arXiv subjects

Geert Leus

Publications and source records attributed to Geert Leus.

At least 73 records · Page 4Linked to original sources

arXiv2019

Non-cooperative Aerial Base Station Placement via Stochastic Optimization

Autonomous unmanned aerial vehicles (UAVs) with on-board base station equipment can potentially provide connectivity in areas where the terrestrial infrastructure is overloaded, damaged, or absent. Use cases comprise emergency response, wildfire suppression, surveillance, and cellular communications in crowded events to name a few. A central problem to enable this technology is to place such aerial base stations (AirBSs) in locations that approximately optimize the relevant communication metrics. To alleviate the limitations of existing algorithms, which require intensive and reliable communications among AirBSs or between the AirBSs and a central controller, this paper leverages stochastic optimization and machine learning techniques to put forth an adaptive and decentralized algorithm for AirBS placement without inter-AirBS cooperation or communication. The approach relies on a smart design of the network utility function and on a stochastic gradient ascent iteration that can be evaluated with information available in practical scenarios. To complement the theoretical convergence properties, a simulation study corroborates the effectiveness of the proposed scheme.

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arXiv2018

Convolutional Neural Network Architectures for Signals Supported on Graphs

Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best performing GNN architecture.

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arXiv2018

Joint Ranging and Clock Synchronization for Dense Heterogeneous IoT Networks

Synchronization and ranging in internet of things (IoT) networks are challenging due to the narrowband nature of signals used for communication between IoT nodes. Recently, several estimators for range estimation using phase difference of arrival (PDoA) measurements of narrowband signals have been proposed. However, these estimators are based on data models which do not consider the impact of clock-skew on the range estimation. In this paper, clock-skew and range estimation are studied under a unified framework. We derive a novel and precise data model for PDoA measurements which incorporates the unknown clock-skew effects. We then formulate joint estimation of the clock-skew and range as a two-dimensional (2-D) frequency estimation problem of a single complex sinusoid. Furthermore, we propose: (i) a two-way communication protocol for collecting PDoA measurements and (ii) a weighted least squares (WLS) algorithm for joint estimation of clock-skew and range leveraging the shift invariance property of the measurement data. Finally, through numerical experiments, the performance of the proposed protocol and estimator is compared against the Cramer Rao lower bound demonstrating that the proposed estimator is asymptotically efficient.

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arXiv2018

Online Graph-Adaptive Learning with Scalability and Privacy

Graphs are widely adopted for modeling complex systems, including financial, biological, and social networks. Nodes in networks usually entail attributes, such as the age or gender of users in a social network. However, real-world networks can have very large size, and nodal attributes can be unavailable to a number of nodes, e.g., due to privacy concerns. Moreover, new nodes can emerge over time, which can necessitate real-time evaluation of their nodal attributes. In this context, the present paper deals with scalable learning of nodal attributes by estimating a nodal function based on noisy observations at a subset of nodes. A multikernel-based approach is developed which is scalable to large-size networks. Unlike most existing methods that re-solve the function estimation problem over all existing nodes whenever a new node joins the network, the novel method is capable of providing real-time evaluation of the function values on newly-joining nodes without resorting to a batch solver. Interestingly, the novel scheme only relies on an encrypted version of each node's connectivity in order to learn the nodal attributes, which promotes privacy. Experiments on both synthetic and real datasets corroborate the effectiveness of the proposed methods.

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arXiv2018

Observing and Tracking Bandlimited Graph Processes

One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling single snapshots of graph signals ignoring their evolution over time. However, time can bring forth new insights, since many real signals like sensor measurements, biological, financial, and network signals in general, have intrinsic correlations in both domains. In this work, {we fill this lacuna} by jointly considering the graph-time nature of graph signals, named \emph{graph processes} for two main tasks: \emph{i)} observability of graph processes; and \emph{ii)} tracking of graph processes via Kalman filtering; both from a (possibly time-varying) subset of nodes. A detailed mathematical analysis ratifies the proposed methods and provides insights into the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed. Several numerical tests on both synthetic and real data validate our theoretical findings and illustrate the performance of the proposed methods in coping with time-varying graph signals.

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arXiv2018

Advances in Distributed Graph Filtering

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this work generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize the subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parametrization the proposed graph filters provide insights in approximating linear operators through the succession and composition of local operators, i.e., fixed support matrices, which span applications beyond the field of graph signal processing. A set of numerical results shows the benefits of the edge-variant filters over current methods and illustrates their potential to a wider range of applications than graph filtering.

