Power Allocation Robust to Time-Varying Wireless Channels in Femtocell Networks

We investigate the power-allocation problem in a two-tier femtocell network including a macrocell and multiple femtocells. Due to shadowing and fading effects, at each cell (macrocell or femtocell), the power levels of desired signal and interference signals vary with time. Under this circumstance, one method to achieve transmission quality in the cells is to first get channel state information (CSI) of all desired links and interference links and then perform power allocation. This method has very large communication and computation overhead. In this paper, we focus on power allocation in which the transmit power levels of the users in the cells do not need to change when the wireless channels fluctuate. We formulate a power-allocation problem subject to bounded outage probability in any cell (macrocell or femtocell). The formulated problem has probabilistic constraints. It is hard to have closed-form expressions of the probabilistic constraints. To solve this, we propose novel transformations of the constraints, based on which we obtain constraints in the format of worst-case value-at-risk. Such constraints can be converted to convex constraints, and thus, the research problem is transformed to a convex problem. For the convex problem, we provide an iterative algorithm that converges quickly. We also investigate the case when the channel gain distributions are unknown. Our proposed schemes have the merits of very small communication and computation overhead and are particularly useful in fast-fading environments.