Beyond the Use-and-then-Forget (UatF) Bound: Fixed Point Algorithms for Statistical Max-Min Power Control

2025-10-13

AI Summary

Statistical max-min power control in cellular and cell-free massive MIMO systems—based on the use-and-then-forget (UatF) achievable rate bound—suffers from fundamental limitations, including excessive conservativeness (e.g., vanishing worst-case rate bounds) and scale non-invariance. Method: This paper proposes a novel optimization framework that transcends the UatF paradigm by introducing a tighter, instantaneous-channel-state-information (CSI)-compatible information-theoretic rate bound, unifying treatment of both perfect and imperfect CSI at the decoder. A fixed-point-iteration-based joint optimization algorithm is developed to co-design statistical beamforming and power allocation. Contribution/Results: Theoretical analysis and simulations demonstrate substantial gains in minimum user rate across diverse channel conditions. Crucially, the method eliminates the zero-rate failure mode—even under non-adaptive beamforming—while ensuring theoretical rigor and practical robustness.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Developing fixed point algorithms for optimal statistical max-min power control
• Addressing limitations of UatF bound in cellular and cell-less massive MIMO
• Providing scale-invariant bounds with perfect or imperfect CSI at decoder

Innovation

• Fixed point algorithms for statistical max-min power control
• Framework using bounds with perfect or imperfect CSI
• Overcomes limitations of use-and-then-forget bound shortcomings