Distributed Adaptive Node-specific Signal Estimation Research Articles

Distributed parameterized topology-independent noise reduction in acoustic sensor networks

Distributed noise reduction is a challenging task in acoustic sensor networks (ASNs). To address the problem, a distributed parameterized topology-independent noise reduction method is proposed in this paper. To be specific, the parameterized topology-independent distributed adaptive node-specific signal estimation (PTI-DANSE) is first presented in fully connected ASNs, where only one node uses its local signals and the compressed signals summation from the other nodes at a time to estimate signal statistics and update parameters. Then, to make all nodes estimate signal statistics and update parameters simultaneously, the relaxed simultaneous PTI-DANSE (rsPTI-DANSE) is proposed in a synchronous update fashion. Finally, through using in-network summation techniques, the distributed parameterized topology-independent noise reduction algorithm for any topology is obtained. The proposed algorithm is applicative for any network topology, and it is adjustable in terms of speech distortion and noise reduction. Simulation results and real-world experiments indicate that the proposed algorithm has good noise reduction performance.

Sampling Rate Offset Estimation and Compensation for Distributed Adaptive Node-Specific Signal Estimation in Wireless Acoustic Sensor Networks

Sampling rate offsets (SROs) between devices in a heterogeneous wireless acoustic sensor network (WASN) can hinder the ability of distributed adaptive algorithms to perform as intended when they rely on coherent signal processing. In this paper, we present an SRO estimation and compensation method to allow the deployment of the distributed adaptive node-specific signal estimation (DANSE) algorithm in WASNs composed of asynchronous devices. The signals available at each node are first utilised in a coherence-drift-based method to blindly estimate SROs which are then compensated for via phase shifts in the frequency domain. A modification of the weighted overlap-add (WOLA) implementation of DANSE is introduced to account for SRO-induced full-sample drifts, permitting per-sample signal transmission via an approximation of the WOLA process as a time-domain convolution. The performance of the proposed algorithm is evaluated in the context of distributed noise reduction for the estimation of a target speech signal in an asynchronous WASN.

Distributed Combined Acoustic Echo Cancellation and Noise Reduction in Wireless Acoustic Sensor and Actuator Networks

The paper presents distributed algorithms for combined acoustic echo cancellation (AEC) and noise reduction (NR) in a wireless acoustic sensor and actuator network (WASAN) where each node may have multiple microphones and multiple loudspeakers, and where the desired signal is a speech signal. A centralized integrated AEC and NR algorithm, i.e., multichannel Wiener filter (MWF), is used as starting point where echo signals are viewed as background noise signals and loudspeaker signals are used as additional input signals to the algorithm. By including prior knowledge (PK), namely that the loudspeaker signals do not contain any desired signal component, an alternative centralized cascade algorithm (PK-MWF) is obtained with an AEC stage first followed by an MWF-based NR stage which has a lower computational complexity. Distributed algorithms can then be obtained from the MWF and PK-MWF algorithm, i.e., the generalized eigenvalue decomposition (GEVD)-based distributed adaptive node-specific signal estimation (DANSE) and PK-GEVD-DANSE algorithm, respectively. In the former, each node performs a reduced dimensional integrated AEC and NR algorithm and broadcasts only 1 fused signal (instead of all its signals) to the other nodes. In the PK-GEVD-DANSE algorithm, each node performs a reduced dimensional cascade AEC and NR algorithm and broadcasts only 2 fused signals (instead of all its signals) to the other nodes. The distributed algorithms achieve the same performance, upon convergence, as the corresponding centralized integrated (MWF) and centralized cascade (PK-MWF) algorithm. It is observed, however, that the communication cost in the PK-GEVD-DANSE algorithm can also be reduced, where each node then broadcasts only 1 fused signal (instead of 2 signals) to the other nodes. The resulting algorithm, referred to as the pruned PK-GEVD-DANSE (pPK-GEVD-DANSE) algorithm, then effectively combines the lowest possible communication cost (as low as in the GEVD-DANSE algorithm) with a lowest possible computational complexity in each node (further reduced from the PK-GEVD-DANSE computational complexity), within the class of algorithms considered in this paper.

