Robust power control with probability constraint for co-channel two-tier femtocell networks

In this paper, considering the uncertain channel gains of the interference links, we investigate a robust power control algorithm and a robust power allocation in two-tier femtocell networks is proposed. We are aiming at finding the minimum power of femtocell users to save the energy and suppress the interference. Since the channel gains are changeable with environment, tracking the instantaneous channel gains may be difficult in practice. Here we consider the mean channel gains are available. In order to solve the problem with uncertainty, a robust optimization problem is researched. Considering the Signal-of-Interference-Plus-Noise ratio of macrocell user and femtocell users as probabilistic constraint conditions, we turn the uncertain factors into the deterministic factors. Since the deterministic form of the outage probability constraint is not convex of power, then a novel but simple method is utilized to solve the power allocation. An admission algorithm is proposed to remove the femtocell users which do not satisfy the requirement. Numerical results illustrate the effectiveness of robust power control algorithm and the admission control algorithm.