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This paper describes a distributed statistical estimation problem, corresponding to a network of agents. The network may be vulnerable to data injection attacks, in which attackers control legitimate nodes in the network and use them to inject false data. We have previously shown [1] that the detection metric by Wu et. al in [2], is vulnerable to sophisticated attacks where the attacker mixes normal behaviour and false data injection. In this paper we propose a novel metric that can be computed locally by each agent to detect and localize the novel attack in the network in a single instance.

This paper presents an inference method to learn a model for complex system based on observations of the perturbed stationary points. We propose to jointly estimate the dynamics parameters and network topology through a regularized regression formulation. A distinguished feature of our approach rests on the direct modeling of rank deficient network data, which is widely found in network science but frequently ignored in the prior research. The new modeling technique allows us to provide the network identifiability condition under the scenarios of insufficient data. In the special case where the dynamics parameters are known, we show how the interplay between dynamics and sparsity in the graph structure can lead to verifiable conditions for network identifiability. Furthermore, relying only on the steady-states equations, our method avoids the necessity to record transient data, and allows to meaningfully combine data from multiple experiments. Numerical experiments are performed on examples with gene regulatory networks and opinion dynamics to justify our claims.

In this work, we study how to implement a distributed algorithm for the power method in a parallel manner. As the existing distributed power method is usually sequentially updating the eigenvectors, it exhibits two obvious disadvantages: 1) when it calculates the $h$th eigenvector, it needs to wait for the results of previous $(h-1)$ eigenvectors, which causes a delay in acquiring all the eigenvalues; 2) when calculating each eigenvector, it needs a certain cost of information exchange within the neighboring nodes for every power iteration, which could be unbearable when the number of eigenvectors or the number of nodes is large. This motivates us to propose a parallel distributed power method, which simultaneously calculates all the eigenvectors at each power iteration to ensure that more information could be exchanged in one shaking-hand of communication. We are particularly interested in the distributed power method for both an eigenvalue decomposition (EVD) and a singular value decomposition (SVD), wherein the distributed process is proceed based on a gossip algorithm. It can be shown that, under the same condition, the communication cost of the gossip-based parallel method is only $1/H$ times of that for the sequential counterpart, where $H$ is the number of eigenvectors we want to compute, while the convergence time and error performance of the proposed parallel method are both comparable to those of its sequential counterpart.

The underlying theme of this paper is to explore the various facets of power systems data through the lens of graph signal processing (GSP), laying down the foundations of the Grid-GSP framework. Grid-GSP provides an interpretation for the spatio-temporal properties of voltage phasor measurements, by showing how the well-known power systems modeling supports a generative low-pass graph filter model for the state variables, namely the voltage phasors. Using the model we formalize the empirical observation that voltage phasor measurement data lie in a low-dimensional subspace and tie their spatio-temporal structure to generator voltage dynamics. The Grid-GSP generative model is then successfully employed to investigate the problems pertaining to the grid of data sampling and interpolation, network inference, detection of anomalies and data compression. Numerical results on a large synthetic grid that mimics the real-grid of the state of Texas, ACTIVSg2000, and on real-world measurements from ISO-New England verify the efficacy of applying Grid-GSP methods to electric grid data., Comment: 15 Pages, under review in IEEE Transactions on Signal Processing

To introduce more automation in the distribution level of the power system, increasingly more data are needed to serve as input to control algorithms. To examine the complex interaction between the various layers of the system and verify the effectiveness of automation, difficult to obtain, realistic test systems are necessary. An algorithm for automatically synthesizing realistic medium voltage distribution feeders, and thus circumvent the data access problem, is presented. The algorithm treats distribution system feeders as graphs with nodes and edges, each with various properties, and leverages this structure to search for emerging statistical patterns. Using a large data set from a DSO in The Netherlands, clear statistical distributions are identified linking properties, such as load, node degree, or cable length, to the feeder structure. Specifically, many properties are linked to a node's or edge's distance, in hops, from the primary substation. With consideration for standard engineering practices, the statistical trends are exploited in the synthesis process, to generate feeders, which display similar characteristics to the real samples. The KL-divergence is used in the evaluation of analysis and synthesis results. Beyond solving the data access problem, the use of automatically generated, synthetic, distribution systems will enable testing and validation techniques, such as Monte Carlo simulations, which are currently not possible in this field, where single test cases are the norm.

