We provide a combinatorial characterization of interference coupling in wireless systems, with the intent of obtaining a better insight into interference coordination and management. We introduce two bipartite graphs, namely the power graph and interference graph. We utilize these graphs and global dependency matrix containing only binary (0 and 1) entries to capture the effects of interference coupling in communication systems. We show that the irreducibility of the global dependency matrix G is related to the connectivity of the power graph and the irreducibility of the matrix GGTis related to the connectivity of the interference graph. We prove that for strictly positive and strictly log-convex interference functions, the irreducibility of the matrices G and GGTare necessary and sufficient conditions for the considered utility sets to be strictly convex. In this case there exists a unique optimizer for the problem of maximizing the product of utilities. We show that an interference balancing function is strictly log-convex, if and only if matrices G and GGTare irreducible. We provide a simple yet comprehensive combinatorial characterization of interference coupled systems which abstracts away certain complexities of the physical layer.

Pareto optimality is an important property in game theory and mechanism design, which can be utilized to design resource allocation strategies in wireless systems. We analyze the structure of the boundary points of certain utility sets based on interference functions. We particularly investigate the cases with no power constraints, with individual power constraints, and with a total power constraint. We display the dependency between Pareto optimality and interference coupling in wireless systems. An axiomatic framework of interference functions and a global dependency matrix is used to characterize interference coupling in wireless systems. The relationship between interference-balancing functions and Pareto optimality of the boundary points is elucidated. Among other results, it is shown that the boundary points of utility sets with individual power constraints and with strictly monotonic interference functions are Pareto-optimal if and only if the corresponding restricted global dependency matrix is irreducible. The obtained results provide certain insight when suitable algorithms can be designed for network utility maximization.

The paper characterizes the class of all concave resource allocation problems in interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows that there exists no transformation, which ensures concavity for all linear interference functions for all functions of SINR. The paper then characterizes the largest class of utility functions under a certain requirement, such that the corresponding class of utility functions functions, which are a function of SINR in the s-domain are concave. The paper shows that such a class of utility functions is a restricted class due to a requirement, which ensures concavity. Furthermore, the paper shows that the largest class of interference functions, which ensures concavity for resource allocation problems are the log-convex interference functions. These results differ from the convex case, where we are interested in minimizing utility functions of inverse SINR.

This paper investigates the possibility of having convex formulations of optimization problems for interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows, that under certain very natural assumptions -- the exponential mapping is the unique transformation (up to a constant), for ``convexification'' of resource allocation problems for linear interference functions. The paper shows that it is sufficient to check for the joint convexity of the sum of weighted utility functions of inverse signal-to-interference (plus noise)-ratio, if we would like the resulting resource allocation problem to be convex. The paper characterizes the largest class of interference functions, which allow a convex formulation of a problem for interference coupled wireless systems. It extends previous literature on log--convex interference functions and provides boundaries on the class of problems in wireless systems, which are jointly convex and hence can be efficiently solved at least from a numerical perspective.

This paper studies the properties of Nash equilibrium for noncooperative games in interference coupled wireless systems, where it serves as an incentive-compatible solution concept and an operating point. A broad class of noncooperative power control games played among the users of the wireless system is defined based on a general interference function framework, which models the interference coupling through a set of axioms. Both cases of coupling with and without self-interference are considered. The special properties of the underlying interference functions as well as relevant sufficient conditions are investigated to establish the existence and uniqueness of a Nash equilibrium solution. These properties play an important role in developing incentive-compatible distributed algorithms for a variety of wireless networks with interference coupling.

This paper investigates the properties of social choice functions that represent resource allocation strategies in interference coupled wireless systems. The allocated resources can be physical layer parameters such as power vectors or antenna weights. Strategy proofness and efficiency of social choice functions are used to capture the respective properties of resource allocation strategy outcomes being non-manipulable and Pareto optimal. In addition, this paper introduces and investigates the concepts of (strict) intuitive fairness and non-participation in interference coupled systems. The analysis indicates certain inherent limitations when designing strategy proof and efficient resource allocation strategies, if the intuitive fairness and non-participation are imposed. These restrictions are investigated in an analytical social choice function framework for interference coupled wireless systems. Among other results, it is shown that a strategy proof and efficient resource allocation strategy for interference coupled wireless systems cannot simultaneously satisfy continuity and the frequently encountered property of non-participation.

