Cellular, Cell-less, and Everything in Between: A Unified Framework for Utility Region Analysis in Wireless Networks
Renato Luis Garrido Cavalcante, Tomasz Piotrowski, Slawomir Stanczak

TL;DR
This paper presents a unified mathematical framework for analyzing utility regions in wireless networks, offering new insights into interference, convexity, and optimization of network performance.
Contribution
It introduces a spectral radius-based characterization of feasible utility regions, enabling tractable analysis and optimization in modern wireless architectures.
Findings
Spectral radius characterization simplifies utility region analysis.
Identifies convex sum-rate maximization problems for efficient solutions.
Provides a new perspective on interference and beamforming in massive MIMO.
Abstract
We introduce a unified framework for analyzing utility regions of wireless networks, with a focus on signal-to-interference-plus-noise-ratio (SINR) and achievable rate regions. The framework provides valuable insights into interference patterns of modern network architectures, including extremely large MIMO and cell-less networks. A central contribution is a simple characterization of feasible utility regions using the concept of spectral radius of nonlinear mappings. This characterization provides a powerful mathematical tool for wireless system design and analysis. For example, it allows us to generalize existing characterizations of the weak Pareto boundary using compact notation. It also allows us to derive tractable sufficient conditions for the identification of convex utility regions. This property is particularly important because, on the weak Pareto boundary, it guarantees that…
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