In this study we derive novel optimal algorithms for joint power control and beamforming design in modern large-scale MIMO systems, such as those based on the cell-free massive MIMO and XL-MIMO concepts. In particular, motivated by the need for scalable system architectures, we formulate and solve nontrivial two-timescale extensions of the classical uplink power minimization and max-min fair resource allocation problems. In our formulations, we let the beamformers be functions mapping partial instantaneous channel state information (CSI) to beamforming weights, and jointly optimize these functions and the power control coefficients based on long-term statistical CSI. This long-term approach mitigates the severe scalability issues of competing short-term iterative algorithms in the literature, where a central controller endowed with global instantaneous CSI must solve a complex optimization problem for every channel realization, hence imposing very demanding requirements in terms of computational complexity and signaling overhead. Moreover, our approach outperforms the available long-term approaches, which do not jointly optimize powers and beamformers. The obtained optimal long-term algorithms are then illustrated and compared against existing short-term and long-term algorithms via numerical simulations in a cell-free massive MIMO setup with different levels of cooperation.

翻译：本研究针对现代大规模MIMO系统（如基于无蜂窝大规模MIMO与XL-MIMO概念的系统），推导了联合功率控制与波束成形设计的新型最优算法。特别地，基于对可扩展系统架构的需求，我们构建并求解了经典上行链路功率最小化与最大最小公平资源分配问题的非平凡双时间尺度扩展形式。在我们的建模中，令波束成形器为将部分瞬时信道状态信息映射至波束权重的函数，并基于长期统计CSI联合优化这些函数与功率控制系数。这种长期方法缓解了现有短期迭代算法存在的严重可扩展性问题——该类算法需要配备全局瞬时CSI的中心控制器为每个信道实现求解复杂优化问题，从而对计算复杂度与信令开销提出极高要求。此外，本方法优于现有未联合优化功率与波束成形器的长期方案。最后，通过在具有不同协作层级的无蜂窝大规模MIMO场景中进行数值仿真，对所获得的最优长期算法进行了展示，并与现有短期及长期算法进行了对比。