Efficient algorithms are studied in this thesis to solve the resource allocation problems for the Gaussian Multiple Access Channel (MAC) and the Gaussian Interference Channel. There are two fundamental problems in resource allocation: the first one is the weighted sum-rate maximization problem, characterizing the capacity region of a Gaussian MAC or the achievable region of a Gaussian interference channel; the other is its dual problem, the weighted sum power minimization problem, characterizing the power profile achieving given rate tuple.; There are three main results in this thesis. The first result shows that the geometrical property of the power spectral densities that achieve ANY boundary point of an OFDM MAC can be viewed as multi-user water-filling, thus extending the single-user water-filling to the multi-user case. This also provides a sufficient channel condition with geometrical intuition that successive interference cancellation can achieve any boundary point of an OFDM MAC. Thus only single user signal processing/coding is needed. A real communication channels in an OFDM MAC should satisfy this condition. Further, it is shown that for these channels FDMA is the unique solution that achieves the sum rate. The second result considers the structure of the KKT conditions of these two resource allocation problems. This reveals that a unified and efficient central algorithm can be applied to both problems, with only basic arithmetic, thus eliminating expensive software/hardware requirements for solving these problems. For the third result, the challenging multi-user discrete bit-loading problem in Gaussian interference channels is solved with a very simple structure and very low complexity. The algorithm converges very fast, and can easily be extended to OFDM MAC and OFDM broadcast channels.
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