Distributed Optimization and Data Recovery for Wireless Networking
Riccardo Masiero · Padua Research Archive (University of Padova) · 2011
My research activity focused on the field of heterogeneous wireless networks and has been particularly inspired by the problem of sensing a city-wide environment through a large scale, partially distributed, mobile and low cost network (possibly composed of mobile phones or similar user’s equipment). In my PhD thesis I have been guided by the grand vision of a two tier architecture which integrates existing cellular systems with different types of distributed networks (these could be mixtures of ad hoc, sensor networks and soon). In fact, a fully distributed infrastructure alone would be inappropriate when the network is very large in size and highly populated (e.g., urban area networks). In such a case, the network organization itself would be energy draining and probably impractical. On the other hand, a cellular system alone does not have the flexibility and the instruments to get a fine grained view of all the data generated within such a network. This envisioned scenario, besides featuring a number of mobile phones, also consists of a mixture of embedded devices, which are expected to have on-board radio and sensing capabilities. Nowadays technology makes us more and more able to control the environment we are in through motion sensors, GPS, health care devices, microphones and video-cameras. Wireless Sensor Networks (WSNs), for instance, are infrastructures made of small devices (nodes) equipped with “intelligent sensors” able to sense their surroundings for, e.g., light, temperature, humidity and/or pollution. Therefore, mobile phones as well as other network elements, including base stations, routers and access points hosting diverse wireless and wired technologies, can cooperate to accomplish a common task like the detection of a fire or the monitoring of a physical phenomenon. Exploiting the fact that cell phones are becoming a communication hub in our daily life, we can foresee the integration of standard cellular systems with overlayed distributed networks such as WSNs. The ultimate goal of this is to “connect” everything has some communication capability, possibly providing self-configurability and self-adaptability of the network. We note that current cellular networks already implement some of these features: user positions, to a certain extent, can be tracked already and services can be provided based on contextual information. As a matter of fact, we are depicting a Delay Tolerant Network (DTN) scenario, where heterogeneous, sparse and/or mobile wireless networks communicate with each other, but where, due to the inherent nature of the infrastructure itself, no continuous connectivity can be assumed. The above grand vision entails quite a few challenges, and during my research activity I have been focusing on the following ones: 1) the design of reconstruction algorithms that from a subset of the data (i.e., from the collection of the sensor readings from a small fraction of nodes) are able to reconstruct with high accuracy the data monitored over the entire sensor field (these algorithms allow for scalability of the system as they decrease the number of data packets to collect for a given accuracy goal); 2) the design of cooperative networking protocols, where cooperation is utilized to reach a common goal such as the detection of a fire or/and to increase the network performance in terms of optimization of given performance metrics, e.g., energy consumption, delivery time, delivery probability. Concerning the first point, my study explores the capabilities of Compressive Sensing (CS), a technique that has been proved to be very effective for the compression and recovery of correlated signals, with the objective of designing and implementing a system for the efficient acquisition of large data sets in distributed (sensor) networks. The goal of this system is to reconstruct large signals through the collection of the smallest number of samples that will keep the reconstruction quality above a minimum target level. The steps of my research activity can be summarized as follows: 1.a) assess the applicability and potential benefits of CS in networking applications; 1.b) provide a sound theoretical justification of the effectiveness of CS recovery when coupled with Principal Component Analysis (PCA) along with a characterization of the optimality of the reconstruction process as a function of the statistics of the input signal; 1.c) design an algorithm for signal reconstruction based on CS and validating the proposed method through Matlab simulations as well as real signal traces. For the second point, my work has been centered around distributed optimization methods whose objective is that of optimizing network wide (global) performance metrics. In detail, in the investigated scenario nodes collaborate to minimize the sum of local objective functions, which in general depend on global variables such as the network protocol parameters or actions taken by all the nodes in the network. In the case where the local objective functions are convex, it is possible to adopt a framework that relies on local subgradient methods and consensus algorithms to average the information from each node, while granting convergence towards global optimal solutions. However, existing convergence results for this framework can only be applied in the case of synchronous operations of the nodes and mobility models without memory. My research addresses and solves these issues, and its fundamental steps were: 2.a) the extension of the convergence results to the optimal solution for a more general class of mobility models; 2.b) the application of distributed sub-gradient methods under asynchronous operations; 2.c) the presentation of a possible networking scenario to validate the analysis, showing the effectiveness of the considered distributed optimization technique. The outcomes of my research are useful tools for the optimization of practical network protocols and provide recommendations for the design of the integrated communication and sensing system that we have envisioned above.