Two-Timescale Joint Power Control and Beamforming Design With Applications to Cell-Free Massive MIMO

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">functions</i> mapping partial instantaneous channel state information (CSI) to beamforming weights, and we 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.