Cellular, Cell-less, and Everything in Between: A Unified Framework for Utility Region Analysis in Wireless Networks

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 time sharing (or user grouping) cannot simultaneously improve the utilities of all users. Beyond geometrical insights, these sufficient conditions have two key implications. First, they identify a family of (weighted) sum-rate maximization problems that are inherently convex, thus paving the way for the development of efficient, provably optimal solvers for this family. Second, they provide justification for formulating sum-rate maximization problems directly in terms of achievable rates, rather than SINR levels. Our theoretical insights also motivate an alternative to the concept of favorable propagation in the massive MIMO literature -- one that explicitly accounts for self-interference and the beamforming strategy.