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arXiv2018

Relative kinematics of an anchorless network

Estimating the location of N coordinates in a P dimensional Euclidean space from pairwise distances (or proximity measurements), is a principal challenge in a wide variety of fields. Conventionally, when localizing a static network of immobile nodes, non-linear dimensional reduction techniques are applied on the measured Euclidean distance matrix (EDM) to obtain the relative coordinates upto a rotation and translation. In this article, we focus on an anchorless network of mobile nodes, where the distance measurements between the mobile nodes are time-varying in nature. Furthermore, in an anchorless network the absolute knowledge of any node positions, motion or reference frame is absent. We derive a novel data model which relates the time-varying EDMs to the time-varying relative positions of an anchorless network. Using this data model, we estimate the relative position, relative velocity and higher order derivatives, which are collectively termed as the relative kinematics of the anchorless network. The derived data model is inherently ill-posed, however can be solved using certain relative immobility constraints. We propose elegant closed form solutions to recursively estimate the relative kinematics of the network. For the sake of completeness, estimators are also proposed to find the absolute kinematics of the nodes, given known reference anchors. Cramer-Rao bounds are derived for the new data model and simulations are performed to analyze the performance of the proposed solutions.

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arXiv2018

Self-Estimation of Path-Loss Exponent in Wireless Networks and Applications

The path-loss exponent (PLE) is one of the most crucial parameters in wireless communications to characterize the propagation of fading channels. It is currently adopted for many different kinds of wireless network problems such as power consumption issues, modelling the communication environment, and received signal strength (RSS)-based localization. PLE estimation is thus of great use to assist in wireless networking. However, a majority of methods to estimate the PLE require either some particular information of the wireless network, which might be unknown or some external auxiliary devices, such as anchor nodes or the Global Positioning System. Moreover, this external information might sometimes be unreliable, spoofed, or difficult to obtain. Therefore, a self-estimator for the PLE, which is able to work independently, becomes an urgent demand to robustly and securely get a grip on the PLE for various wireless network applications. This paper is the first to introduce two methods that can solely and locally estimate the PLE. To start, a new linear regression model for the PLE is presented. Based on this model, a closed-form total least squares (TLS) method to estimate the PLE is first proposed, in which, with no other assistance or external information, each node can estimate the PLE merely by collecting RSSs. Second, to suppress the estimation errors, a closed-form weighted TLS method is further developed, having a better performance. Due to their simplicity and independence of any auxiliary system, our two proposed methods can be easily incorporated into any kind of wireless communication stack. Simulation results show that our estimators are reliable, even in harsh environments, where the PLE is high. Many potential applications are also explicitly illustrated in this paper, such as secure RSS-based localization, kth nearest neighbour routing, etc.

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arXiv2018

Robust Differential Received Signal Strength-Based Localization

Source localization based on signal strength measurements has become very popular due to its practical simplicity. However, the severe nonlinearity and non-convexity make the related optimization problem mathematically difficult to solve, especially when the transmit power or the path-loss exponent (PLE) is unknown. Moreover, even if the PLE is known but not perfectly estimated or the anchor location information is not accurate, the constructed data model will become uncertain, making the problem again hard to solve. This paper particularly focuses on differential received signal strength (DRSS)-based localization with model uncertainties in case of unknown transmit power and PLE. A new whitened model for DRSS-based localization with unknown transmit powers is first presented and investigated. When assuming the PLE is known, we introduce two estimators based on an exact data model, an advanced best linear unbiased estimator (A-BLUE) and a Lagrangian estimator (LE), and then we present a robust semidefinite programming (SDP)-based estimator (RSDPE), which can cope with model uncertainties (imperfect PLE and inaccurate anchor location information). The three proposed estimators have their own advantages from different perspectives: the A-BLUE has the lowest complexity; the LE holds the best accuracy for a small measurement noise; and the RSDPE yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties. Finally, we propose a robust SDP-based block coordinate descent estimator (RSDP-BCDE) to deal with a completely unknown PLE and its performance converges to that of the RSDPE using a perfectly known PLE.