In this paper, we present a distributed array processing algorithm to analyze the power output of solar photo-voltaic (PV) installations, leveraging the low-rank structure inherent in the data to estimate possible faults. Our multi-agent algorithm requires near-neighbor communications only and is also capable of jointly estimating the common low rank cloud profile and local shading of panels. To illustrate the workings of our algorithm, we perform experiments to detect shading faults in solar PV installations within a single ZIP code. Additionally, we also derive a Bayesian lower bound on the shading parameter’s mean squared estimation error. The results are promising and show that we can successfully estimate the fraction of partial shading in solar installations that can usually go unnoticed.

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the observability barrier, they mostly rely on recognizing spatio-temporal patterns, without giving insights on how the performance are tied with the system features and the sensor deployment. In this paper, we try to fill this gap and investigate the limitations and performance limits of fault localization using Phasor Measurement Units (PMUs), in the low measurements regime, i.e., when the system is unobservable with the measurements available. Our main contribution is to show how one can leverage the scarce measurements to localize different type of distribution line faults (three-phase, single-phase to ground, ...) at the level of sub-graph, rather than with the resolution of a line. We show that the resolution we obtain is strongly tied with the graph clustering notion in network science., Accepted in IEEE SmartGridComm 2018 Conference

This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on a `low-pass' property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical experiments demonstrate that our approach is effective., Single column format, 32 pages, 9 figures

This paper presents new results on network inference from observations of steady state behaviors emerging from perturbations of complex networks dynamics. We focus on the estimation of network and flow parameters using a general regularized inference formulation, which is tackled numerically using the standard technique of alternating optimization. We argue that relying only on the steady states equations removes the requirement of precisely recording transient data, and allows to meaningfully combine data from multiple experiments. To provide theoretical benchmarks we study the relationship between topological and functional characteristics of the system and the divergence between the steady state behavior observed, to give rigorous performance benchmarks. Numerical results are presented on examples with social networks and gene regulatory networks to justify our claims.

This paper considers the problem of inferring the topology of a graph from noisy outputs of an unknown graph filter excited by low-rank signals. Limited by this low-rank structure, we focus on solving the community detection problem, whose aim is to partition the node set of the unknown graph into subsets with high edge densities. We propose to detect the communities by applying spectral clustering on the low-rank output covariance matrix. To analyze the performance, we show that the low-rank covariance yields a sketch of the eigenvectors of the unknown graph. Importantly, we provide theoretical bounds on the error introduced by this sketching procedure based on spectral features of the graph filter involved. Finally, our theoretical findings are validated via numerical experiments.

An implicit assumption made in several studies on sensor systems is that the time and frequency at which sensor measurements are taken is consistent across all the distributed sensing sites. In reality, the times of measurement often lack consistency and integrity, and this is an intrinsic vulnerability of wide area sensor system. Data logs coming from different analog to digital converters (ADCs) are not in phase and may differ also in the sampling rate, in some cases because heterogeneity in the sensors and in others because the data are simply not refreshed in the data historians with the same frequency. Lack of good synchronization in sensing may be the result of a malfunction or also due to intentional delay attacks. This premise motivates our work, where we advance the area of decentralized signal processing and consider explicitly timing errors and nonhomogenous sampling rates in least square estimation problems with distributed sensing. For linear observations models, we provide a necessary and sufficient condition for identifiability of the time offsets. We propose an algorithm for the joint regression on the state vector and time offsets. The algorithm also exploits the asynchrony and redundancy in the spatial sampling to attain sub-Nyquist sampling resolution of the slow sensor feeds. Importantly, this also leads to the development of a novel decentralized algorithm. The efficacies of the proposed decentralized algorithm are shown by both convergence analysis and numerical simulations.

We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of training data is $m$ and $m \gg d \gg 1$, the CIAG method seeks to accelerate incremental aggregated gradient (IAG) methods using aids from the curvature (or Hessian) information, while avoiding the evaluation of matrix inverses required by the incremental Newton (IN) method. Specifically, our idea is to exploit the incrementally aggregated Hessian matrix to trace the full gradient vector at every incremental step, therefore achieving an improved linear convergence rate over the state-of-the-art IAG methods. For strongly convex problems, the fast linear convergence rate requires the objective function to be close to quadratic, or the initial point to be close to optimal solution. Importantly, we show that running one iteration of the CIAG method yields the same improvement to the optimality gap as running one iteration of the full gradient method, while the complexity is $O(d^2)$ for CIAG and $O(md)$ for the full gradient. Overall, the CIAG method strikes a balance between the high computation complexity incremental Newton-type methods and the slow IAG method. Our numerical results support the theoretical findings and show that the CIAG method often converges with much fewer iterations than IAG, and requires much shorter running time than IN when the problem dimension is high., Comment: Final version submitted to Allerton Conference 2017 on Oct 8, 2017

