The role of asymptotic functions in network optimization and feasibility studies

Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important tool in science and engineering is the notion of asymptotic function, which is often hidden in many influential studies on nonlinear analysis and related fields. Therefore, we can also expect that asymptotic functions are deeply connected to many results in the wireless domain, even though they are rarely mentioned in the wireless literature. In this study, we show connections of this type. By doing so, we explain many properties of centralized and distributed solutions to wireless resource allocation problems within a unified framework, and we also generalize and unify existing approaches to feasibility analysis of network designs. In particular, we show sufficient and necessary conditions for mappings widely used in wireless communication problems (more precisely, the class of standard interference mappings) to have a fixed point. Furthermore, we derive fundamental bounds on the utility and the energy efficiency that can be achieved by solving a large family of max-min utility optimization problems in wireless networks.Comment: GlobalSIP 2017 (to appear

Low complexity iterative algorithms for power estimation in ultra-dense load coupled networks

This study investigates the interplay between load and power in load coupled interference networks. In more detail, the first objective of this study is to derive a positive concave mapping having as its fixed point the power allocation inducing a desired network load. Knowledge of this mapping is important for many theoretical and practical reasons. First, it opens up the possibility of applying many existing algorithms to compute the power inducing a desired load, which is an estimation problem typically used to obtain energy efficient network configurations. With the results in this study, systems designers can now select an algorithm based on practical considerations such as the computational complexity, memory requirements, and convergence speed. In particular, we show that algorithms based on simple fixed point iterations already have many advantages over the previously only known method for the power estimation problem. Second, knowledge of specific properties of the mapping, such as concavity, enables us to use standard tools in convex analysis to analyze the network, and it may also give rise to novel optimization tools for self-organizing networks. The second main objective of this study is the development of a truly distributed algorithm for power estimation in real networks. This algorithm uses only information that is readily available at base stations, and it does not require any additional signaling overhead. These two characteristics make the proposed algorithm especially useful in ultra-dense wireless networks, one of the main visions for 5G networks