Most of the existing massive multi-input-multi-output (mMIMO) relaying works assume ideal transceiver hardware and spatially uncorrelated channels. A practical mMIMO relay, however, due to limited antenna spacing and the use of cost-effective equipment, usually experiences spatially-correlated channels and hardware impairments, respectively. We consider a hardware-impaired two-way full-duplex (FD) spatially-correlated mMIMO relaying with multiple MIMO FD user-pairs, and derive a closed-form spectral efficiency (SE) expression which is valid for a practical number of finite relay antennas. We use this expression to develop a quadratic transformation approach to optimize the non-convex global energy efficiency (GEE) and weighted sum energy efficiency (WSEE) metrics, which are fractional functions of optimization variables. The proposed approach first converts the fractional problem into its equivalent fraction-free counterpart, and then uses novel transformations to make the problem concave, and solve it using an iterative algorithm. We use this optimization to i) investigate the impact of spatial correlation and hardware impairments on GEE; ii) decide hardware impairment values for a tolerable reduction in GEE; and iii) investigate the impact of weights in WSEE on the users energy efficiency.

中文翻译：

---

节能型空间相关硬件受损的大规模MIMO FD中继

大多数现有的大规模多输入多输出（mMIMO）中继工作都假设理想的收发器硬件和空间上不相关的信道。然而，由于有限的天线间隔和使用经济高效的设备，实际的mMIMO中继通常通常会遇到空间相关的信道和硬件损坏。我们考虑了具有多个MIMO FD用户对的硬件受损的双向全双工（FD）空间相关的mMIMO中继，并得出了对实际数量的有限中继有效的闭式频谱效率（SE）表达式天线。我们使用该表达式来开发二次变换方法，以优化非凸全局能量效率（GEE）和加权总能量效率（WSEE）指标，它们是优化变量的分数函数。所提出的方法首先将分数问题转换为其等效的无分数对应项，然后使用新颖的变换使问题变为凹面，并使用迭代算法进行求解。我们使用这种优化来：i）研究空间相关性和硬件损伤对GEE的影响；ii）确定硬件减损值以允许GEE的可容忍降低；iii）研究WSEE中权重对用户能效的影响。