Robust uplink power allocation for two-tier heterogeneous networks

Traditional power allocation algorithms in heterogeneous networks (HeNets) are given under the assumption of perfect channel state information (CSI). However, the perfect CSI is difficult to obtain due to the efficiency of channel fading and feedback delays. In this paper, a robust power allocation algorithm is proposed to minimize the total transmit power of femtocell users under the constraints of macrocell interference power, maximum transmit power and signal-to-interference-noise-ratio (SINR). Though the original optimization problem becomes a semi-infinite programming problem (SIP) when using ellipsoidal uncertainty model. The SIP can be converted into a deterministic convex optimization problem by the worst-case approach, which can be easily solved in sub-gradient method. Simulation results show our proposal has good robustness and energy efficiency.