Alexander Bertrand

Distributed Adaptive Node-Specific Signal Estimation in Fully Connected Sensor Networks—Part I: Sequential Node Updating

We introduce a distributed adaptive algorithm for linear minimum mean squared error (MMSE) estimation of node-specific signals in a fully connected broadcasting sensor network where the nodes collect multichannel sensor signal observations. We assume that the node-specific signals to be estimated share a common latent signal subspace with a dimension that is small compared to the number of available sensor channels at each node. In this case, the algorithm can significantly reduce the required communication bandwidth and still provide the same optimal linear MMSE estimators as the centralized case. Furthermore, the computational load at each node is smaller than in a centralized architecture in which all computations are performed in a single fusion center. We consider the case where nodes update their parameters in a sequential round robin fashion. Numerical simulations support the theoretical results. Because of its adaptive nature, the algorithm is suited for real-time signal estimation in dynamic environments, such as speech enhancement with acoustic sensor networks.

Applications and trends in wireless acoustic sensor networks: A signal processing perspective

Wireless microphone networks or so-called wireless acoustic sensor networks (WASNs) are a next-generation technology for audio acquisition and processing. As opposed to traditional microphone arrays that sample a sound field only locally, often at large distances from the relevant sound sources, WASNs allow to use many more microphones to cover a large area of interest. However, the design of such WASNs is very challenging, especially for real-time audio acquisition and signal enhancement due to the significant data traffic in the network. There is a need for scalable solutions, both on the signal processing level and on the network-communication level. In this paper, we give an overview of applications and trends in the field of WASNs, and we address the core challenges that need to be tackled. We mainly focus on the signal processing level, and we explain how advances in the area of signal processing can relax the high-demanding constraints on the network layer design. Furthermore, we address the interaction between the application layer and the network layer, and we explain why cross-layer design can be important to improve the performance of WASN applications.

Distributed Adaptive Estimation of Node-Specific Signals in Wireless Sensor Networks With a Tree Topology

We present a distributed adaptive node-specific signal estimation (DANSE) algorithm that operates in a wireless sensor network with a tree topology. The algorithm extends the DANSE algorithm for fully connected sensor networks, as described in previous work. It is argued why a tree topology is the natural choice if the network is not fully connected. If the node-specific desired signals share a common latent signal subspace, it is shown that the distributed algorithm converges to the same linear MMSE solutions as obtained with the centralized version of the algorithm. The computational load is then shared between the different nodes in the network, and nodes exchange only linear combinations of their sensor signal observations and data received from their neighbors. Despite the low connectivity of the network and the multi-hop signal paths, the algorithm is fully scalable in terms of communication bandwidth and computational power. Two different cases are considered concerning the communication protocol between the nodes: point-to-point transmission and local broadcasting. The former assumes that there is a reserved communication link between node-pairs, whereas with the latter, nodes communicate the same data to all of their neighbors simultaneously. The convergence properties of the algorithm are demonstrated by means of numerical examples.

Distributed Adaptive Node-Specific Signal Estimation in Fully Connected Sensor Networks—Part II: Simultaneous and Asynchronous Node Updating

In this paper, we revisit an earlier introduced distributed adaptive node-specific signal estimation (DANSE) algorithm that operates in fully connected sensor networks. In the original algorithm, the nodes update their parameters in a sequential round-robin fashion, which may yield a slow convergence of the estimators, especially so when the number of nodes in the network is large. When all nodes update simultaneously, the algorithm adapts more swiftly, but convergence can no longer be guaranteed. Simulations show that the algorithm then often gets locked in a suboptimal limit cycle. We first provide an extension to the DANSE algorithm, in which we apply an additional relaxation in the updating process. The new algorithm is then proven to converge to the optimal estimators when nodes update simultaneously or asynchronously, be it that the computational load at each node increases in comparison with the algorithm with sequential updates. Finally, based on simulations it is demonstrated that a simplified version of the new algorithm, without any extra computational load, can also provide convergence to the optimal estimators.

Seeing the Bigger Picture: How Nodes Can Learn Their Place Within a Complex Ad Hoc Network Topology

This article explained how nodes in a network graph can infer information about the network topology or its topology related properties, based on in-network distributed learning, i.e., without relying on an external observer who has a complete overview over the network. Some key concepts from the field of SGT were reviewed, with a focus on those that allow for a simple distributed implementation, i.e., eigenvector or Katz centrality, algebraic connectivity, and the Fiedler vector. This paper also explained how the nodes themselves can quantify their individual network-wide influence, as well as identify densely connected node clusters and the sparse bridge links between them. The addressed concepts, as well as more advanced concepts from the field of SGT, are believed to be crucial catalysts in the design of topology-aware distributed algorithms. Examples were provided on how these techniques can be exploited in several nontrivial distributed signal processing tasks.