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arXiv2018

On a unified framework for linear nuisance parameters

Estimation problems in the presence of deterministic linear nuisance parameters arise in a variety of fields. To cope with those, three common methods are widely considered: (1) jointly estimating the parameters of interest and the nuisance parameters, (2) projecting out the nuisance parameters, (3) selecting a reference and then taking differences between the reference and the observations, which we will refer to as "differential signal processing." A lot of literature has been devoted to these methods, yet all follow separate paths. Based on a unified framework, we analytically explore the relations between these three methods, where we particularly focus on the third one and introduce a general differential approach to cope with multiple distinct nuisance parameters. After a proper whitening procedure, the corresponding best linear unbiased estimators (BLUEs) are shown to be all equivalent to each other. Accordingly, we unveil some surprising facts, which are in contrast to what is commonly considered in literature, e.g., the reference choice is actually not important for the differencing process. Since this paper formulates the problem in a general manner, one may specialize our conclusions to any particular application. Some localization examples are also presented in this paper to verify our conclusions.

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arXiv2018

Sampling and Reconstruction of Signals on Product Graphs

In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.

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arXiv2018

Filter Design for Autoregressive Moving Average Graph Filters

In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing autoregressive moving average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression and prediction.

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arXiv2018

Sparse Sampling for Inverse Problems with Tensors

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multi-antenna communications to graph signal processing, to validate the developed theory.

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arXiv2018

Sparse Antenna and Pulse Placement for Colocated MIMO Radar

Multiple input multiple output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this work, the Cram'er-Rao lower bound (CRLB) for the angle and velocity estimator is employed as a performance metric to design the antenna and pulse placement. It is shown that the CRLB derived for two targets is a more appropriate criterion in comparison with the single-target CRLB since the two-target CRLB takes into account both the mainlobe width and sidelobe level of the ambiguity function. In this paper, several algorithms for antenna and pulse selection based on convex and submodular optimization are proposed. Numerical experiments are provided to illustrate the developed theory.

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arXiv2018

Joint Detection and Localization of an Unknown Number of Sources Using Algebraic Structure of the Noise Subspace

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods which rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both apriori knowledge of the number of sources, and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms, and when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of SNRs. Further, no performance sacrifice in simple scenarios is observed.

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arXiv2018

MIMO Graph Filters for Convolutional Neural Networks

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-structured data such as audio or images, application of CNNs to contemporary datasets where the information is defined in irregular domains is challenging. This paper investigates CNNs architectures to operate on signals whose support can be modeled using a graph. Architectures that replace the regular convolution with a so-called linear shift-invariant graph filter have been recently proposed. This paper goes one step further and, under the framework of multiple-input multiple-output (MIMO) graph filters, imposes additional structure on the adopted graph filters, to obtain three new (more parsimonious) architectures. The proposed architectures result in a lower number of model parameters, reducing the computational complexity, facilitating the training, and mitigating the risk of overfitting. Simulations show that the proposed simpler architectures achieve similar performance as more complex models.

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arXiv2018

Convolutional Neural Networks Via Node-Varying Graph Filters

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are convolution and pooling, this type of networks is implicitly designed to act on data described by regular structures such as images. Motivated by the recent interest in processing signals defined in irregular domains, we advocate a CNN architecture that operates on signals supported on graphs. The proposed design replaces the classical convolution not with a node-invariant graph filter (GF), which is the natural generalization of convolution to graph domains, but with a node-varying GF. This filter extracts different local features without increasing the output dimension of each layer and, as a result, bypasses the need for a pooling stage while involving only local operations. A second contribution is to replace the node-varying GF with a hybrid node-varying GF, which is a new type of GF introduced in this paper. While the alternative architecture can still be run locally without requiring a pooling stage, the number of trainable parameters is smaller and can be rendered independent of the data dimension. Tests are run on a synthetic source localization problem and on the 20NEWS dataset.

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arXiv2017

Eigendecomposition-Based Partial FFT Demodulation for Differential OFDM in Underwater Acoustic Communications

Differential orthogonal frequency division multiplexing (OFDM) is practically attractive for underwater acoustic communications since it has the potential to obviate channel estimation. However, similar to coherent OFDM, it may suffer from severe inter-carrier interference over time-varying channels. To alleviate the induced performance degradation, we adopt the newly-emerging partial FFT demodulation technique in this paper and propose an eigendecomposition-based algorithm to compute the combining weights. Compared to existing adaptive methods, the new algorithm can avoid error propagation and eliminate the need for parameter tuning. Moreover, it guarantees global optimality under the narrowband Doppler assumption, with the optimal weight vector of partial FFT demodulation achieved by the eigenvector associated with the smallest eigenvalue of the pilot detection error matrix. Finally, the algorithm can also be extended straightforwardly to perform subband-wise computation to counteract wideband Doppler effects.

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