In this thesis, I propose, develop, and analyze novel optimization techniques which solve resource allocation problems in partial frequency reuse (PFR) networks. In Long Term Evolution (LTE), multiple access in the downlink is established by Orthogonal Frequency Division Multiple Access (OFDMA). As a consequence, the cell edge users suffer from strong inter cell interference (ICI). This effect becomes even more severe, due to the low signal power which the cell edge users receive from the base station. Therefore, in this work, we have formulated algorithms that mitigate the ICI by optimizing the Radio Resource Allocation (RRA). An efficient use of radio resources (bandwidth and transmit power) is indispensable, since they are expensive and limited by spectrum licenses. For Inter Cell Interference (ICI) reduction, we define Partial Frequency Reuse (PFR) such that frequency reuse-1 is allocated to center-cell users and frequency reuse-3 is allocated to cell-edge users.

Near the cell edges, the Orthogonal Frequency Division Multiplexing (OFDM) sub-carriers are allocated such that the users within do not use the same frequencies simultaneously (frequency reuse-3). We note that some bandwidth remains unused if the users spatial distribution is inhomogeneous in the cell. In this case, such a PFR scheme does not lead to an efficient utilization of radio resources. To mitigate this apparent inefficiency, I propose a novel bandwidth re-allocation scheme by maximizing the cell capacity density (i.e. achievable data rate per bandwidth per unit area). The proposed scheme re-allocates bandwidth from the cell edge to the center of the cell. The cell capacity density is a metric that represents the expected capacity per unit area for a randomly positioned user (uniformly distributed) in the cell. The network operators are interested in the achievable transmission rate per user. Therefore, we formulate the optimization problem as a maximization of the sum-rate under power and bandwidth constraints. We proved that this sum-rate maximization problem becomes convex for a fixed PFR bandwidth allocation scheme under a suitable additional power equality constraint. Using the Lagrangian, the analytical solutions are derived for the optimal power allocation, in a manner which is closely related to water-filling. Furthermore, we formulated two specific problems for the joint optimization of power and bandwidth allocation as convex geometric programs, i.e. the maximization of the minimum rate and the sum-power minimization, respectively.

In PFR, a fundamental issue is to classify the users to the cell edge and center-cell regions. Two user classification schemes are investigated in this thesis in detail: The first classification scheme is based on the distance between the user and its serving base station.

The second classification scheme is based on the user's Large-Scale Path-Loss Attenuation (LSPLA). Compared to the first classification scheme, the LSPLA scheme is proved to enhance the achievable user-rates.

We have shown that the LSPLA classification scheme is successfully applicable to all discussed problems. Finally, we conclude that the LSPLA scheme allows to formulate spectrally efficient RRA algorithms in a form which can be implemented with fairly low numerical complexity.