Which Distributed Averaging Algorithm Should I Choose for my Sensor Network?

Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of sensor networks measurements by iterating local averages until a desired level of convergence. Confronted with the diversity of these algorithms, the engineer may be puzzled in his choice for one of them. As an answer to his/her need, we develop precise mathematical metrics, easy to use in practice, to characterize the convergence speed and the cost (time, message passing, energy...) of each of the algorithms. In contrast to other works focusing on time-invariant scenarios, we evaluate these metrics for ergodic time- varying networks. Our study is based on Oseledec’s theorem, which gives an almost-sure description of the convergence speed of the algorithms of interest. We further provide upper bounds on the convergence speed. Finally, we use these tools to make some experimental observations illustrating the behavior of the convergence speed with respect to network topology and reliability in both average consensus and gossip algorithms.

Interference management in impulse-radio ultra-wide band networks

Ruben Merz

We consider networks of impulse-radio ultra-wide band (IR-UWB) devices. We are interested in the architecture, design, and performance evaluation of these networks in a low data-rate, self-organized, and multi-hop setting. IR-UWB is a potential physical layer for sensor networks and emerging pervasive wireless networks. These networks are likely to have no particular infrastructure, might have nodes embedded in everyday life objects and have a size ranging from a few dozen nodes to large-scale networks composed of hundreds of nodes. Their average data-rate is low, on the order of a few megabits per second. IR-UWB physical layers are attractive for these networks because they potentially combine low-power consumption, robustness to multipath fading and to interference, and location/ranging capability. The features of an IR-UWB physical layer greatly differ from the features of the narrow-band physical layers used in existing wireless networks. First, the bandwidth of an IR-UWB physical layer is at least 500 MHz, which is easily two orders of magnitude larger than the bandwidth used by a typical narrow-band physical layer. Second, this large bandwidth implies stringent radio spectrum regulations because UWB systems might occupy a portion of the spectrum that is already in use. Consequently, UWB systems exhibit extremely low power spectral densities. Finally IR-UWB physical layers offer multi-channel capabilities for multiple and concurrent access to the physical layer. Hence, the architecture and design of IR-UWB networks are likely to differ significantly from narrow-band wireless networks. For the network to operate efficiently, it must be designed and implemented to take into account the features of IR-UWB and to take advantage of them. In this thesis, we focus on both the medium access control (MAC) layer and the physical layer. Our main objectives are to understand and determine (1) the architecture and design principles of IR-UWB networks, and (2) how to implement them in practical schemes. In the first part of this thesis, we explore the design space of IR-UWB networks and analyze the fundamental design choices. We show that interference from concurrent transmissions should not be prevented as in protocols that use mutual exclusion (for instance, IEEE 802.11). Instead, interference must be managed with rate adaptation, and an interference mitigation scheme should be used at the physical layer. Power control is useless. Based on these findings, we develop a practical PHY-aware MAC protocol that takes into account the specific nature of IR-UWB and that is able to adapt its rate to interference. We evaluate the performance obtained with this design: It clearly outperforms traditional designs that, instead, use mutual exclusion or power control. One crucial aspect of IR-UWB networks is packet detection and timing acquisition. In this context, a network design choice is whether to use a common or private acquisition preamble for timing acquisition. Therefore, we evaluate how this network design issue affects the network throughput. Our analysis shows that a private acquisition preamble yields a tremendous increase in throughput, compared with a common acquisition preamble. In addition, simulations on multi-hop topologies with TCP flows demonstrate that a network using private acquisition preambles has a stable throughput. On the contrary, using a common acquisition preamble exhibits an effect similar to exposed terminal issues in 802.11 networks: the throughput is severely degraded and flow starvation might occur. In the second part of this thesis, we are interested in IEEE 802.15.4a, a standard for low data-rate, low complexity networks that employs an IR-UWB physical layer. Due to its low complexity, energy detection is appealing for the implementation of practical receivers. But it is less robust to multi-user interference (MUI) than a coherent receiver. Hence, we evaluate the performance of an IEEE 802.15.4a physical layer with an energy detection receiver to find out whether a satisfactory performance is still obtained. Our results show that MUI severely degrades the performance in this case. The energy detection receiver significantly diminishes one of the most appealing benefits of UWB, specifically its robustness to MUI and thus the possibility of allowing for parallel transmissions. This performance analysis leads to the development of an IR-UWB receiver architecture, based on energy detection, that is robust to MUI and adapted to the peculiarities of IEEE 802.15.4a. This architecture greatly improves the performance and entails only a moderate increase in complexity. Finally, we present the architecture of an IR-UWB physical layer implementation in ns-2, a well-known network simulator. This architecture is generic and allows for the simulation of several multiple-access physical layers. In addition, it comprises a model of packet detection and timing acquisition. Network simulators also need to have efficient algorithms to accurately compute bit or packet error rates. Hence, we present a fast algorithm to compute the bit error rate of an IR-UWB physical layer in a network setting with MUI. It is based on a novel combination of large deviation theory and importance sampling.

EPFL2008

Gossip along the way: order-optimal consensus through randomized path averaging

Florence Bénézit, Patrick Thiran, Martin Vetterli

Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. However for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges very slowly. A recently proposed algorithm called geographic gossip improves gossip efficiency by a

\sqrt{n / \log n}

factor for random geometric graphs, by exploiting geographic information of node locations. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional

\sqrt{n / \log n}

factor and is order optimal for grids and random geometric graphs. Our analysis provides some general techniques and can be used to provide bounds on the performance of randomized message passing algorithms operating over various graph topologies.

2007

Distributed average consensus for wireless sensor networks

Florence Bénézit

Wireless sensor networks have emerged a few years ago, enabling large scale sensing at low cost. There are many interesting problems related to this new sensing tool: designing robust and small hardware, defining adapted routing protocols, minimizing the energy consumption of each component, synchronizing the sensors, etc. In this thesis, we focus on the processing of the sensed data within the network itself. We study a specific network signal processing problem, called distributed average consensus. In this problem, the sensors, which are connected in a wireless network, need to know the average of all the measurements in the network. Instead of gathering the data at a central node, which would compute the average and broadcast it to the network, average consensus algorithms offer a distributed solution to the averaging problem. By local message passing and iterative local computations only, nodes can learn the average of the measurements. More precisely, in average consensus algorithms, nodes iteratively compute local weighted averages that conserve the global average of the estimates in the network. The estimates at each node contract until they all converge to the average. Many distributed average consensus algorithms were designed and the literature is vast. This thesis starts by classifying the existing algorithms. Then it describes a small number of useful techniques, which can handle the analysis of all the algorithms. Preexisting algorithms as well as algorithms that we designed are revisited with these unifying and simple techniques. In addition, the performance of the algorithms depends on the topology of the network, and a variety of networks are explored: simple graphs as circles or trees, lattices, random geometric graphs, complete graphs etc. Finally, an extension of average consensus to voting consensus is derived. In particular, we show that with two bits of memory at each node, a network can reach consensus in finite time on majority, when the initial measurements are binary. Distributed algorithms to compute majority with finite memory for ternary and quaternary signals are also given.

EPFL2009