besides the constraint on the total transmit power, per-antenna transmit power constraints, and a total weighted power constraint are jointly considered. Moreover, a quality-of-service constraint is also considered. Both linear and nonlinear high power amplifier (HPA) cases are studied. Because the original problem for the linear HPA case is a fractional convex problem, Dinkelbach's algorithm is implemented to reformulate the problem. By investigating the Karush-Kuhn-Tucker conditions, the mathematical properties of the globally' optimal solution are studied and proved, which provides a deeper understanding of the structure of power allocation among antennas. These properties also lead to a reduction of the complexity of the algorithms proposed to find the global optimum. For the nonlinear HPA cases, the reformulated problem after successive convex approximation is shown to be exactly in the same form as that of the previous problem with linear HPA with different weights of power consumption at each antenna. On the basis of numerical results comparing our EE maximization algorithms against different benchmarks, the efficiency and the superiority of our algorithms can be concluded.