Slow adaptive energy-efficient resource allocation in OFDMA HetNets considering demand uncertainty

In this paper, we consider the downlink of a hybrid heterogeneous network with femtocells overlaid on a macrocell. Considering the rate requirements of femtocell users and interference thresholds for both co-tier and cross-tier users, we formulate the joint power and subchannel allocation problem to maximize the energy efficiency in orthogonal frequency-division multiple access-based open-access 2-tier heterogeneous networks. Due to user's mobility and fluctuating data rate demand, data rate requirements of users are subject to uncertainty, which is ignored in previous works. Toward this end, we study the demand uncertainty by an error model in which femtocells do not have knowledge about the exact distributions and instead assume that each user demand follows a probability distribution function, which belongs to a set of distributions with specific properties (ie, mean and variance). Since these statistics are obtained from historical data, we also take into account the moment uncertainty. Under this error model, the distributionally robust energy-efficient optimization problem is formulated, which is intractable. To make it tractable, we present the problem in an equivalent form by using the duality theory and then propose decomposition techniques to divide the problem into a fractional programming and a semi-infinite subproblem. Moreover, we provide optimization methods to solve each one. Our extensive experimental results highlight the effectiveness of our robust solution in uncertain environments, examine the cost of robustness, and demonstrate the convergence of our proposed algorithm. As shown by simulations, our approach provides robustness while incurring minor loss (less than 5%) in optimality.