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The rapid pace of innovations in information and communication technology (ICT) industry over the past decade has greatly improved people’s mobile communication experience. This, in turn, has escalated exponential growth in the number of connected mobile devices and data traffic volume in wireless networks. Researchers and network service providers have faced many challenges in providing seamless, ubiquitous, reliable, and high-speed data service to mobile users. Mathematical optimization, as a powerful tool, plays an important role in addressing such challenging issues. This dissertation addresses several radio resource allocation problems in 4G and 5G mobile communication systems, in order to improve network performance in terms of throughput, energy, or fairness. Mathematical optimization is applied as the main approach to analyze and solve the problems. Theoretical analysis and algorithmic solutions are derived. Numerical results are obtained to validate our theoretical findings and demonstrate the algorithms’ ability of attaining optimal or near-optimal solutions. Five research papers are included in the dissertation. In Paper I, we study a set of optimization problems of consecutive-channel allocation in single carrier-frequency division multiple access (SCFDMA) systems. We provide a unified algorithmic framework to optimize the channel allocation and improve system performance. The next three papers are devoted to studying energy-saving problems in orthogonal frequency division multiple access (OFDMA) systems. In Paper II, we investigate a problem of jointly minimizing energy consumption at both transmitter and receiver sides. An energy-efficient scheduling algorithm is developed to provide optimality bounds and near-optimal solutions. Next in Paper III, we derive fundamental properties for energy minimization in loadcoupled OFDMA networks. Our analytical results suggest that the maximal use of time-frequency resources can lead to the lowest network energy consumption. An iterative power adjustment algorithm is developed to obtain the optimal power solution with guaranteed convergence. In Paper IV, we study an energy minimization problem from the perspective of scheduling activation and deactivation of base station transmissions. We provide mathematical formulations and theoretical insights. For problem solution, a column generation approach, as well as a bounding scheme are developed. Finally, towards to 5G communication systems, joint power and channel allocation in non-orthogonal multiple access (NOMA) is investigated in Paper V in which an algorithmic solution is proposed to improve system throughput and fairness

From Orthogonal to Non-orthogonal Multiple Access: Energy- and Spectrum-Efficient Resource Allocation