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Characterized by sudden structural changes, fault-prone systems are modeled using the framework of systems with switching parameters or hybrid systems. Since a closed-form mean-square optimal filtering algorithm for this class of systems does not exist, it is of particular interest to derive a lower bound on the state estimation error covariance. The well known Crameacuter-Rao bound is not applicable to fault-prone systems because of the discrete distribution of the fault indicators, which violates the regularity conditions associated with this bound. On the other hand, the Weiss-Weinstein lower bound is essentially free from regularity conditions. Moreover, a sequential version of the Weiss-Weinstein bound, suitable for Markovian dynamic systems, is presented by the authors in a companion paper. In the present paper, this sequential version is applied to several classes of fault-prone dynamic systems. The resulting bounds can be used to examine fault detectability and identifiability in these systems. Moreover, it is shown that several recently reported lower bounds for fault-prone systems are special cases of, or closely related to, the sequential version of the Weiss-Weinstein lower bound [ABSTRACT FROM PUBLISHER]

This paper presents a game theory approach to the constrained state estimation of linear discrete time dynamic systems. In the application of state estimators, there is often known model or signal information that is either ignored or dealt with heuristically. For example, constraints on the state values (which may be based on physical considerations) are often neglected because they do not easily fit into the structure of the state estimator. This paper develops a method for incorporating state equality constraints into a minimax state estimator. The algorithm is demonstrated on a simple vehicle tracking simulation. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of unsupervised Bayesian hidden Markov chain restoration. When the hidden chain is stationary, the classical "Hidden Markov Chain" (HMC) model is quite efficient, and associated unsupervised Bayesian restoration methods using the "Expectation-Maximization" (EM) algorithm work well. When the hidden chain is non stationary, on the other hand, the unsupervised restoration results using the HMC model can be poor, due to a bad match between the real and estimated models. The novelty of this paper is to offer a more appropriate model for hidden nonstationary Markov chains, via the theory of evidence. Using recent results relating to Triplet Markov Chains (TMCs), we show, via simulations, that the classical restoration results can be improved by the use of the theory of evidence and Dempster-Shafer fusion. The latter improvement is performed in an entirely unsupervised way using an original parameter estimation method. Some application examples to unsupervised image segmentation are also provided. [ABSTRACT FROM AUTHOR]

Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper. [ABSTRACT FROM AUTHOR]

This paper quantifies the adaptive performance of a blind adaptive multiuser detector (MUD) based on the linearly constrained constant modulus algorithm (LCCMA) in both a stationary and nonstationary channel. A framework is developed to apply the feedback analysis method to analyzing adaptive MUD schemes. A closed-form expression for the excess mean square error (EMSE) of LCCMA blind adaptive MUD in a CDMA communications system is derived for both of the steady-state and tracking cases. The effects of additive noise and multiple access interference are considered. A transient analysis is performed that predicts the learning curve of the adaptive filter. Computer simulation is used to verify the accuracy of the analysis. [ABSTRACT FROM AUTHOR]

A maximum likelihood (ML)-based algorithm for frequency estimation and synchronization of frequency hopping signals is proposed in this paper. By using a two-hop signal model that incorporates the unknown hop transition time, the likelihood function of the received frequency hopping signal is formulated. A new iterative method is then derived to estimate the hopping frequencies and hop transition time. Without using any pilot signal or sync bit, the new algorithm is able to implement synchronization and frequency estimation at the same time. Unlike the time-frequency distribution (TFD) and the wavelet-based algorithms in papers by Barbarossa and Scaglione and by Khalil and Hippenstiel, the new ML algorithm does not require the selection of a kernel or mother wavelet function. In addition, compared with the TFD-based algorithm, it has a better performance with a lower implementation complexity. [ABSTRACT FROM AUTHOR]

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over R[x] or C[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9. [ABSTRACT FROM AUTHOR]

