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Two-timescale weighted sum-rate maximization for large cellular and cell-free massive MIMO

Lorenzo Miretti, Emil Björnson, Sławomir Stańczak

TL;DR

The paper tackles scalable sum-rate optimization in large cellular and cell-free MIMO by introducing a two-timescale framework that optimizes transmit powers and beamformers based on slow-varying channel statistics. It derives an MMSE-SINR relation for the UatF ergodic-rate bound and reformulates the long-term WSR problem into an equivalent WMMSE problem, solvable via a block-coordinate ascent that respects information-sharing constraints. The algorithm updates beamformers through MSE minimization under feasible information sets, with $d_k$ and $p_k$ updated in closed-form; in the ideal centralized case, beamformers reduce to the standard MMSE form. Numerical results show that the proposed two-timescale method significantly outperforms prior long-term approaches across centralized and distributed cell-free deployments, with centralized CF delivering the largest gains and distributed CF offering modest improvements over small cells. Overall, the approach provides a scalable, practical framework for joint power control and beamforming in next-generation massive MIMO systems, balancing performance with reduced signaling and computation.

Abstract

We reconsider the problem of joint power control and beamforming design to maximize the weighted sum rate in large and potentially cell-free massive MIMO networks. In contrast to the available short-term methods, where an iterative algorithm is run for every instantaneous channel realization, we derive an iterative algorithm that can be run only sporadically leveraging known channel statistics, with minor performance loss. In addition, our algorithm also applies to the design of non-trivial cooperative beamforming schemes subject to limited sharing of instantaneous channel state information. Furthermore, our algorithm generalizes and outperforms the competing long-term methods from the massive MIMO literature, which are restricted to long-term power control only or to long-term joint power control and large-scale fading decoding design.

Two-timescale weighted sum-rate maximization for large cellular and cell-free massive MIMO

TL;DR

The paper tackles scalable sum-rate optimization in large cellular and cell-free MIMO by introducing a two-timescale framework that optimizes transmit powers and beamformers based on slow-varying channel statistics. It derives an MMSE-SINR relation for the UatF ergodic-rate bound and reformulates the long-term WSR problem into an equivalent WMMSE problem, solvable via a block-coordinate ascent that respects information-sharing constraints. The algorithm updates beamformers through MSE minimization under feasible information sets, with and updated in closed-form; in the ideal centralized case, beamformers reduce to the standard MMSE form. Numerical results show that the proposed two-timescale method significantly outperforms prior long-term approaches across centralized and distributed cell-free deployments, with centralized CF delivering the largest gains and distributed CF offering modest improvements over small cells. Overall, the approach provides a scalable, practical framework for joint power control and beamforming in next-generation massive MIMO systems, balancing performance with reduced signaling and computation.

Abstract

We reconsider the problem of joint power control and beamforming design to maximize the weighted sum rate in large and potentially cell-free massive MIMO networks. In contrast to the available short-term methods, where an iterative algorithm is run for every instantaneous channel realization, we derive an iterative algorithm that can be run only sporadically leveraging known channel statistics, with minor performance loss. In addition, our algorithm also applies to the design of non-trivial cooperative beamforming schemes subject to limited sharing of instantaneous channel state information. Furthermore, our algorithm generalizes and outperforms the competing long-term methods from the massive MIMO literature, which are restricted to long-term power control only or to long-term joint power control and large-scale fading decoding design.
Paper Structure (12 sections, 3 theorems, 15 equations, 1 figure)

This paper contains 12 sections, 3 theorems, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Two-timescale formulation
  3. Contributions of this study
  4. System model and problem statement
  5. Ergodic achievable rates
  6. Weighted sum-rate maximization
  7. Information constraints
  8. Approximate solution
  9. SINR maximization via MSE minimization
  10. Equivalent problem formulation
  11. Block coordinate ascent algorithm
  12. Numerical results and conclusion

Key Result

Proposition 1

For all $k\in\mathcal{K}$ and $\bm{p}\in\mathbbmss{R}_{+}^K$, Furthermore, $\exists!\mathbbm{v}_k^\star \in \mathcal{V}_k$ attaining $\inf_{\mathbbm{v}_k\in \mathcal{V}_k}\mathsf{MSE}_k(\mathbbm{v}_k,\bm{p})$. Moreover, this $\mathbbm{v}_k^\star$ also attains $\sup_{\mathbbm{v}_k\in \mathcal{V}_k} \mathsf{SINR}_k(\mathbbm{v}_k,\bm{p})$.

Figures (1)

  • Figure 1: Comparison of the proposed long-term joint power control and beamforming design method against the competing techniques in demir2021foundationsemil2019lsfdshi2011wmmse for: (a) clustered centralized beamforming (case (i)); and (b) clustered distributed beamforming (case (ii)). Figure (c) compares the three information constraints corresponding to case (i), (ii), and (iii).

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Proposition 1
  • proof
  • Remark 3
  • Proposition 2
  • proof
  • Proposition 3
  • proof