We introduce mathematical tools and fixed point algorithms for optimal statistical max-min power control in cellular and cell-less massive MIMO systems. Unlike previous studies that rely on the use-and-then-forget (UatF) lower bound on Shannon achievable (ergodic) rates, our proposed framework can deal with alternative bounds that explicitly consider perfect or imperfect channel state information (CSI) at the decoder. In doing so, we address limitations of UatF-based power control algorithms, which inherit the shortcomings of the UatF bound. For example, the UatF bound can be overly conservative: in extreme cases, under fully statistical (nonadaptive) beamforming in zero-mean channels, the UatF bound produces trivial (zero) rate bounds. It also lacks scale invariance: merely scaling the beamformers can change the bound drastically. In contrast, our framework is compatible with information-theoretic bounds that do not suffer from the above drawbacks. We illustrate the framework by solving a max-min power control problem considering a standard bound that exploits instantaneous CSI at the decoder.

翻译：本文针对蜂窝和无蜂窝大规模MIMO系统，引入数学工具与定点算法以实现最优统计最大最小功率控制。与以往依赖香农可达（遍历）速率"使用后遗忘"(UatF)下界的研究不同，我们提出的框架能够处理在解码器端显式考虑完美或不完美信道状态信息(CSI)的替代界。通过这种方法，我们解决了基于UatF的功率控制算法所固有的局限性，这些局限性继承自UatF界本身的缺陷。例如，UatF界可能过于保守：在零均值信道中采用完全统计（非自适应）波束成形的极端情况下，UatF界会产生平凡（零值）速率界。该界还缺乏尺度不变性：仅缩放波束成形器就会导致界值剧烈变化。相比之下，我们的框架与不受上述缺陷影响的信息论界相兼容。我们通过求解考虑解码器端利用瞬时CSI的标准界的最大最小功率控制问题，具体阐释了该框架的应用。