Enabling low power wireless devices to adopt Nyquist sampling at high carriers is prohibitive. In spectrum sensing, this limit calls for an analog front-end that can sweep different bands quickly, in order to use the available spectrum opportunistically. In this paper we propose a new framework that allows to optimize a sub-Nyquist sampling front-end to combine the benefits of optimum sequential sensing with those of Compressive Spectrum Sensing (CSS). The sensing strategy we propose is formulated as a sequential utility optimization problem. The utility function decreases linearly with the number of measurements (accrued to make a decision) and increases as a function of the signal components binary states. The optimization selects the best linear combinations of sub-bands to mix, in order to accrue maximum utility. The structure of the utility represents the trade-off between exploration, exploitation and risk of making an error, that is characteristic of the spectrum sensing problem. We first present the analog front-end architecture, and then map the measurement model into the abstract optimization problem proposed, and analyzed, in the remainder of the paper. We characterize the optimal policy under constraints on the sensing matrix and derive the approximation factor of the greedy approach. Numerical simulations showcase the benefits of combining opportunistic spectrum sensing with sub-Nyquist sampling., Comment: submitted to IEEE Transactions on Cognitive Communications and Networking

This paper considers a decentralized projection free algorithm for non-convex optimization in high dimension. More specifically, we propose a Decentralized Frank-Wolfe (DeFW) algorithm which is suitable when high dimensional optimization constraints are difficult to handle by conventional projection/proximal-based gradient descent methods. We present conditions under which the DeFW algorithm converges to a stationary point and prove that the rate of convergence is as fast as O(l/√T), where T is the iteration number. This paper provides the first convergence guarantee for FrankWolfe methods applied to non-convex decentralized optimization. Utilizing our theoretical findings, we formulate a novel robust matrix completion problem and apply DeFW to give an efficient decentralized solution. Numerical experiments are performed on realistic and synthetic data to support our findings.

When cooperative terminals transmit concurrently, the receiver experiences additional distortion by the presence of radios carrier offsets and time delays. With the inevitable inaccuracy in estimating the channel at the receiving end, is it realistic to assume that relays transmissions do not collide? To address this question, we provide an analytical framework to model the effect of channel estimation methods that treat the channel as deterministic and unknown, and derive the average symbol error rate (SER) of a maximum likelihood sequence decoder (MLSD) and of a linear minimum mean squared error (LMMSE) equalizer using such estimates. We select the appropriate architecture by mapping two different channel estimation techniques onto the proposed analytical framework, and derive their diversity gain. First we analyze the well known linear least square channel estimation (LLSE), then, we show how to cast a compressed channel sensing (CCS) method onto our analytical model, by a novel approximation of the estimator noise and modeling mismatch. We observe that the latter is the key bottleneck in LLSE whereas the CCS appears sufficiently flexible to deliver the promised gains. This conclusion shows that collisions models are overly pessimistic, but it also underscores the need for an advanced receiver synchronization design.

In this paper, we are concerned with the identification of linear systems' impulse responses modeled as deterministic multipath channels. In the class of channels we study, we consider the effect of delays, Doppler shifts, and different angles of arrival and departure for each signal path. We explore the efficacy of techniques based on sparse signal recovery, which typically define a basis constructed using a finite quantization grid over the parameter space, and approximate the impulse response as a sparse linear combination over such basis. Our goal is to provide guidelines on the design of pilot sequences that are sufficiently informative (SI), i.e., those inputs that guarantee identifiability of system impulse responses that fit in the sparse model. Inputs that are SI provide minimal requirements for uniquely identifying the system response. However, a smaller class of inputs leads to good mean squared estimation error in the presence of noise and modeling errors, due to the finite precision of the parameter space quantization. To single out the class of robust designs, we provide a new metric, called localized coherence, in lieu of the so called mutual coherence, as a measure for ranking SI designs in terms of robustness to noise and to modeling errors.

The 17 papers in this special issue focus on the design and applications of gossiping algorithms.

Motivated by applications in multi-sensor array detection and estimation, this paper studies the problem of tracking the principal eigenvector and the principal subspace of a signal's covariance matrix adaptively in a fully decentralized wireless sensor network (WSN). Sensor networks are traditionally designed to simply gather raw data at a fusion center, where all the processing occurs. In large deployments, this model entails high networking cost and creates a computational and storage bottleneck for the system. By leveraging both sensors' abilities to communicate and their local computational power, our objective is to propose distributed algorithms for principal eigenvector and principal subspace tracking. We show that it is possible to have each sensor estimate only the corresponding entry of the principal eigenvector or corresponding row of the p-dimensional principal subspace matrix and do so by iterating a simple computation that combines data from its network neighbors only. This paper also examines the convergence properties of the proposed principal eigenvector and principal subspace tracking algorithms analytically and by simulations.

