System-level optimization in poisson cellular networks: An approach based on the generalized benders decomposition

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.