This dissertation aims at establishing optimal power allocation/control schemes to achieve maximal system utilities in a multi-carrier communication system, such as a digital subscriber line system and open spectrum wireless network. In such a system, users share tones to enhance the efficiency of spectrum usage due to its scarcity. However, this brings the system's intrinsic problem of inter-user interference, which has a crucial impact on communication quality. Therefore, the goal is to eliminate or diminish the impact of interference on the achievable data rate, which is a conventional measure of a user's communication quality. Based on the users' achievable data rates, system utility is defined. Hence, the goal comes to finding power allocation that can maximize the system utilities. According to different system requirements, we consider three system utilities: the weighted sum rate, "user capacity" and harmonic mean rate. For each utility function, we develop an efficient algorithm designed according to the features of the corresponding utility function.;Spectral Spectrum Balancing (SSB) aims to maximize the first goal (weighted sum rate). The algorithm partitions the N tones into three sections and efficiently determines the tones that lie in each section. Appropriate signalling structure is imposed on each section: The first section where the tones for which the crosstalk coefficients are small uses iterative water filling signalling method, the second section consists of tones with intermediate crosstalk coefficients and uses a delicate method to identify the user pairs that should share tones and Lagrangian method to allocate the power, and the third section where users suffer large crosstalk coefficients uses a dual FDMA algorithm.;While weighted sum rate is a popular measure of system utilities, we introduce "user capacity", which is a more practical goal of commercial service provider's. "User capacity" denotes the maximum number of users that can be supported by the system, provided that each user is guaranteed a data rate that lies within a prescribed range. However, allocating power directly to approach this capacity can be quite cumbersome because it involves solving an integer programming problem which is NP-hard. In order to circumvent this difficulty, an alternate approach is proposed that is based on exploiting the fairness and per-tone convexity of the harmonic mean-rate objective. Thus an iterative scheme is proposed to approximate the harmonic mean rate objective function based on its Taylor expansion.;We further exploit its convex lower bound, the dual form of which can be decomposed into several convex problems decoupled across tones. We show by broad simulation results that the algorithms we develop serve their purposes and outperform existing counterparts. We further consider the case when a malicious jammer is presents in the system, where the jammer's goal is to minimize the total sum of the rates communicated over the network. Each user, on the other hand, allocates its power across the N tones so as to maximize the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise. For this non-cooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and a jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium in this non-cooperative game as well as conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game.
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