During the last decade, stochastic geometry has been widely employed for system-level analysis in cellular networks. The resulting analytical frameworks are, however, not always amenable for system-level optimization. This is due to three main reasons: (i) the performance metric of interest may not be formulated in closed-form; (ii) under some analytically tractable modeling assumptions, important system parameters may not explicitly appear in the analytical frameworks; and (iii) the optimization problem may not possess any structural properties, e.g., convexity, that facilitate the development of numerical algorithms for optimizing multiple (continuous- and discrete-valued) parameters at an affordable computational complexity and with performance-guarantee, e.g., the convergence to the global optimum is provable. In this letter, by leveraging a recently proposed definition of coverage probability, we formulate mixed-integer non-linear system-level resource allocation problems in Poisson cellular networks and prove that their global optimum can be efficiently calculated by applying the generalized Benders decomposition. Numerical results are illustrated in order to compare the proposed approach against brute-force and greedy-like optimization algorithms.

中文翻译：

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Poisson 蜂窝网络中的系统级优化：一种基于广义 Benders 分解的方法

在过去的十年中，随机几何已被广泛用于蜂窝网络中的系统级分析。然而，由此产生的分析框架并不总是适合系统级优化。这是由于三个主要原因：(i) 感兴趣的性能指标可能无法以封闭形式制定；(ii) 在一些易于分析的建模假设下，重要的系统参数可能不会明确出现在分析框架中；(iii) 优化问题可能不具有任何结构特性，例如凸性，这有助于开发以负担得起的计算复杂性和性能保证来优化多个（连续和离散值）参数的数值算法，例如，收敛到全局最优是可证明的。在这封信中，通过利用最近提出的覆盖概率定义，我们制定了泊松蜂窝网络中的混合整数非线性系统级资源分配问题，并证明可以通过应用广义 Benders 分解有效地计算它们的全局最优值。说明了数值结果，以便将所提出的方法与蛮力和类似贪婪的优化算法进行比较。