Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods

Several practical multi-user multi-carrier communication systems are characterized by a multi-carrier interference channel system model where the interference is treated as noise. For these systems, spectrum optimization is a promising means to mitigate interference. This however corresponds to a challenging nonconvex optimization problem. Existing iterative convex approximation (ICA) methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. However they do not take this typical iterative implementation into account in their design. This paper proposes a novel class of iterative approximation methods that focuses explicitly on the per-user iterative implementation, which allows to relax the problem significantly, dropping joint convexity and even convexity requirements for the approximations. A systematic design framework is proposed to construct instances of this novel class, where several new iterative approximation methods are developed with improved per-user convex and nonconvex approximations that are both tighter and simpler to solve (in closed-form). As a result, these novel methods display a much faster convergence speed and require a significantly lower computational cost. Furthermore, a majority of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality compared to existing ICA methods.Comment: 33 pages, 7 figures. This work has been submitted for possible publicatio

Game theoretic models for resource sharing in wireless networks

Wireless communications have been recently characterized by rapid proliferation of wireless networks, impressive growth of standard and technologies, evolution of the end-user terminals, and increasing demand in the wireless spectrum. New, more flexible schemes for the management of the available resources, from both the user and the network side, are necessary in order to improve the efficiency in the usage of the available resources.This work aims at shedding light on the performance modeling of radio resource sharing/allocation situations. Since, in general, the quality of service perceived by a system (e.g., user, network) strictly depends on the behavior of the other entities, and the involved interactions are mainly competitive, this work introduces a framework based on non–cooperative game theoretic tools. Furthermore, non–cooperative game theory is suitable in distributed networks, where control and management are inherently decentralized.First, we consider the case in which many users have to make decisions on which wireless access point to connect to. In this scenario, the quality perceived by the users mainly depends on the number of other users choosing the very same accessing opportunity. In this context, we also consider two–stage games where network make decisions on how to use the available resources, and users react to this selecting the network that maximizes their satisfaction. Then, we refer to the problem of spectrum sharing, where users directly compete for portions of the available spectrum. Finally, we provide a more complex model where the users utility function is based on the Shannon rate. The aim of this second part is to provide a better representation of the satisfaction perceived by the users, i.e., in terms of achievable throughput. Due to the complexity of the game model, we first provide a complete analytical analysis of the two–user case. Then, we extend the model to the N–user case. We mainly analyze this game through simulations. Finally, inspired by the results obtained numerically, we introduce stochastic geometry in the analysis of spectrum games in order to predict the performance of the game in large networks.Ph.D., Electrical Engineering -- Drexel University, 201

Optimal Spectrum Management in Multiuser Interference Channels

In this paper, we investigate the optimal spectrum management problem in multiuser frequency selective interference channels. First, a simple pairwise condition for FDMA to be optimal is discovered: for any two among all the users, as long as the normalized cross couplings between them two are both larger than or equal to 1/2, orthogonalization between these two users is optimal for every existing user. Therefore, this single condition applies to achieving all Pareto optimal points of the rate region. Furthermore, not only is this condition sufficient, but in symmetric channels, it is also necessary for FDMA to be always optimal. When the normalized cross couplings are less than 1/2, the optimal spectrum management strategy can be a mixture of frequency sharing and FDMA, depending on users’ power constraints. We first explicitly solve the sum-rate maximization problem in two user symmetric flat channels by solving a closed form equation, providing the optimal spectrum management with a clear intuition as the optimal combination of flat FDMA and flat frequency sharing. Next, we show that this result leads to a primal domain convex optimization formulation for generalizations to frequency selective channels. Finally, we show that all the general optimization problems with n>=2 users and an arbitrary weighted sum-rate objective function in non-symmetric frequency selective channels can be solved by primal domain convex optimization with the same methodology