While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that the proposed algorithm can achieve an $\epsilon$ -stationary solution under a constant step size with $\mathcal {O}(1/\epsilon ^2)$ computation complexity and $\mathcal {O}(1/\epsilon)$ communication complexity when the epigraph of the non-smooth term is a polyhedral set. When compared to the existing gradient tracking based methods, the proposed algorithm has the same order of computation complexity but lower order of communication complexity. To the best of our knowledge, the presented result is the first stochastic algorithm with the $\mathcal {O}(1/\epsilon)$ communication complexity for non-convex and non-smooth problems. Numerical experiments for a distributed non-convex regression problem and a deep neural network based classification problem are presented to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel adaptive importance sampling (AIS) algorithm for probabilistic inference. The sampler learns a proposal distribution adaptation strategy by framing AIS as a reinforcement learning problem. Under this structure, the proposal distribution of the sampler is treated as an agent whose state is controlled using a parameterized policy. At each iteration of the algorithm, the agent earns a reward that is related to its contribution to the variance of the AIS estimator of the normalization constant of the target distribution. Policy gradient methods are employed to learn a locally optimal policy that maximizes the expected value of the sum of all rewards. Numerical simulations on two different examples demonstrate promising results for the future application of the proposed method to complex Bayesian models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the policy evaluation problem in reinforcement learning with agents on a decentralized and directed network. In order to evaluate the quality of a fixed policy in this decentralized setting, one option is for agents to run decentralized temporal-difference (TD) collaboratively. To account for the practical scenarios where the state and action spaces are large and malicious attacks emerge, we focus on the decentralized TD learning with linear function approximation in the presence of malicious agents (often termed as Byzantine agents). We propose a trimmed mean-based Byzantine-resilient decentralized TD algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents algorithms for the parallelization of inference in hidden Markov models (HMMs). In particular, we propose a parallel forward-backward type of filtering and smoothing algorithm as well as a parallel Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements and operators to pose these inference problems as all-prefix-sums computations and parallelize them using the parallel-scan algorithm. The advantage of the proposed algorithms is that they are computationally efficient in HMM inference problems with long time horizons. We empirically compare the performance of the proposed methods to classical methods on a highly parallel graphics processing unit (GPU). [ABSTRACT FROM AUTHOR]

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP’ SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate designs of linear precoders for vector Gaussian channels via stochastic optimizations and deep neural networks (DNNs). We assume that the channel inputs are drawn from practical finite alphabets, and we search for precoders maximizing the mutual information between channel inputs and outputs. Though the problem is generally non-convex, we prove that when the right singular matrix of precoder is fixed, any local optima of this problem is a global optima. Based on this fact, an efficient projected stochastic gradient descent (PSGD) algorithm is designed to search the optimal precoders. Moreover, to reduce the complexity of calculating a posterior means involved in gradients calculation, K-best algorithm is adopted to make approximations of a posterior means with negligible loss of accuracy. Furthermore, to avoid explicit calculation of mutual information and its gradients, DNN-based autoencoders (AEs) are constructed for this precoding task, and an efficient training algorithm is proposed. We also prove that the AEs, with ‘softmax’ activation function and ‘categorical cross entropy’ loss, maximize the mutual information under reasonable assumptions. Then, in order to extend the AE methods to large scale systems, ‘sigmoid’ activation function and ‘binary cross entropy’ loss are used such that the size of AEs will not grow prohibitively large. We prove that this maximizes a lower bound of the mutual information under reasonable assumptions. Finally, to make the precoders practical for high speed wireless scenarios, we propose an offline training paradigm which trains DNNs to infer optimal precoders given channel state information instead of training online for every different channel. Simulation results show that all the proposed methods work well in maximizing mutual information and improving bit error rate (BER) performance. [ABSTRACT FROM AUTHOR]

Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these approaches can be viewed within the mathematical context of functional composition. This paper re-interprets and generalizes within the functional composition framework one such approach known as filter sharpening, i.e., interconnecting filter modules which have significant approximation error in order to obtain improved filter characteristics. More specifically, filter sharpening is approached by determining the composing polynomial to minimize the infinity-norm of the approximation error, utilizing the First Algorithm of Remez. This is applied both to sharpening for FIR, even-symmetric filters and for the more general case of subfilters that have complex-valued frequency responses including causal IIR filters and for continuous-time filters. Within the framework of functional composition, this paper also explores the use of functional decomposition to approximate a desired system as a composition of simpler functions based on a two-norm on the approximation error. Among the potential advantages of this decomposition is the ability for modular implementation in which the inner component of the functional decomposition represents the subfilters and the outer the interconnection. [ABSTRACT FROM AUTHOR]

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing “related” objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the union-of-subspaces model, and is termed the metric-constrained union-of-subspaces (MC-UoS) model. The second one of these models—suited for data drawn from a mixture of nonlinear manifolds—generalizes the kernel subspace model, and is termed the metric-constrained kernel union-of-subspaces (MC-KUoS) model. The main contributions of this paper in this regard include the following. First, it motivates and formalizes the problems of MC-UoS and MC-KUoS learning. Second, it presents algorithms that efficiently learn an MC-UoS or an MC-KUoS underlying data of interest. Third, it extends these algorithms to the case when parts of the data are missing. Last, but not least, it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed geometric models and learning algorithms over existing approaches in the literature. These experiments also help clarify the connections between this work and the literature on (subspace and kernel k-means) clustering. [ABSTRACT FROM AUTHOR]

In Part I of the study of the tensor deflation for CANDECOMP/PARAFAC, we have shown that the rank-1 tensor deflation is applicable under some conditions. Part II of the study presents several initialization algorithms suitable for the algorithm proposed in Part I. In addition, Part II contains an algorithm for the case when one or more factor matrices in the estimated model is constrained to be orthogonal. Finally, Part II provides an error analysis of the tensor deflation algorithm, which shows that there is a marginal loss of accuracy of the deflation algorithm compared to the ordinary CP decomposition. [ABSTRACT FROM PUBLISHER]

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting \ell^1-regularized least squares problem by coupling the primal dual active set strategy with a continuation technique (on the regularization parameter). In the active set strategy, we first determine the active set from primal and dual variables, and then update the primal and dual variables by solving a low-dimensional least square problem on the active set, which makes the algorithm very efficient. The continuation technique globalizes the convergence of the algorithm, with provable global convergence under restricted isometry property (RIP). Further, we adopt two alternative methods, i.e., a modified discrepancy principle and a Bayesian information criterion, to choose the regularization parameter automatically. Numerical experiments indicate that our algorithm is very competitive with state-of-the-art algorithms in terms of accuracy and efficiency, without a priori information about the regularization parameter. [ABSTRACT FROM AUTHOR]

In traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper, we consider a signal model where each column in the dictionary matrix is affected by a structured noise. This formulation is common in direction-of-arrival (DOA) estimation of off-grid targets, encountered in both radar systems and array processing. We propose to use joint sparse signal recovery to solve the compressed sensing problem with structured dictionary mismatches and also give an analytical performance bound on this joint sparse recovery. We show that, under mild conditions, the reconstruction error of the original sparse signal is bounded by both the sparsity and the noise level in the measurement model. Moreover, we implement fast first-order algorithms to speed up the computing process. Numerical examples demonstrate the good performance of the proposed algorithm and also show that the joint-sparse recovery method yields a better reconstruction result than existing methods. By implementing the joint sparse recovery method, the accuracy and efficiency of DOA estimation are improved in both passive and active sensing cases. [ABSTRACT FROM PUBLISHER]

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is slightly above the number of frequency channels. [ABSTRACT FROM AUTHOR]

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that 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 a priori 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 signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed. [ABSTRACT FROM AUTHOR]

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multikernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a preselected dictionary. The novel multikernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives. [ABSTRACT FROM AUTHOR]