In recent years, many sparse estimation methods, also known as compressed sensing, have been developed. However, most of these methods presume that the measurement matrix is completely known. We develop a new blind maximum likelihood method — the expectation-sparse-maximization (ESpaM) algorithm — for models where the measurement matrix is the product of one unknown and one known matrix. This method is a variant of the expectation-maximization algorithm to deal with the resulting problem that the maximization step is no longer unique. The ESpaM algorithm is justified theoretically. We present as well numerical results for two concrete examples of blind channel identification in digital communications, a doubly-selective channel model and linear time invariant sparse channel model.

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the ldquomixing parameterrdquo on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results.

In this paper, we consider the problem of lossy coding of correlated vector sources with uncoded side information available at the decoder. In particular, we consider lossy coding of vector source xisinRN which is correlated with vector source yisinRN, known at the decoder. We propose two compression schemes, namely, distributed adaptive compression (DAC) and distributed universal compression (DUC) schemes. The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loegraveve transform (CKLT) of the data at the encoder. The DUC algorithm, however, does not require knowledge of the CKLT at the encoder. The DUC algorithms are based on the approximation of the correlation model between the sources y and x through a linear model y=Hx+n in which H is a matrix and n is a random vector and independent of x. This model can be viewed as a fictitious communication channel with input x and output y. Utilizing channel equalization at the receiver, we convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose for both compression schemes a rate allocation policy which minimizes the decoding error rate under a total rate constraint. Equalization and bit loading are paired with a quantization scheme for each vector source entry (a slightly simplified version of the so called DISCUS scheme). The merits of our work are as follows: 1) it provides a simple, yet optimized, implementation of Wyner-Ziv quantizers for correlated vector sources, by using the insight gained in the design of communication systems; 2) it provides encoding schemes that, with or without the knowledge of the correlation model at the encoder, enjoy distributed compression gains

In handling massive-scale signal processing problems arising from ‘big-data’ applications, key technologies could come from the development of decentralized algorithms. In this context, consensus-based methods have been advocated because of their simplicity, fault tolerance and versatility. This paper presents a new consensus-based decentralized algorithm for a class of non-convex optimization problems that arises often in inference and learning problems, including ‘sparse dictionary learning’ as a special case. For the proposed algorithm, we provide sufficient conditions for convergence to a stationary point. Numerical results demonstrate the efficacy of the proposed algorithm and provide evidence that validates our convergence claim.

In this paper, affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols. The channel input is a training vector superimposed on a linearly precoded vector of symbols. A block-fading frequency-selective multi-input multi-output (MIMO) channel is considered. To highlight the tradeoffs between training and data symbols, the Fisher information matrix (FIM) is derived under two circumstances: the random parameter vector to be estimated contains 1) only fading channel coefficients and 2) unknown data symbols as well as the channel coefficients. While strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols, strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly. The interesting outcome of the study in this paper is that minimizing the channel Cramer-Rao bound (CRB) for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines.

Our goal in this paper is to study the effect of the receiver structure upon the achievable data rates. We consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output (MIMO) wireless channel. To encompass a number of transmission schemes, we study this problem utilizing affine precoding, which is a unified model of linearly precoded data symbols with superimposed training. We focus on Bayesian receivers that estimate both the unknown fading coefficients and the data symbols. The receiver may adopt either of the following strategies to retrieve the data symbols: strategy (i) the receiver obtains joint Bayesian channel and symbol estimates, strategy, (ii) the receiver obtains a Bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols. For both strategies, we provide lower bounds on the mutual information between the data symbols and their corresponding estimates, and we relate these bounds to the symbol Cramer-Rao bound (CRB) matrices. In contrast to strategy (ii), for strategy (i) the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error. For strategy (ii) we show that asymptotically (as the size of the transmission block grows) there is no loss of information after the maximum a posteriori (MAP) estimate of Gaussian symbols. We also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint.

We introduce a new paradigm for the design of transmitter space-time coding that we refer to as linear precoding. It leads to simple closed-form solutions for transmission over frequency-selective multiple-input multiple-output (MIMO) channels, which are scalable with respect to the number of antennas, size of the coding block, and transmit average/peak power. The scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension. The specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses, under average and peak power constraints. The solutions are shown to convert the MIMO channel with memory into a set of parallel flat fading subchannels, regardless of the design criterion, while appropriate power/bits loading on the subchannels is the specific signature of the different designs. The proposed designs are compared in terms of various performance measures such as information rate, BER, and symbol mean square error.

