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.

翻译：我们提出了一种统一框架，用于分析无线网络的效用区域，重点关注信干噪比（SINR）和可达速率区域。该框架为现代网络架构（包括超大规模MIMO和无蜂窝网络）的干扰模式提供了重要见解。一个核心贡献是，利用非线性映射的谱半径概念，对可行效用区域进行了简洁刻画。这种刻画为无线系统设计与分析提供了强大的数学工具。例如，它使我们能够用紧凑的符号泛化现有对弱帕累托边界的刻画，并推导出识别凸效用区域的可处理充分条件。这一性质尤为重要，因为在弱帕累托边界上，它保证了时间共享（或用户分组）无法同时提升所有用户的效用。除了几何洞察，这些充分条件还有两个关键意义：其一，它们识别出一类本质凸的（加权）和速率最大化问题，从而为开发此类问题的高效、可证明最优求解器铺平了道路；其二，它们为直接基于可达速率（而非SINR水平）构建和速率最大化问题提供了合理性依据。此外，我们的理论洞察还启发了一种替代大规模MIMO文献中“有利传播”概念的方法——该方法明确考虑了自干扰和波束赋形策略。