Decentralized Network Optimization in Wireless Networks

Abstract: Distributed estimation and distributed resource allocation are two important services in future cyber-physical wireless networks. The former aims to estimate, or track, physical variables of a phenomenon monitored by a wireless network, whereas the latter aims to optimally assign the limited communication resources to the nodes in a wireless network. These two have one common background theory: optimization problems that are in general nonlinear, non-convex, mixed integer, and need to be solved by distributed algorithms over networks. In this thesis, we report the work from three article submissions, where these distributed optimization problems are considered. The first class of distributed optimization problems that we consider in this thesis is studied in the context of distributed estimation. Here, the design methods and fundamental performance analysis of an adaptive peer-to-peer estimator are established for networks exhibiting message losses. Based on a signal state model, estimates are locally computed at each node of the network by adaptively filtering neighboring nodes’ estimates and measurements communicated over lossy channels. The computation is based on a distributed optimization approach that guarantees the stability of the estimator while minimizing the estimation error variance. The fundamental performance limitations of the estimator are established based on the variance of the estimation error in relation to the message loss process. A non-convex distributed optimization problem with mixed integer and real variables is considered for a resource allocation scenario in a cognitive radio network. In hierarchical cognitive radio networks, unlicensed secondary users can maximize the achievable rates by cooperating with licensed primary users. A maximization of the secondary users achievable rates is proposed by controlling the transmit radio power, the secondary users relaying selection, and power splitting of the relays while guaranteeing primary users performance. Centralized and distributed methods are developed to find the solution to such a challenging mixed integer and non-convex problem. The methods provide a centralized and a distributed algorithm for finding the optimal power allocations for secondary users, and a sub-optimal centralized algorithm and a greedy distributed algorithm for finding the associations between primary and secondary users. Lastly, a distributed binary optimization problem is considered for a millimeterWave wireless access network. At the access level the typical rapidly fading behavior of the millimeterWave channel imposes the careful design of node association to access points, or relaying to other nodes. This challenge is addressed by a distributed approach that optimally solves the joint node association and relaying problem. The problem is posed as a novel multi-assignment optimization problem, for which an original solution method is established by a series of transformations that lead to a tractable minimum cost flow problem. The method allows to design distributed auction solution algorithms where the nodes and relays act asynchronously to achieve optimal node-relay-access point association. It is shown that computational complexity of the new algorithms is much better than centralized general-purpose solvers for multi-assignment optimization, and the algorithms converge to a solution that maximizes the total network throughput within a desired bound. It is concluded that, to the best of our knowledge, there is no general distributed approach for solving the non-convex optimization problems with mixed integer and real decision variables that arises in the scenarios studied in this thesis. The long run goal is to establish a general theoretical framework, which will be pursued for the doctoral dissertation.