Siddharth Naik

Characterization of Convex and Concave Resource Allocation Problems in Interference Coupled Wireless Systems

This paper investigates the possibility of having convex or concave 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 natural assumptions, the exponential transformation is the unique transformation (up to a positive constant) for “convexification” of resource allocation problems for linear interference functions. Furthermore, it is shown that under certain intuitive assumptions, it is sufficient to check for the joint concavity (convexity) of sum of weighted functions of SINR (inverse SINR) with respect to s (p=es , where p is the power vector of the users), if we would like the resulting resource allocation problem to be concave (convex). This paper characterizes the largest class of utility functions and the largest class of interference functions (respectively), which allow a convex and concave 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 can be algorithmically tackled by convex optimization techniques.

Pareto boundary of utility sets for multiuser wireless systems

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.

Universal pricing mechanism for utility maximization for interference coupled systems

This paper investigates pricing mechanisms for utility maximization in interference coupled systems. An axiomatic framework of interference functions similar to the one proposed by Yates is utilized to capture interference coupling in wireless systems. Pricing mechanisms are used as a design tool to shift the solution outcome of a utility maximization problem to a desired point in the region. The paper explores the restrictions required on the class of utility functions and the restrictions on the class of interference functions such that a pricing mechanism can always guarantee the designer the ability of being able to shift the solution outcome to any desired point in the region, i.e. it is a universal pricing mechanism.

An improved successive interference cancellation multiuser detector for narrowband signals

This paper examines the possibility of reducing error propagation in the successive interference cancellation multiuser detector (SIC-MUD) for a narrowband system. A simple sequence estimation algorithm is employed, working on a symbol by symbol user basis, not affecting the operation of FEC decoding if present. Operating along the stages of the SIC-MUD scheme, this algorithm has a complexity that increases only linearly with the number of users and thus can be used for a larger number of users, as against the optimum joint detection-MUD (JD-MUD), whose complexity increases exponentially with the number of users. Investigation is carried out for both AWGN and Rayleigh fading channels. The obtained results show that the Improved SIC-MUD scheme reduces the error propagation considerably and, with its low complexity, can be a good alternative for the JD-MUD scheme.

Characterization of Non-Manipulable and Pareto Optimal Resource Allocation Strategies for Interference Coupled Wireless Systems

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.

Revisiting Proportional Fairness: Anonymity Among Users in Interference Coupled Wireless Systems

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.

Combinatorial Characterization of Interference Coupling in Wireless Systems

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 GGT is 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 GGT are 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 GGT are irreducible. We provide a simple yet comprehensive combinatorial characterization of interference coupled systems which abstracts away certain complexities of the physical layer.

Concave resource allocation problems for interference coupled wireless systems

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.

Mechanism design and implementation theoretic perspective of interference coupled wireless systems

This paper investigates the properties of social choice functions, that represent resource allocation strategies in interference coupled wireless systems. The resources can be physical layer parameters such as power vectors or antenna weights. The paper investigates the permissible social choice functions, which can be implemented by a mechanism in either Nash equilibria or dominant strategy — for utility functions representing interference coupled wireless systems. Strategy proofness and efficiency properties of social choice functions are used to capture the properties of non-manipulability and Pareto optimality of solution outcomes of resource allocation strategies, respectively. The analysis indicates certain inherent limitations when designing strategy proof and efficient resource allocation strategies. These restrictions are investigated in an analytical mechanism design framework of interference coupled wireless systems. Furthermore, the paper characterizes the Pareto optimal boundary points (efficient) of utility sets of interference coupled wireless system. An axiomatic framework of interference functions is used to capture interference coupling. The Pareto optimal boundary points for the cases of individual power constraints and a total power constraint are described based on the properties of the underlying interference functions.

Structure of solutions of resource allocation problems under general fairness constraints

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 its properties for all feasible utility regions.