Energy-Efficient Sparse Beamforming for Multiuser MIMO Systems With Nonideal Power Amplifiers

In this paper, we consider energy-efficiency (EE) optimization problems with nonideal power amplifier (PA) models, per-antenna power constraints, and minimal spectral efficiency (SE) requirements in block-diagonalization-based multiuser multiple-input–multiple-output (MU-MIMO) systems. In the problem formulation, a joint optimization of the transmit covariance and the active transmit antenna set at the base station is considered. In general, the problem is a mixed-integer fractional programming problem, and it is difficult to solve it globally optimally. By reformulating the original problem as a sparse beamforming design problem and using a successive convex approximation method, we propose an iterative algorithm to solve it locally. In each iteration step, a concave fractional programming is solved, and the solution can be expressed in closed form with the help of the Lagrange dual method. Simulation results are used to verify the performance of our proposed algorithms. We also study the EE–SE tradeoff for the considered system. In fact, the relationship between EE and SE under an ideal PA model is not accurate for realistic systems. We characterize the EE–SE tradeoff under nonideal PA models by solving the EE maximization problems under different SE values. In this way, we can also shed light on the design of the system parameters to optimize the EE–SE curve. We find that with nonideal PA considered, the SE corresponding to the optimal EE will increase, compared with the ideal case. If we design the system parameters according to the optimal SE under an ideal PA model to maximize the EE, both the EE and the SE of the realistic system will decrease. We also find that when the proposed antenna selection algorithm is applied, the achieve region of the EE and the SE is expanded, particularly when the SE is low. In other words, the EE–SE win–win region is enlarged, and the EE–SE tradeoff is improved.