Adaptive diffusion schemes for heterogeneous networks

In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or step size. Although such heterogeneous networks have been considered from the first works on diffusion networks, obtaining practical and robust schemes to adaptively adjust the combiners in different scenarios is still an open problem. In this paper, we study a diffusion strategy specially designed and suited to heterogeneous networks. Our approach is based on two key ingredients: 1) the adaptation and combination phases are completely decoupled, so that network nodes keep purely local estimations at all times and 2) combiners are adapted to minimize estimates of the network mean-square-error. Our scheme is compared with the standard adapt-Then-combine scheme and theoretically analyzed using energy conservation arguments. Several experiments involving networks with heterogeneous nodes show that the proposed decoupled adapt-Then-combine approach with adaptive combiners outperforms other state-of-The-Art techniques, becoming a competitive approach in these scenarios

Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load

We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable performance with the full information exchange configurations, even if the diffused information is compressed into a scalar or a single bit. To this end, we provide a complete performance analysis for the compressive diffusion strategies. We analyze the transient, steady-state and tracking performance of the configurations in which the diffused data is compressed into a scalar or a single-bit. We propose a new adaptive combination method improving the convergence performance of the compressive diffusion strategies further. In the new method, we introduce one more freedom-of-dimension in the combination matrix and adapt it by using the conventional mixture approach in order to enhance the convergence performance for any possible combination rule used for the full diffusion configuration. We demonstrate that our theoretical analysis closely follow the ensemble averaged results in our simulations. We provide numerical examples showing the improved convergence performance with the new adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin

Distributed Diffusion-Based LMS for Node-Specific Adaptive Parameter Estimation

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of global interest to the whole network. To address the different node-specific parameter estimation problems, this novel algorithm relies on a diffusion-based implementation of different Least Mean Squares (LMS) algorithms, each associated with the estimation of a specific set of local, common or global parameters. Coupled with the estimation of the different sets of parameters, the implementation of each LMS algorithm is only undertaken by the nodes of the network interested in a specific set of local, common or global parameters. The study of convergence in the mean sense reveals that the proposed algorithm is asymptotically unbiased. Moreover, a spatial-temporal energy conservation relation is provided to evaluate the steady-state performance at each node in the mean-square sense. Finally, the theoretical results and the effectiveness of the proposed technique are validated through computer simulations in the context of cooperative spectrum sensing in Cognitive Radio networks.Comment: 13 pages, 6 figure

A Sparsity-Aware Adaptive Algorithm for Distributed Learning

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. Moreover, sparsity is also imposed by employing variable metric projections onto weighted $\ell_1$ balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme, compared to other algorithms, which have been developed in the context of sparse adaptive learning

Distributed adaptive estimation based on the APA algorithm over diffusion networks with changing topology

In this paper, we present a novel distributed affine projection algorithm (APA) to solve distributed estimation problem within dynamic diffusion networks. In addition, mean-square stability of the proposed algorithm is also studied through exploitation of the energy conservation approach due to Sayed. Simulations confirm that the novel algorithm achieves a greatly improved performance as compared with a noncooperative scheme

