Optimal power control in Rayleigh-fading heterogeneous networks

Heterogeneous wireless networks employ varying degrees of network coverage using power control in a multi-tier configuration, where low-power femtocells are used to enhance performance, e.g., optimize outage probability. We study the worst outage probability problem under Rayleigh fading. 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 condition. We propose a dynamic algorithm that adapts the outage probability specification in a heterogeneous network to minimize the total energy consumption and simultaneously guarantees all the femtocell users a min-max fairness in terms of the worst outage probability.