As a design goal of green wireless communication, it is an important consideration to maximize energy efficiency of a Massive multiple-input multiple-output (MIMO) downlink system. By considering the case where the base station and all the users have the imperfect channel state information, a power allocation optimization problem is formulated to achieve the maximization of energy efficiency. Also, we derive the tractable closed-form expressions of lower bound on the achievable downlink rate utilizing maximum-ratio transmission (MRT) and zero-forcing precoding. Since the proposed optimization problem is non-convex, we strive to find a sub-optimal power allocation scheme. By decomposing the expression of the non-convex objective function, an energy-efficient power allocation algorithm that maximizes the energy efficiency is developed based on the difference of convex programming. Numerical results verify the tightness of the derived closed-form expressions, and show the performance improvement of the proposed energy-efficient power allocation scheme over the existing power allocation schemes.

作为绿色无线通信的设计目标，重要的考虑因素是使大规模多输入多输出（MIMO）下行链路系统的能量效率最大化。通过考虑基站和所有用户具有不完善的信道状态信息的情况，提出了功率分配优化问题以实现能量效率的最大化。此外，我们利用最大比率传输（MRT）和迫零预编码，得出了可实现的下行链路速率下限的易于处理的闭式表达式。由于提出的优化问题是非凸的，因此我们努力找到次优的功率分配方案。通过分解非凸目标函数的表达式，基于凸规划的差异，提出了一种能效最大化的节能功率分配算法。数值结果验证了所推导的闭合形式表达式的紧密性，并表明了所提出的节能型功率分配方案相对于现有功率分配方案的性能改进。