Distributionally Robust Optimization for Energy Efficiency in Heterogeneous Wireless Networks

Energy efficiency (EE) is vital for 5G networks to manage the increased traffic demand while minimizing operational costs and reducing environmental impact. Optimizing energy usage also supports scalability and helps meet regulatory sustainability goals as network infrastructure expands. In a practical commercial 5G network, a widely-used method to reduce energy consumption is to dynamically shut down underutilization cells and reduce the overlapping cell coverage based on real-time traffic patterns. However, the inherent uncertainty of traffic demands, coupled with the unknown distribution function, significantly complicates the optimization of cell shutdown strategies, rendering both conventional deterministic and stochastic optimization methods ineffective. To tackle these challenges, we propose a distributionally robust optimization framework for EE optimization that does not rely on distributional knowledge. First, we construct a data-driven uncertainty set to model traffic distribution and apply Lagrangian duality to transform the infinite-dimensional optimization problem into a more tractable finite-dimensional one. Then, we employ a Bayesian optimization algorithm to efficiently solve this reformulated problem, which involves a mixed space of high-dimensional combinatorial cell shutdown and continuous Lagrangian multipliers, even with constrained black-box evaluations. Simulations on real-world field data show that our proposed solution outperforms existing benchmarks, achieving energy efficiency improvements ranging from 0.7 % to 11.05 %.