A Stochastic Geometric Programming Approach for Power Allocation in Wireless Networks

In this paper, we consider the power allocation problem for 5 G wireless networks using massive multiple input multiple output technologies. Two non-linear optimization models are considered to maximize the worst user signal-to-interference noise ratio and the total capacity of the network subject to power constraints. In particular, we transform the first one into a geometric programming (GP) problem. Whereas the second one leads to a signomial programming formulation. The main contributions of the paper are first to propose novel formulations for power allocation in wireless networks while using stochastic, geometric, and signomial programming frameworks altogether. We derive stochastic formulations for each GP model to deal with the uncertainty of wireless channels. Secondly, since solving optimally the stochastic models represents a challenging task, we obtain tight bounds using approximation solution methods. In particular, the piece-wise linear programming and the sequential approximation methods allow us to obtain tight intervals for the objective function values of the stochastic models. Notice that these intervals contain the optimal solutions. In particular, we propose an approximated GP model that allows obtaining lower bounds for the signomial problem. This is achieved by using the arithmetic–geometric mean inequality. Finally, we compare the deterministic and stochastic models and prove the robustness of the stochastic models. Notice that we solve all the instances and obtain near-optimal solutions for most of them. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.