Power Allocation for Energy Efficient Optimization of Distributed MIMO System with Beamforming

This paper presents three energy-efficient power allocation (PA) schemes for the downlink of a distributed multiple-input multiple-output (D-MIMO) system with beamforming at distributed antenna ports and antenna selection (AS) at a mobile station over composite Rayleigh channels. Subject to maximum power constraints, a constrained maximization problem on energy efficiency (EE) is formulated. Based on theoretical analysis, the optimal beamforming is shown to be aligned with the channel direction that renders the joint design problem to be a PA optimization one. It is shown that the optimization problem is strictly pseudo-concave with a unique maximum. Thus, an optimal PA scheme based on a gradient projection method is proposed to obtain the global solution. To speed up the gradient projection method, a closed-form initialization is derived. Furthermore, a low-complexity optimal PA schemes based on the Karush–Kuhn–Tucker conditions is proposed. This optimal scheme has a closed-form PA expression for a certain condition or else computes the PA by the Lambert function or the bisection method, and gives the same EE performance as that of the optimal gradient-based scheme. The performances of these two optimal schemes are optimal and verified to be valid in contrast to the inaccurate optimal scheme in the literature. For large maximum power, the closed-form initial PA will become the optimal solution and can be considered as a suboptimal solution with no iterative computation. Making use of the tight upper and lower bounds of the Lambert function, a very low-complexity suboptimal PA scheme is developed. Simulation results show that the proposed suboptimal scheme can achieve nearly optimal performance. Maximum EE and maximum channel power, which are optimal and suboptimal criteria, are adopted for antenna selection. The simple suboptimal criterion can provide EE performance very close to that of the optimal one. The D-MIMO with AS is shown to give considerable EE gain over the single receive antenna system. Moreover, the proposed three PA schemes can be used for multiuser diversity D-MIMO systems to achieve superior EE performance.