An implicit assumption made in studies on state estimation is that the time and frequency at which these measurements are taken is consistent across all the distributed sensing sites. For instance, in the literatures on Wide Area Measurement Systems (WAMS) deployed in the power grid, where the sensors equipped with Global Positioning Signals (GPS), the sensing sites are deemed capable to provide perfectly synchronous readings at the various sampling sites. The validity of the assumption may need to be re-examined with the recent advancements in decentralized state estimation algorithms. Importantly, when there are timing offsets between sampling devices, the effects on the measurement system's performance can be catastrophic. The prevalent point of view is to either study the resulting error, or to resort to Kalman filtering for aligning the measurements. Taking on this view typically requires additional information about the underlying state. In this paper, we revisit the problem of state estimation and propose a new model for data acquisition under asynchronous sampling. The key idea is to apply sampling theory and to exploit the redundancy in the spatial sampling to interpolate the system state. We provide a necessary and sufficient condition for identifiability of the time offsets and propose an algorithm for the joint regression on state and timing offsets. The efficacy of the proposed algorithm is shown by numerical simulations.

In this paper we formulate a Multi-Armed Bandit Compressive Spectrum Sensing (MAB-CSS) problem, in which a Cognitive Receiver (CR) decides dynamically how to best sense N sub-channels states, that switch from being occupied to being available as independent and statistically identical Markov chains. We assume that the CR is endowed with K CSS samplers each sensing an arbitrary mixture of the N signals in the sub-channels, and upon deciding what channels are available, it collects an equal reward from each channel unoccupied that is sensed. The MAB-CSS problem accounts for the ability of the CR of sweeping a large spectrum and being able to reconstruct the exact support of the N channels occupancy pattern, as long as the latter is sufficiently sparse. This is a generalization of the typical model in which the CR can sense K out of the N sub-channels. In choosing the compressive sensing strategy, the CR needs to consider how to gather the most informative statistics on the spectrum while not exceeding the limits beyond which the occupancy is no longer identifiable. In this work, we study a simplified and noiseless discrete sensing model and establish the structure of the optimum MAB-CSS myopic policy.

In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying $N$ dimensional random vector, by collecting at most $K$ arbitrary projections of it. The $N$ components of the latent vector represent sub-channels states, that change dynamically from "busy" to "idle" and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense $K$ out of the $N$ sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes $K$ linear combinations of the $N$ dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable., 8 pages, 2 figures

For pt.I see ibid., vol.47, no.7, p.1988-2006 (1999). Transmitter redundancy introduced using finite impulse response (FIR) filterbank precoders offers a unifying framework for single- and multiuser transmissions. With minimal rate reduction, FIR filterbank transmitters with trailing zeros allow for perfect (in the absence of noise) equalization of FIR channels with FIR zero-forcing equalizer filterbanks, irrespective of the input color and the channel zero locations. Exploiting this simple form of redundancy, blind channel estimators, block synchronizers, and direct self-recovering equalizing filterbanks are derived in this paper. The resulting algorithms are computationally simple, require small data sizes, can be implemented online, and remain consistent (after appropriate modifications), even at low SNR colored noise. Simulations illustrate applications to blind equalization of downlink CDMA transmissions, multicarrier modulations through channels with deep fades, and superior performance relative to CMA and existing output diversity techniques relying on multiple antennas and fractional sampling.

Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPSs) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results.

This paper considers a large sensor network with its nodes taking measurements from certain distributions, while a small subset of the nodes draw anomalous measurements from distributions that differ from the majority. Since all the distributions are unknown a priori, the compressive anomaly detection (CAD) algorithm is proposed at the fusion center to identify the set of anomalous sensors and estimate both the common and anomaly distributions, using only few compressed sensor observations under the type-based multiple access (TB-MA) protocol. Simulations demonstrate that the proposed CAD algorithm can efficiently single out the set of anomalies and estimate the distributions accurately.

In this paper, we formulate a cognitive radio (CR) systems spectrum sensing (SS) problem in which Secondary Users (SU), with multiple receive antennae, sense a channel shared among multiple asynchronous Primary Users (PU) transmitting Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) signals. The method we propose to estimate the opportunities available to the SUs combines advances in array processing and compressed channel sensing, and leverages on both the so called “shrinkage method” as well as on an over-complete basis expansion of the PUs interference covariance matrix to detect the occupied and idle angles of arrivals and subcarriers. The covariance “shrinkage” step and the sparse modeling step that follows, allow to resolve ambiguities that arise when the observations are scarce, reducing the sensing cost for the SU, thereby increasing its spectrum exploitation capabilities compared to competing sensing methods. Simulations corroborate these claims.

