Optimal Power Control in Rayleigh-Fading Heterogeneous Wireless Networks

Heterogeneous wireless networks provide varying degrees of network coverage in a multi-tier configuration in which low-powered small cells are used to enhance performance. Due to the ad-hoc deployment of small cells, optimal resource allocation is important to provision fairness and enhance energy efficiency. We first study the worst outage probability problem in Rayleigh-fading channels, and solve this nonconvex stochastic program using mathematical tools from nonlinear Perron-Frobenius theory. As a by-product, we solve an open problem of convergence for a previously proposed algorithm in the interference-limited case. We then address a total power minimization problem with outage specification constraints and its feasibility issue. We propose a dynamic algorithm that adapts the outage probability specification in a heterogeneous wireless network to minimize the total energy consumption and to simultaneously provide fairness guarantees in terms of the worst outage probability. Finally, we provide numerical evaluation on the performance of the algorithms and the effectiveness of deploying closed-access small cells in heterogeneous wireless networks to address the tradeoff between energy saving and feasibility of users satisfying their outage probability specifications.