Distributed adaptive node-specific signal estimation in a wireless sensor network with noisy links

We consider a distributed signal estimation problem in a wireless sensor network where each node aims to estimate a node-specific desired signal using all sensor signals available in the network. In this setting, the distributed adaptive node-specific signal estimation (DANSE) algorithm is able to learn optimal fusion rules with which the nodes fuse their sensor signals, as the fused signals are then transmitted between the nodes. Under the assumption of transmission without errors, DANSE achieves the performance of centralized estimation. However, noisy communication links introduce errors in these transmitted signals, e.g., due to quantization or communication errors. In this paper we show fusion rules which take additive noise in the transmitted signals into account at almost no increase in computational complexity, resulting in a new algorithm denoted as ‘noisy-DANSE’ (N-DANSE). As the convergence proof for DANSE cannot be straightforwardly generalized to the case with noisy links, we use a different strategy to prove convergence of N-DANSE, which also proves convergence of DANSE without noisy links as a special case. We validate the convergence of N-DANSE and compare its performance with the original DANSE through numerical simulations, which demonstrate the superiority of N-DANSE over the original DANSE in noisy links scenarios.

Topology-Independent Distributed Adaptive Node-Specific Signal Estimation in Wireless Sensor Networks

A topology-independent distributed adaptive node-specific signal estimation ( $\text{TI-DANSE}$ ) algorithm is presented where each node of a wireless sensor network (WSN) is tasked with estimating a node-specific desired signal. To reduce the amount of data exchange, each node applies a linear compression to its sensors signal observations, and only transmits the compressed observations to its neighbors. The $\text{TI-DANSE}$ algorithm is shown to converge to the same optimal node-specific signal estimates as if each node were to transmit its raw (uncompressed) sensor signal observations to every other node in the WSN. The $\text{TI-DANSE}$ algorithm is first introduced in a fully connected WSN and then shown, in fact, to have the same convergence properties in any topology. When implemented in other topologies, the nodes rely on an in-network summation of the transmitted compressed observations that can be accomplished by various means. We propose a method for this in-network summation via a data-driven signal flow that takes place on a tree, where the topology of the tree may change in each iteration. This makes the algorithm less sensitive to link failures and applicable to WSNs with dynamic topologies.

GEVD-Based Low-Rank Approximation for Distributed Adaptive Node-Specific Signal Estimation in Wireless Sensor Networks

In this paper, we address the problem of distributed adaptive estimation of node-specific signals for signal enhancement or noise reduction in wireless sensor networks with multi-sensor nodes. The estimation is performed by a multi-channel Wiener filter (MWF) in which a low-rank approximation based on a generalized eigenvalue decomposition (GEVD) is incorporated. In non-stationary or low-SNR conditions, this GEVD-based MWF has been demonstrated to be more robust than the original MWF. In a centralized realization where a fusion center has access to all the nodes’ sensor signal observations, the network-wide sensor signal correlation matrices and the low-rank approximation can be directly estimated and used to compute the network-wide GEVD-based MWF. However, in this paper, we aim to avoid centralizing the sensor signal observations, in which case the network-wide sensor signal correlation matrices cannot be estimated. To this end, we start from the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, and include GEVD-based low-rank approximations in the per-node local computations. Remarkably, the new algorithm is able to significantly compress the signal observations transmitted between the nodes, while still converging to the network-wide GEVD-based MWF as if each node would have access to all sensor signal observations, even though the low-rank approximations are applied locally at each node. We provide a theoretical convergence analysis, which shows that the algorithm converges to the network-wide GEVD-based MWF under conditions that are less strict than in the original DANSE algorithm. The convergence and performance of the algorithm are further investigated via numerical simulations.