The demand for accurate localization in complex environments continues to increase despite the difficulty in extracting positional information from measurements. Conventional range-based localization approaches rely on distance estimates obtained from measurements (e.g., delay or strength of received waveforms). This paper goes one step further and develops localization techniques that rely on all probable range values rather than on a single estimate of each distance. In particular, the concept of soft range information (SRI) is introduced, showing its essential role for network localization. We then establish a general framework for SRI-based localization and develop algorithms for obtaining the SRI using machine learning techniques. The performance of the proposed approach is quantified via network experimentation in indoor environments. The results show that SRI-based localization techniques can achieve performance approaching the Cramér–Rao lower bound and significantly outperform the conventional techniques especially in harsh wireless environments. [ABSTRACT FROM AUTHOR]

This paper proposes an online multiple object tracker that can operate under unknown detection profile and clutter rate. In a majority of multiple object tracking applications, model parameters for background processes such as clutter and detection are unknown and vary with time; hence, the ability of the algorithm to adaptively learn these parameters is essential in practice. In this paper, we detail how the generalized labeled multibernoulli filter, a tractable and provably Bayes optimal multiobject tracker, can be tailored to learn clutter and detection parameters on-the-fly while tracking. Provided that these background model parameters do not fluctuate rapidly compared to the data rate, the proposed algorithm can adapt to the unknown background yielding better tracking performance. [ABSTRACT FROM AUTHOR]

This paper considers the mean-reverting portfolio (MRP) design problem arising from statistical arbitrage (a.k.a. pairs trading) in the financial markets. It aims at designing a portfolio of underlying assets by optimizing the mean reversion strength of the portfolio, while taking into consideration the portfolio variance and an investment budget constraint. Several specific design problems are considered based on different mean reversion criteria. Efficient algorithms are proposed to solve the problems. Numerical results on both synthetic and market data show that the proposed MRP design methods can generate consistent profits and outperform the traditional design methods and the benchmark methods in the literature. [ABSTRACT FROM AUTHOR]

This paper develops a novel algorithm, termed SPARse Truncated Amplitude flow (SPARTA), to reconstruct a sparse signal from a small number of magnitude-only measurements. It deals with what is also known as sparse phase retrieval (PR), which is NP-hard in general and emerges in many science and engineering applications. Upon formulating sparse PR as an amplitude-based nonconvex optimization task, SPARTA works iteratively in two stages: In stage one, the support of the underlying sparse signal is recovered using an analytically well-justified rule, and subsequently a sparse orthogonality-promoting initialization is obtained via power iterations restricted on the support; and in the second stage, the initialization is successively refined by means of hard thresholding based gradient-type iterations. SPARTA is a simple yet effective, scalable, and fast sparse PR solver. On the theoretical side, for any n-dimensional k-sparse (k ≪ n) signal x with minimum (in modulus) nonzero entries on the order of (1/√k)||x||2, SPARTA recovers the signal exactly (up to a global unimodular constant) from about k2 log n random Gaussian measurements with high probability. Furthermore, SPARTA incurs computational complexity on the order of k2 n log n with total runtime proportional to the time required to read the data, which improves upon the state of the art by at least a factor of k. Finally, SPARTA is robust against additive noise of bounded support. Extensive numerical tests corroborate markedly improved recovery performance and speedups of SPARTA relative to existing alternatives. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into expectation-maximization-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector case to the temporally correlated multiple measurement vector case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments. [ABSTRACT FROM AUTHOR]