This paper formulates the Central Detection Officer (CDO) problem in which a central officer decides if some agents in a network observe data from an anomalous distribution compared to the majority. Since the data statistics are unknown in advance, the goal of the CDO is to identify the data pattern of each agent and detect the presence and locations of anomalies by polling the agents strategically. To solve the CDO problem in a Gaussian multiple access channel, the Sparsity-Aware Least Squares Anomaly (SALSA) detection scheme is proposed, which combines a type-based encoder for the agents data with a compressive network polling scheme. The performances of the proposed scheme are analyzed theoretically and demonstrated numerically.

This paper considers the problem of separating streams of unknown non-stationary signals from under-determined mixtures of sources. The source signals are modeled as a hidden Markov model (HMM) where each state in the Markov chain is determined by a set of on (i.e., active) or off (i.e., inactive) states of the sources, with some unknown probability density functions (pdfs) in the on-state. Under the assumption that the number of active sources is small compared to the total number of sources (thus the sources are sparse), the goal is to recursively estimate the HMM state and the over-complete mixing matrix (subsequently the source signals) for signal recovery. The proposed approach combines the techniques of HMM-based filtering and manifold-based dictionary learning for estimating both the state and the mixing matrix. Specifically, we model the on/off state of the source signals as a hidden Markov model. In particular, we consider only a sparse set of simultaneously active sources. Thus, this setting generalizes the typical scenario considered in dictionary learning in which there is a sparse number of temporally independent active signals. To extract the activity profile of the sources from the observations, a technique known as change-of-measure is used to decouple the observations from the sources by introducing a new probability measure over the set of observations. Under this new measure, the un-normalized conditional densities of the state and the transition matrix of the Markov chain can be computed recursively. Due to the scaling ambiguity of the mixing matrix, we introduce an equivalence relation, which partitions the set of mixing matrices into a set of equivalence classes. Rather than estimating the mixing matrix by imposing the unit-norm constraint, the proposed algorithm searches directly for an equivalence class that contains the true mixing matrix. In our simulations, the proposed recursive algorithm with manifold-based dictionary learning, compared to algorithms with unit-norm constraint, estimates the mixing matrix more efficiently while maintaining high accuracy.

An important receiver operation is to detect the presence specific preamble signals with unknown delays in the presence of scattering, Doppler effects and carrier offsets. This task, referred to as "link acquisition", is typically a sequential search over the transmitted signal space. Recently, many authors have suggested applying sparse recovery algorithms in the context of similar estimation or detection problems. These works typically focus on the benefits of sparse recovery, but not generally on the cost brought by compressive sensing. Thus, our goal is to examine the trade-off in complexity and performance that is possible when using sparse recovery. To do so, we propose a sequential sparsity-aware compressive sampling (C-SA) acquisition scheme, where a compressive multi-channel sampling (CMS) front-end is followed by a sparsity regularized likelihood ratio test (SR-LRT) module. The proposed C-SA acquisition scheme borrows insights from the models studied in the context of sub-Nyquist sampling, where a minimal amount of samples is captured to reconstruct signals with Finite Rate of Innovation (FRI). In particular, we propose an A/D conversion front-end that maximizes a well-known probability divergence measure, the average Kullback-Leibler distance, of all the hypotheses of the SR-LRT performed on the samples. We compare the proposed acquisition scheme vis-\`{a}-vis conventional alternatives with relatively low computational cost, such as the Matched Filter (MF), in terms of performance and complexity., Comment: to appear in IEEE Transactions on Signal Processing

A sensitive receiver operation in multi-access reception is to detect the presence of training signals and identify sources from which the signals are sent, with a certain physical delay and center frequency. This is typically a sequential search, where the receiver tests the presence of specific signals and then acquires synchronization parameters (delays, Dopplers), for each component. In this paper, we develop an optimal compressive multichannel sampling (CMS) architecture, the output samples of which are fed to the proposed Sparsity Regularized (SR) Generalized Likelihood Ratio Test (GLRT). It is shown that SR-GLRT using the optimal sampling scheme exhibits better performance than conventional compressed sensing structure, and furthermore effectively scales down the storage requirement and complexity with greater flexibility than conventional architectures.