The paper revisits the problem of proportional fairness in interference coupled wireless systems. It models interference coupling in wireless systems based on an interference function framework through a set of axioms (introduced by Yates in 1995). It utilizes the collective choice function to represent resource allocation strategies and an axiomatic framework to emulate certain desirable properties of resource allocation strategies. We introduce the axiom of equal priority in the power domain (and in the interference domain) and motivate it as interference coordination fairness. We consider this as an anonymity among the users, from the perspective of a central controller, e.g. a base station or an operator. We show that the proportional fair resource allocation strategy is anonymous to the identity of the users at the signal processing layer. Such an anonymity is relevant to obtain interference coordination fairness in iterative resource allocation strategies frequently encountered in wireless systems.

Power management and energy-aware communications systems have become increasingly important in mobile computing as well as mobile communications. In future wireless communication systems, the energy efficiency of terminals and base stations has to be improved significantly. Therefore, we propose a new utility function, which is the difference of the capacity and a weighted power cost term. The generally used individual power constraint is removed. Next, the utility region for single-antenna and multi-antenna multiple access channels is characterized. We show using basic principles that the single-input single-output (SISO) multiple-access channel (MAC) utility region is convex and provide a closed form expression for its Pareto boundary. We need the Pareto boundary to compute efficient operating points. Furthermore, the extension to multiple antenna channels is indicated by an iterative algorithm for weighted sum utility maximization in multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) MAC. All discussed results are illustrated by numerical simulations.

In interference coupled wireless systems, where it is not possible to "orthogonalize" all the users in the system, we characterize the impact of interference coupling on the convexity of certain utility functions and problems. We introduce a general class of competitive user utility functions and natural competitive user utility functions. We further introduce the signal-to-interference based utility functions, which are based on physical layer parameters in wireless systems. We prove the conditions, which when satisfied result in a competitive user utility function being a signal-to-interference ratio based utility function. We further show that there exists no natural competitive user utility function, which is convex or concave. Furthermore, we show that a sum of weighted combination of natural competitive user utility functions is not convex or concave. Such functions are commonly encountered in wireless communication systems, e.g. rate or MMSE as a function of signal-to-interference ratio. We show that such rate maximization or MMSE minimization problems are not convex programs under our specified conditions.

We utilize axiomatic bargaining theory to depict certain implications of continuity properties of resource allocation strategies in wireless systems. Feasible utility sets are characterized as sub-level sets of interference functions. The collective choice function is used to represent resource allocation strategies. We use an axiomatic framework to emulate certain desirable properties of resource allocation strategies. We focus on the axiom of feasible set continuity, to emulate robustness of the resource allocation strategy to channel estimation and prediction errors. The connection between the axiom of feasible set continuity, lower semi-continuity and upper semi-continuity is elucidated. We investigate continuity properties, which allow a resource allocation strategy to be a strict monotone path collective choice function (MPCCF). We provide a result, which displays the practical importance of the axiom of feasible set continuity to develop bounds on the uncertainty region, resulting from channel estimation and prediction errors. We provide examples to show that the strict MPCCF is a useful tool to characterize solution outcomes of resource allocation strategies, e.g. egalitarian solution and dictatorial solution.

Collective choice functions and an axiomatic framework will be used to characterize the structure of solutions of resource allocation problems on feasible utility sets. Feasible utility sets will be characterized as level sets of general interference functions. General fairness constraints will be introduced and solution outcomes satisfying the properties of efficiency, robustness and fairness will be analyzed. A new type of sets, basic bargaining sets will be defined and if the properties of the solution outcome are known on these sets then we know it's properties for all feasible utility regions.

The paper investigates the performance of HIPERLAN/2 (H/2) with sub-carrier based adaptive modulation, with respect to average throughput. The results obtained are compared with the case where the same modulation is used across all the subcarriers as in the current H/2. We suggest a bit loading algorithm "simple rate adaptive algorithm" (SRA) based on the criteria of maximizing the throughput. Our work displays that this bit loading scheme improves the throughput compared to the existent H/2. The cost incurred is the complexity added by the adaptive modulation scheme. However, the total complexity of the system is decreased due to simplification in channel coding.