This paper considers coordinated multicast beamforming in a multicell multigroup multiple-input single-output system. Each base station (BS) serves multiple groups of users by forming a single beam with common information per group. We propose centralized and distributed beamforming algorithms for two different optimization targets. The first objective is to minimize the total transmission power of all the BSs while guaranteeing the user-specific minimum quality-of-service targets. The semidefinite relaxation (SDR) method is used to approximate the nonconvex multicast problem as a semidefinite program (SDP), which is solvable via centralized processing. Subsequently, two alternative distributed methods are proposed. The first approach turns the SDP into a two-level optimization via primal decomposition. At the higher level, intercell interference powers are optimized for fixed beamformers, whereas the lower level locally optimizes the beamformers by minimizing BS-specific transmit powers for the given intercell interference constraints. The second distributed solution is enabled via an alternating direction method of multipliers, where the intercell interference optimization is divided into a local and a global optimization by forcing the equality via consistency constraints. We further propose a centralized and a simple distributed beamforming design for the signal-to-interference-plus-noise ratio (SINR) balancing problem in which the minimum SINR among the users is maximized with given per-BS power constraints. This problem is solved via the bisection method as a series of SDP feasibility problems. The simulation results show the superiority of the proposed coordinated beamforming algorithms over traditional noncoordinated transmission schemes, and illustrate the fast convergence of the distributed methods. [ABSTRACT FROM PUBLISHER]

In this paper, we study the target tracking problem in a wireless sensor network. A sensor receives a measurement from an energy emitting target and employs binary quantization to the received measurement to generate its decision. A sinusoidal waveform with a certain duration is then used to transmit the sensor decision to the fusion center (FC). All sensor decisions are transmitted to the FC over erroneous wireless channels based on a time division multiple access scheme. We introduce the proportional time allocation (PTA) algorithm where at each time step of tracking, PTA jointly determines the sensors binary quantization thresholds and their time allocations devoted for the transmissions of binary sensor decisions. Simulation results show that, PTA optimally and dynamically distributes the available transmission time among the sensors near the target so that the decisions of such sensors become less subject to channel errors, and turns off the non-informative sensors located far away from the target. Hence, PTA both saves from the number of sensors transmitting to the FC and provides better estimation performance as compared to ad hoc equal time allocation approaches. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of distributed detection in tree topologies in the presence of Byzantines. The expression for minimum attacking power required by the Byzantines to blind the fusion center (FC) is obtained. More specifically, we show that when more than a certain fraction of individual node decisions are falsified, the decision fusion scheme becomes completely incapable. We obtain closed-form expressions for the optimal attacking strategies that minimize the detection error exponent at the FC. We also look at the possible countermeasures from the FC's perspective to protect the network from these Byzantines. We formulate the robust topology design problem as a bi-level program and provide an efficient algorithm to solve it. We also provide some numerical results to gain insights into the solution. [ABSTRACT FROM PUBLISHER]

In this paper, a recursive sliding transform (RST) algorithm is proposed for the fast implementation of the Walsh Hadamard Transform (WHT) on sliding windows. The proposed RST algorithm accelerates the sliding WHT process by recursively reducing the order of WHT. Theoretical analysis shows that the proposed RST algorithm requires only 1.33 additions per sample for each WHT basis vector regardless of the size or dimension of the basis vector. The computational requirement of the proposed RST algorithm is the lowest among existing fast sliding WHT algorithms. [ABSTRACT FROM PUBLISHER]

Node self-localization is a key research topic for wireless sensor networks (WSNs). There are two main algorithms, the triangulation method and the maximum likelihood (ML) estimator, for angle of arrival (AOA) based self-localization. The ML estimator requires a good initialization close to the true location to avoid divergence, while the triangulation method cannot obtain the closed-form solution with high efficiency. In this paper, we develop a set of efficient closed-form AOA based self-localization algorithms using auxiliary variables based methods. First, we formulate the self-localization problem as a linear least squares problem using auxiliary variables. Based on its closed-form solution, a new auxiliary variables based pseudo-linear estimator (AVPLE) is developed. By analyzing its estimation error, we present a bias compensated AVPLE (BCAVPLE) to reduce the estimation error. Then we develop a novel BCAVPLE based weighted instrumental variable (BCAVPLE-WIV) estimator to achieve asymptotically unbiased estimation of locations and orientations of unknown nodes based on prior knowledge of the AOA noise variance. In the case that the AOA noise variance is unknown, a new AVPLE based WIV (AVPLE-WIV) estimator is developed to localize the unknown nodes. Also, we develop an autonomous coordinate rotation (ACR) method to overcome the tangent instability of the proposed algorithms when the orientation of the unknown node is near \pi/2. We also derive the Cramér-Rao lower bound (CRLB) of the ML estimator. Extensive simulations demonstrate that the new algorithms achieve much higher localization accuracy than the triangulation method and avoid local minima and divergence in iterative ML estimators. [ABSTRACT FROM PUBLISHER]