In this paper, we propose an efficient acquisition scheme for GPS receivers. It is shown that GPS signals can be effectively sampled and detected using a bank of randomized correlators with much fewer chip-matched filters than those used in existing GPS signal acquisition algorithms. The latter use correlations with all possible shifted replicas of the satellite-specific C/A code and an exhaustive search for peaking signals over the delay-Doppler space. Our scheme is based on the recently proposed analog compressed sensing framework, and consists of a multichannel sampling structure with far fewer correlators. The compressive multichannel sampler outputs are linear combinations of a vector whose support tends to be sparse; by detecting its support one can identify the strongest satellite signals in the field of view and pinpoint the correct code-phase and Doppler shifts for finer resolution during tracking. The analysis in this paper demonstrates that GPS signals can be detected and acquired via the proposed structure at a lower cost in terms of number of correlations that need to be computed in the coarse acquisition phase, which in current GPS technology scales like the product of the number of all possible delays and Doppler shifts. In contrast, the required number of correlators in our compressive multichannel scheme scales as the number of satellites in the field of view of the device times the logarithm of number of delay-Doppler bins explored, as is typical for compressed sensing methods., 25 pages, 7 figures, submitted to Physical Communication, Elsevier, Special Issue on Compressive Sensing in Communications

In this paper we are concerned with the estimation of doubly-selective multi-path communication channels trough methods referred to as compressed channel sensing. Many authors have used the Restricted Isometry Property (RIP) as a guiding principle to select training to ensure good estimation performance. In this paper we discuss why this approach can be restrictive and why its entanglement with modeling aspects can be misleading. More importantly, we provide an alternative approach to classify inputs based on a new metric that we call localized coherence.

Consensus algorithms permit the computation of global statistics via local communications and without centralized control. We extend previous results by taking into account fading and unidirectional links in ring and random 2-D topologies. We study conditions for convergence and present simulation results to verify the analytical results in this paper. We compare the performance of consensus algorithms with a tree-based (centralized) approach. Additionally, we implement a slotted ALOHA protocol and compare its performance to that under the initial assumption of perfect scheduling.

In recent years many sparse estimation methods, also known as compressed sensing, have been developed for channel identification problems in digital communications. However, all these methods presume the transmitted sequence of symbols to be known at the receiver, i.e. in form of a training sequence. We consider blind identification of the channel based on maximum likelihood (ML) estimation via the EM algorithm incorporating a sparsity constraint in the maximization step. We apply this algorithm to an OFDM transmission over a doubly-selective multipath channel with strong Doppler and delay spread.

We consider the design of sufficiently informative inputs for estimating the parameters of a time-varying linear system. Specifically, we assume the output of the system may be modeled as linear combinations of known time-varying elements whose parameters are points in an appropriately chosen grid for the parameter space, such that these parameters are sparse in comparison with the grid size. The sufficiently informative inputs we study are signals that guarantee a unique sparsest solution thereby satisfying minimum requirements for numerically solving the estimation problem. Since in practice the parameters of interest may not lie on the grid constructed for the parameter space, we discuss how our input designs can be modified to provide robustness in the presence of modeling error and noise.

We consider a fully decentralized model for adaptively tracking the signal’s principal subspace, which arises in multi-sensor array detection and estimation problems. Our objective is to equip the network of dispersed sensors with a primitive for online spectrum sensing, which does not require a central fusion node. In this model, each node updates its local subspace estimate with its received data and a weighted average of the neighbors’ data. The quality of the estimate is measured by the total subspace mismatch of the individual subspace component estimates, which converge asymptotically in the Lyapunov sense.

We examine the application of current research in sparse signal recovery to the problem of channel estimation. Specifically, using an orthogonal frequency division multiplexed (OFDM) transmission scheme with pilot symbol assisted modulation (PSAM), we consider the problem of identifying a frequency selective channel from a limited number Q out of a possible M tones of an OFDM symbol. The main observation is that if M is chosen as prime, one can identify the channel uniquely if Q ges 2T, where T is the number of nonzero taps in the frequency-selective channel. The identifiability result requires the minimization of the lo norm, leading to an intractable combinatorial search problem. Several methods have been proposed to deal with these issues, and the one we examine involves l1 norm regularization known as basis pursuit, We apply these methods specifically to the problem of estimating a frequency selective channel with PSAM. As a result, the bandwidth efficiency of the system is increased due to the sparsity of the channel.