Diffusion Bias-Compensated RLS Estimation Over Adaptive Networks

We study the problem of distributed least-squares estimation over ad hoc adaptive networks, where the nodes have a common objective to estimate and track a parameter vector. We consider the case where there is stationary additive colored noise on both the regressors and the output response, which results in biased local least-squares estimators. Assuming that the noise covariance can be estimated (or is known a priori), we first propose a bias-compensated recursive least-squares algorithm (BC-RLS). However, this bias compensation increases the variance or the mean-square deviation (MSD) of the local estimators, and errors in the noise covariance estimates may still result in residual bias. We demonstrate that the MSD and residual bias can then be significantly reduced by applying diffusion adaptation, i.e., by letting nodes combine their local estimates with those of their neighbors. We derive a necessary and sufficient condition for mean-square stability of the algorithm, under some mild assumptions. Furthermore, we derive closed-form expressions for its steady-state mean and mean-square performance. Simulation results are provided, which agree well with the theoretical results. We also consider some special cases where the mean-square stability improvement of diffusion BC-RLS over BC-RLS can be mathematically verified.

Robust distributed noise reduction in hearing aids with external acoustic sensor nodes

The benefit of using external acoustic sensor nodes for noise reduction in hearing aids is demonstrated in a simulated acoustic scenario with multiple sound sources. A distributed adaptive node-specific signal estimation (DANSE) algorithm, that has a reduced communication bandwidth and computational load, is evaluated. Batch-mode simulations compare the noise reduction performance of a centralized multi-channel Wiener filter (MWF) with DANSE. In the simulated scenario, DANSE is observed not to be able to achieve the same performance as its centralized MWF equivalent, although in theory both should generate the same set of filters. A modification to DANSE is proposed to increase its robustness, yielding smaller discrepancy between the performance of DANSE and the centralized MWF. Furthermore, the influence of several parameters such as the DFT size used for frequency domain processing and possible delays in the communication link between nodes is investigated.

Consensus-Based Distributed Total Least Squares Estimation in Ad Hoc Wireless Sensor Networks

Total least squares (TLS) is a popular solution technique for overdetermined systems of linear equations, where both the right-hand side and the input data matrix are assumed to be noisy. We consider a TLS problem in an ad hoc wireless sensor network, where each node collects observations that yield a node-specific subset of linear equations. The goal is to compute the TLS solution of the full set of equations in a distributed fashion, without gathering all these equations in a fusion center. To facilitate the use of the dual-based subgradient algorithm (DBSA), we transform the TLS problem to an equivalent convex semidefinite program (SDP), based on semidefinite relaxation (SDR). This allows us to derive a distributed TLS (D-TLS) algorithm, that satisfies the conditions for convergence of the DBSA, and obtains the same solution as the original (unrelaxed) TLS problem. Even though we make a detour through SDR and SDP theory, the resulting D-TLS algorithm relies on solving local TLS-like problems at each node, rather than computationally expensive SDP optimization techniques. The algorithm is flexible and fully distributed, i.e., it does not make any assumptions on the network topology and nodes only share data with their neighbors through local broadcasts. Due to the flexibility and the uniformity of the network, there is no single point of failure, which makes the algorithm robust to sensor failures. Monte Carlo simulation results are provided to demonstrate the effectiveness of the method.

Distributed Node-Specific LCMV Beamforming in Wireless Sensor Networks

In this paper, we consider the linearly constrained distributed adaptive node-specific signal estimation (LC-DANSE) algorithm, which generates a node-specific linearly constrained minimum variance (LCMV) beamformer, i.e., with node-specific linear constraints, at each node of a wireless sensor network. The algorithm significantly reduces the number of signals that are exchanged between nodes, and yet obtains the optimal LCMV beamformers as if each node has access to all the signals in the network. We consider the case where all the steering vectors are known, as well as the blind beamforming case where the steering vectors are not known. We formally prove convergence and optimality for both versions of the LC-DANSE algorithm. We also consider the case where nodes update their local beamformers simultaneously instead of sequentially, and we demonstrate by means of simulations that applying a relaxation is often required to obtain a converging algorithm in this case. We also provide simulation results that demonstrate the effectiveness of the algorithm in a realistic speech enhancement scenario.

Distributed computation of the Fiedler vector with application to topology inference in ad hoc networks

The Fiedler vector of a graph is the eigenvector corresponding to the smallest non-trivial eigenvalue of the graphs Laplacian matrix. The entries of the Fiedler vector are known to provide a powerful heuristic for topology inference, e.g., to identify densely connected node clusters, to search for bottleneck links in the information dissemination, or to increase the overall connectivity of the network. In this paper, we consider ad hoc networks where the nodes can process and exchange data in a synchronous fashion, and we propose a distributed algorithm for in-network estimation of the Fiedler vector and the algebraic connectivity of the corresponding network graph. The algorithm is fully scalable with respect to the network size in terms of per-node computational complexity and data transmission. Simulation results demonstrate the performance of the algorithm. Highlights? The Fiedler vector is the eigenvector of the smallest non-zero Laplacian eigenvalue. ? The entries of the Fiedler vector are a powerful heuristic for topology inference. ? We present a distributed algorithm to accurately compute the Fiedler vector. ? The algorithm is fully scalable with respect to the network size. ? One can divide a network into two clusters based on the entries of the Fiedler vector.