<p> The transmit-power control (TPC) problem is a fundamental problem in cognitive radio design, which aims at determining transmit-power levels for secondary users across available subcarriers. This thesis studies both the theory and the algorithms for the TPC problem for cognitive radio networks, and specifically examines the problem under two different limitations: an interference-power limitation and a low-power limitation. First, the TPC problems are cast into game-theoretic models and the sufficient and necessary optimality conditions ·for solutions are derived. Sufficient conditions for the existence, uniqueness and stability of a solution are presented as well. Second, the fast iterative water-filling controller (FIWFC) for the TPC problem is developed, which is linearly convergent under certain conditions. The computational complexity is lower than for the iterative water-filling controller (IWFC) for digital subscriber lines. In order to evaluate the FIWFC, simulations are carried out for both stationary and nonstationary radio environments. In addition, the performance of the FIWFC is evaluated, given the presence of measurement errors. The results of these various simulations show that the FIWFC outperforms IWFC in terms of convergence speed in all cases. </p> / Thesis / Doctor of Philosophy (PhD)