Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

Incremental Adaptive Strategies for Wireless Sensor Networks

Distributed wireless sensor networks play a key role due to its wide range of applications ranging from monitoring environmental parameters to satellite positioning. Adaptive algorithms are applied to the distributed networks to endow the network with adaptation capabilities. The distributed network consists of many small sensors deployed randomly in a geographic area, which are adaptive and share their local information. The efficiency of the adaptive distributed strategy relies on the mode of collaboration between the nodes and incremental mode of cooperation is considered throughout the work. A large number of adaptive algorithms are available in the literature, out of which choice is done according to the type of application, computational complexity and convergence rate. Least means square algorithm is the most popularly used adaptive algorithm due to its simplicity and least computational complexity. Distributed ILMS is used for parameter estimation and a spatial-temporal energy conservation relation is used to evaluate the steady state performance of the entire network. The simulated and theoretical steady state performances are compared. Digital implementation of adaptive filters results in quantization errors and finite precision errors. ILMS suffers from drift problem, where the parameter estimate will go unbounded in non-ideal or practical implementations due to the continuous accumulation of quantization errors, finite precision errors and insufficient spectral excitation or ill conditioning of input sequence. They result in overflow and near singular auto correlation matrix, which provokes slow escape of parameter estimate to go unbound. The proposed method ILLMS uses the Leaky LMS algorithm, which introduces a leakage factor in the update equation, and so prevents the weights to go unbounded by leaking energy out. But the overall performance of ILLMS is similar to ILMS in terms of convergence speed and thus an incremental Modified Leaky LMS is proposed based on MLLMS algorithms which in turn derived from the LSE algorithm. LSE algorithm employs sum of exponentials of errors in its cost function and it results in convex and smooth error surface with more steepness, which results in faster convergence rate. ILLMS and IMLLMS algorithms are simulated and compared, where IMLLMS gives superior performance compared to ILLMS in terms of convergence rate and steady state values

Computationally efficient distributed minimum wilcoxon norm

In the fields related to digital signal processing and communication, as system identification, noise cancellation, channel equalization, and beam forming Adaptive filters play an important role. In practical applications, the computational complexity of an adaptive filter is an important consideration. As it describes system reliability, swiftness to real time environment least mean squares (LMS) algorithm is widely used because of its low computational complexity (O (N)) and simplicity in implementation. The least squares algorithms, having general form as recursive least squares (RLS), conjugate gradient (CG) and Euclidean direction search (EDS), can converge faster and have lower steady-state mean square error (MSE) than LMS. However, for their high computational complexity (O (N2)) makes them unsuitable for many real-time applications. Therefore controlling of computational complexity is obtained by partial update (PU) method for adaptive filters. A partial update method is implemented to reduce the adaptive algorithm complexity by updating a fraction of the weight vector instead of the entire weight vector. An analysis of different PU adaptive filter algorithms is necessary, sufficient so meaningful. The deficient-length adaptive filter addresses a situation in system identification where the length of the estimated filter is shorter than the length of the actual unknown system. System is related to the partial update adaptive filter, but has distinct performance. It can be viewed as a PU adaptive filter, in that machine the deficient-length adaptive filter also updates part of the weight vector. However, it updates some part of the weight vector in every iteration. While the partial update adaptive filter updates a different part of the weight vector for each iteration

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