Robust optimisation of power control for femtocell networks

In this study, the minimum transmission power of each femtocell user in a two-tier network, in which femtocells and macrocell use the spectrum simultaneously, is investigated. That is, the authors are aiming at finding the power that characterises robustness and energy-efficient when taking the uncertain gains into consideration. To solve the optimisation problem with uncertainty, an opportunistic power control strategy for the femtocells is introduced. Since the channel gain from a femtocell user to the femtocell base station is changeable with the environment, it is difficult to track channel gains instantaneously. For the reason that the mean channel gains, from the femtocell users to the femtocell base stations are usually achievable, the information of mean and probability density function are used to model the optimisation problem. Moreover, outage probability for each femtocell user's throughput is originated instead of considering the total throughput of the system, because high total throughput may not ensure that of each femtocell user. The signal-to-interference-plus-noise ratio of the macrocell is ensured by setting appreciate interference temperature. A distributed algorithm is designed to calculate the powers of femtocell users. Numerical results show the effectiveness of the proposed outage probabilistic method and the distributed algorithm.