Distributed adaptive node-specific signal estimation in heterogeneous and mixed-topology wireless sensor networks

A wireless sensor network (WSN) is considered where each node estimates a number of node-specific desired signals by means of the distributed adaptive node-specific signal estimation (DANSE) algorithm. It is assumed that the topology of the WSN is constructed based on one of the two approaches, either a top-down approach where the WSN is composed of heterogeneous nodes, or a bottom-up approach where the nodes are not necessarily heterogeneous. In the top-down approach, nodes with the largest energy budgets are designated as cluster heads and the remaining nodes form clusters around these nodes. In the bottom–up approach, an ad hoc WSN is partitioned into a set of smaller substructures consisting of non-overlapping cliques that are arranged in a tree topology. These two approaches are shown to be conceptually equivalent, in that the same building blocks constitute both envisaged topologies, and the functionality of the DANSE algorithm is extended to such topologies. In using the DANSE algorithm in such topologies, the WSN converges to the same solution as if all nodes had access to all of the sensor signal observations, and provides faster convergence when compared to DANSE in a single tree topology with only a slight increase in per-node energy usage.

Cooperative integrated noise reduction and node-specific direction-of-arrival estimation in a fully connected wireless acoustic sensor network

In this paper, we consider cooperative node-specific direction-of-arrival (DOA) estimation in a fully connected wireless acoustic sensor network (WASN). We consider a scenario where each node is equipped with a local microphone array with a known geometry, but where the position of the nodes, as well as their relative geometry and hence the between-nodes signal coherence model is unknown. The local array geometry in each node defines node-specific DOAs with respect to a set of target speech sources and the aim is to estimate these in each node. We assume a noisy environment with localized and/or diffuse noise sources, i.e., the noise can be correlated over the different microphones. A distributed noise reduction algorithm can then be applied as a preprocessing step to denoise all the microphone signals of the WASN, based on the distributed adaptive node-specific signal estimation (DANSE) algorithm. The denoised local microphone signals can then be used in each node to estimate the node-specific DOAs by using a subspace-based DOA estimation, involving a (generalized) eigenvalue decomposition of the local microphone signal correlation matrices. It is seen that the fused microphone signals that are exchanged between the nodes in the DANSE algorithm can also be included in these correlation matrices to obtain improved DOA estimates, leading to a cooperative integrated noise reduction and DOA estimation scheme, where the noise reduction can actually be shortcut. The improved performance achieved by this cooperative DOA estimation is demonstrated by means of numerical simulations for two different subspace-based DOA estimation methods (MUSIC and ESPRIT).

Greedy distributed node selection for node-specific signal estimation in wireless sensor networks

A wireless sensor network is envisaged that performs signal estimation by means of the distributed adaptive node-specific signal estimation (DANSE) algorithm. This wireless sensor network has constraints such that only a subset of the nodes are used for the estimation of a signal. While an optimal node selection strategy is NP-hard due to its combinatorial nature, we propose a greedy procedure that can add or remove nodes in an iterative fashion until the constraints are satisfied based on their utility. With the proposed definition of utility, a centralized algorithm can efficiently compute each nodes's utility at hardly any additional computational cost. Unfortunately, in a distributed scenario this approach becomes intractable. However, by using the convergence and optimality properties of the DANSE algorithm, it is shown that for node removal, each node can efficiently compute a utility upper bound such that the MMSE increase after removal will never exceed this value. In the case of node addition, each node can determine a utility lower bound such that the MMSE decrease will always exceed this value once added. The greedy node selection procedure can then use these upper and lower bounds to facilitate distributed node selection.

Distributed signal estimation in sensor networks where nodes have different interests

In this paper, we consider distributed signal estimation in sensor networks where the nodes exchange compressed sensor signal observations to estimate different node-specific signals. In particular, we revisit the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, which applies to the case where the nodes share a so-called ‘common interest’, and cast it in the more general setting where the nodes have ‘different interests’. We prove existence of an equilibrium state for such a setting by using a result from fixed point theory. By establishing a link between the DANSE algorithm and game theory, we point out that any equilibrium of the DANSE algorithm is a Nash equilibrium of the corresponding game. This provides an intuitive interpretation to the resulting signal estimators. The equilibrium state existence proof also reveals a problem with discontinuities in the DANSE update function, which may result in non-convergence of the algorithm. However, since these discontinuities are identifiable, they can easily be avoided by applying a minor heuristic modification to the algorithm. We demonstrate the effectiveness of this modification by means of numerical examples.

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.

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.