Distributed Adaptive Learning of Graph Signals

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201

Algorithms for energy-efficient adaptive wireless sensor networks

Mención Internacional en el título de doctorIn this thesis we focus on the development of energy-efficient adaptive algorithms for Wireless Sensor Networks. Its contributions can be arranged in two main lines. Firstly, we focus on the efficient management of energy resources in WSNs equipped with finite-size batteries and energy-harvesting devices. To that end, we propose a censoring scheme by which the nodes are able to decide if a message transmission is worthy or not given their energetic condition. In order to do so, we model the system using a Markov Decision Process and use this model to derive optimal policies. Later, these policies are analyzed in simplified scenarios in order to get insights of their features. Finally, using Stochastic Approximation, we develop low-complexity censoring algorithms that approximate the optimal policy, with less computational complexity and faster convergence speed than other approaches such as Q-learning. Secondly, we propose a novel diffusion scheme for adaptive distributed estimation in WSNs. This strategy, which we call Decoupled Adapt-then-Combine (D-ATC), is based on keeping an estimate that each node adapts using purely local information and then combines with the diffused estimations by other nodes in its neighborhood. Our strategy, which is specially suitable for heterogeneous networks, is theoretically analyzed using two different techniques: the classical procedure for transient analysis of adaptive systems and the energy conservation method. Later, as using different combination rules in the transient and steady-state regime is needed to obtain the best performance, we propose two adaptive rules to learn the combination coefficients that are useful for our diffusion strategy. Several experiments simulating both stationary estimation and tracking problems show that our method outperforms state-of-the-art techniques in relevant scenarios. Some of these simulations reveal the robustness of our scheme under node failures. Finally, we show that both approaches can be combined in a common setup: a WSN composed of harvesting nodes aiming to solve an adaptive distributed estimation problem. As a result, a censoring scheme is added on top of D-ATC. We show how our censoring approach helps to improve both steady-state and convergence performance of the diffusion scheme.La presente tesis se centra en el desarrollo de algoritmos adaptativos energéticamente eficientes para redes de sensores inalámbricos. Sus contribuciones se pueden englobar en dos líneas principales. Por un lado, estudiamos el problema de la gestión eficiente de recursos energéticos en redes de sensores equipadas con dispositivos de captación de energía y baterías finitas. Para ello, proponemos un esquema de censura mediante el cual, en un momento dado, un nodo es capaz de decidir si la transmisión de un mensaje merece la pena en las condiciones energéticas actuales. El sistema se modela mediante un Proceso de Decisión de Markov (Markov Decision Process, MDP) de horizonte infinito y dicho modelo nos sirve para derivar políticas óptimas de censura bajo ciertos supuestos. Después, analizamos estas políticas óptimas en escenarios simplificados para extraer intuiciones sobre las mismas. Por último, mediante técnicas de Aproximación Estocástica, desarrollamos algoritmos de censura de menor complejidad que aproximan estas políticas óptimas. Las numerosas simulaciones realizadas muestran que estas aproximaciones son competitivas, obteniendo una mayor tasa de convergencia y mejores prestaciones que otras técnicas del estado del arte como las basadas en Q-learning. Por otro lado, proponemos un nuevo esquema de difusión para estimación distribuida adaptativa. Esta estrategia, que denominamos Decoupled Adapt-then-Combine (D-ATC), se basa en mantener una estimación que cada nodo adapta con información puramente local y que posteriormente combina con las estimaciones difundidas por los demás nodos de la vecindad. Analizamos teóricamente nuestra estrategia, que es especialmente útil en redes heterogéneas, usando dos métodos diferentes: el método clásico para el análisis de régimen transitorio en sistemas adaptativos y el método de conservación de la energía. Posteriormente, y dado que para obtener el mejor rendimiento es necesario utilizar reglas de combinación diferentes en el transitorio y en régimen permanente, proponemos dos reglas adaptativas para el aprendizaje de los pesos de combinación para nuestra estrategia de difusión. La primera de ellas está basada en una aproximación de mínimos cuadrados (least-squares, LS); mientras que la segunda se basa en el algoritmo de proyecciones afines (Afifne Projection Algorithm, APA). Se han realizado numerosos experimentos tanto en escenarios estacionarios como de seguimiento que muestran cómo nuestra estrategia supera en prestaciones a otras aproximaciones del estado del arte. Algunas de estas simulaciones revelan además la robustez de nuestra estrategia ante errores en los nodos de la red. Por último, mostramos que estas dos aproximaciones son complementarias y las combinamos en mismo escenario: una red de sensores inalámbricos compuesta de nodos equipados con dispositivos de captación energética cuyo objetivo es resolver de manera distribuida y adaptativa un problema de estimación. Para ello, añadimos la capacidad de censurar mensajes a nuestro esquema D-ATC. Nuestras simulaciones muestran que la censura puede ser beneficiosa para mejorar tanto el rendimiento en régimen permanente como la tasa de convergencia en escenarios relevantes de estimación basada en difusión.This work was partially supported by the "Formación de Profesorado Universitario" fellowship from the Spanish Ministry of Education (FPU AP2010-5225).Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Santiago Zazo Bello.- Secretario: Miguel Lázaro Gredilla.- Vocal: Alexander Bertran

Distributed Recursive Least-Squares: Stability and Performance Analysis

The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.Comment: 30 pages, 4 figures, submitted to IEEE Transactions on Signal Processin