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Power Control in Wireless Cellular Networks provides a comprehensive survey of the models, algorithms, analysis, and methodologies in this vast and growing research area. It starts with a taxonomy of the wide range of power control problem formulations, and progresses from the basic formulation to more sophisticated ones. When transmit power is the only set of optimisation variables, algorithms for fixed SIR are presented first, before turning to their robust versions and joint SIR and power optimization. This is followed by opportunistic and non-cooperative power control. Then joint control of power together with beamforming pattern, base station assignment, spectrum allocation, and transmit schedule are surveyed one by one. Power Control in Wireless Cellular Networks highlights the use of mathematical language and tools in the study of power control, including optimisation theory, control theory, game theory, and linear algebra. Practical implementations of some of the algorithms in operational networks are discussed in the concluding chapter.