The focus of this thesis is on studying the tradeoff between efficiency and fairness in interference-limited cellular networks. We start by characterizing the optimal tradeoff between efficiency and fairness in cellular networks, where efficiency is measured by the sum-rate and fairness is measured by the Jain's fairness index. Finding the optimal Efficiency-Jain Tradeoff (EJT) corresponds to solving potentially difficult non-convex optimization problems. To alleviate this difficulty, we derive sufficient conditions, which are shown to be sharp and naturally satisfied in various radio
resource allocation problems. These conditions provide us with a means for identifying cases in which finding the optimal EJT can be reformulated as convex optimization problems. The new formulations are used to devise computationally-efficient resource schedulers that achieve the optimal EJT and surpass baseline schedulers in terms of EJT, median rate, and user satisfaction, without incurring additional complexity.
Finding the optimal EJT in the long-term average rates in interference-limited cellular networks is tackled by designing an efficient inter-cell interference coordination
(ICIC) scheme to manage interference by coordinating the allocation of radio resources across multiple cells. The goal of the ICIC scheme is to solve a multi-cell weighted sum-rate maximization optimization problem. By identifying a separable structure and a network-flow structure, we show that such optimization problem is amenable to powerful optimization methods, including the primal-decomposition method, the projected-subgradient method, and the network-flow optimization methods. Using these optimization methods, we propose a polynomial-time distributed ICIC scheme that finds a
near-optimum multi-cell resource allocations. In comparison with baseline ICIC schemes, the proposed scheme is shown to achieve higher gains in efficiency, Jain’s fairness index, cell-edge rate, and outage probability.