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 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, especially when simple beamforming strategies are employed. 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，提出了用于最优统计最大最小功率控制的数学工具与定点算法。与以往依赖香农可达（遍历）速率的使用后遗忘（UatF）下界的研究不同，本框架能够处理明确考虑解码器端具有完美或不完美信道状态信息（CSI）的替代界。通过这一方法，我们解决了基于UatF算法所固有的UatF界缺陷。例如，UatF界可能过于保守：在极端情况下，对于零均值信道中的完全统计（非自适应）波束成形，UatF界会产生平凡（零）速率界。该界也缺乏尺度不变性：仅缩放波束成形向量就可能显著改变界值，尤其在采用简单波束成形策略时。相比之下，本框架兼容不受上述缺点影响的信息论界。我们通过求解一个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，具体展示了该框架的应用。