In this paper, we study the decentralized version of the classical rate constrained Gaussian parameter estimation problem referred to as the Central Estimation Officer (CEO) problem which we refer to as the Decentralized Estimation Officers (DEO) problem. Like in the CEO case, we consider a group of N sensors observing an independently corrupted version of an infinite i.i.d. sequence of samples from a Gaussian source, in additive Gaussian noise. Unlike the CEO case, the sensors in our study are also the estimation officers. They are uniformly deployed in a circular pattern of radius r and communicate over RF links with limited energy. Their task is to reconstruct the quantity of interest (the samples of the source), without a central fusion node, better than what they are capable of with their local observations. We find achievable scaling laws by structuring our communication protocol as an instance of the so called average consensus algorithm, a gossiping protocol used for averaging original sensor measurements via near neighbors communications. We derive how the Mean Squared Error (MSE) of the sensors' estimation scales with the network size, per node power and ring radius r. Moreover, we compare our results with scaling laws previously derived for the centralized case, i.e, the CEO problem in a comparable scenario.

Average consensus algorithms are gossiping protocols for averaging original measurements taken at different sensors. Without any communication rate restrictions, the algorithms ideally allow every node state to converge to the initial average after some iterations. Noting that brute force quantization is highly suboptimal given the rich temporal and spatial correlation of the messages exchanged, in our previous work we proposed two source coding methods, predictive coding and Wyner-Ziv coding which achieve convergence with vanishing quantization rates in the case of block coding. Both methods ideally require complete information about the network parameters and topology as well as processing and storage of the past state values. The knowledge of the network parameters is not a practical requirement, especially considering that one is implementing average consensus algorithms that are decentralized. In this study we show that as the node density increases or in homogeneously distributed networks, the encoder and decoder parameters become independent on the network size and specific location. We also lower bound the error performance of the predictive coding scheme in terms of eigenvalues of the connectivity and initial state covariance matrices. We show the relation between MSE behavior of the algorithm and network connectivity, as well as quantization rate.

In this paper we consider the problem of estimating a vector source in a sensor network, where each sensor in the network makes a local observation of this vector source. We assume that the local observations are distorted and noise corrupted versions of the original signal source, i.e., the observation of m-th sensor ym and the signal source x are related through ym = Hmx+nm where the matrix Hm represents the distortion (filtering) effect and nm denotes the additive noise. Each sensor encodes its observation separately and sends the encoded message to a central processor (CP), whose task is to form an estimate of source x. Our objective is to design quantizers such that the distortion in the source estimate formed by the CP is minimized, subject to the sum quantization rate constraint. Realizing the resemblance of this problem to the classical CEO problem in multiterminal source coding, and inspired by the work in [S. C. Draper and G. W. Wornell, "Side information aware coding strategies for sensor networks," IEEE Journal on Selected Areas in Comm., Vol.22, No.6, pp 966-976, August 2004.], we propose a successive coding and decoding strategy, based on Wyner-Ziv coding concept. Numerical evaluation of the sum rate-distortion performance of the proposed algorithm reveals an interesting trade off between sum rate, target distortion, and number of sensor nodes which are participating in the sequential coding.

Considering two correlated vector sources x, y isin RN, we address the problem of lossy coding of x with uncoded side information y available at the decoder. The general non-linear mapping between y and x capturing their correlation can be approximated through a linear model y = Hx + n in which x is independent of x. Viewing this model as a virtual communication channel with input x and output y we utilize linear precoding and decoding technique to convert the original vector source coding problem into a set of manageable scalar source coding problems. The scalar source coding problems can be solved using the existing distributed source coding algorithms that are primarily designed for the simple correlation model y = x + n where x and y are scalar jointly Gaussian sources

In this paper we consider lossy coding of vector source x isin R N which is correlated with vector source y isin RN , known at the decoder. The general non-linear mapping between y and x capturing the correlation between the two sources can be approximated through a linear model y = Hx + n in which n is independent of x. We propose a compression scheme, namely, distributed adaptive compression (DAC). The DAC algorithm is inspired by the optimal solution for Gaussian sources and requires computation of the conditional Karhunen-Loeve transform (CKLT) of the data at the encoder. Viewing the dependency model as a fictitious communication channel we utilize linear minimum mean square error (LMMSE) equalizer at the decoder, to convert the original vector source coding problem into a set of manageable scalar source coding problems. Furthermore, inspired by bit loading strategies employed in wireless communication systems, we propose a rate allocation policy which minimizes the decoding error rate under a total rate constraint

In this paper, we address the problem of data transmission over a block fading frequency selective multi-input multi-output (MIMO) channel. The encoded data symbols are passed through an affine precoder and sent over multiple transmit antennas. Affine precoding is a unifying model of the existing training schemes, namely, preamble based training, pilot symbol assisted modulation (PSAM), and superimposed training. Within this general model, we show that the channel Cramer-Rao bound (CRB) is minimized if the precoded data and training symbols satisfy a special form of orthogonality. Under the power constraint on the training and the preceded symbols, we provide optimal and suboptimal training design guidelines