The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented. To this end, an alternative view on the Volterra series is established, which enables the utilization of certain modified linear iterative methods for linearization. For one particular linear iterative method, the Richardson iteration, the corresponding post- and pre-linearizers are discussed in detail. It is motivated that the resulting algorithm can be regarded as a generalization of some existing methods. Furthermore, a simply verifiable condition for convergence is presented, which allows the straightforward evaluation of applicability. The proposed method is demonstrated by means of the linearization of a time-varying nonlinear amplifier, which highlights its capability of linearizing significantly distorted signals, illustrates the advantageous convergence behavior, and depicts its robustness against modeling errors. [ABSTRACT FROM PUBLISHER]

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems—as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity. [ABSTRACT FROM AUTHOR]

The emergence of big data has caused a dramatic shift in the operating regime for optimization algorithms. The performance bottleneck, which used to be computations, is now often communications. Several gradient compression techniques have been proposed to reduce the communication load at the price of a loss in solution accuracy. Recently, it has been shown how compression errors can be compensated for in the optimization algorithm to improve the solution accuracy. Even though convergence guarantees for error-compensated algorithms have been established, there is very limited theoretical support for quantifying the observed improvements in solution accuracy. In this paper, we show that Hessian-aided error compensation, unlike other existing schemes, avoids accumulation of compression errors on quadratic problems. We also present strong convergence guarantees of Hessian-based error compensation for stochastic gradient descent. Our numerical experiments highlight the benefits of Hessian-based error compensation, and demonstrate that similar convergence improvements are attained when only a diagonal Hessian approximation is used. [ABSTRACT FROM AUTHOR]

This paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases. A computationally efficient iterative algorithm for the continuous phase case (IA-CPC) is proposed to sequentially optimize the quadratic objective function. The quadratic optimization problem is turned into multiple one-dimensional optimization problems with closed-form solutions. For the discrete phase case, we present an iterative block optimization algorithm. Specifically, we partition the design variables into $K$ blocks, and then, we sequentially optimize each block via exhaustive search while fixing the remaining $K-1$ blocks. Finally, we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method-like and semidefinite relaxation related techniques. [ABSTRACT FROM PUBLISHER]

The paper is concerned with stabilizing the family of adaptive filtering algorithms based on minimizing the $2Lth$ moment of the estimation error, with $L$ being an integer greater than 1. Stabilization is attained via a proposed normalization of the algorithm. Mean square stability of the normalized algorithm is proved for a Markov plant for all $L > 1$ . Transient and steady-state performances of the algorithm are analyzed for a time-invariant plant. Expressions are derived for the steady-state misadjustment and convergence time. Tradeoff between the transient and steady-state performances is evaluated. Dependence of this tradeoff on the value of L is studied. This tradeoff is compared with the tradeoff of the NLMS algorithm. The proposed algorithm is dramatically superior to the NLMS algorithm for sub-Gaussian noise. The superiority increases with L, initial mean-square deviation and signal-to-noise ratio. Analytical results are supported by simulations. [ABSTRACT FROM PUBLISHER]

Consider the single-group multicast beamforming problem, where multiple users receive the same data stream simultaneously from a single transmitter. The problem is NP-hard and all existing algorithms for the problem either find suboptimal approximate or local stationary solutions. In this paper, we propose an efficient branch-and-bound algorithm for the problem that is guaranteed to find its global solution. To the best of our knowledge, our proposed algorithm is the first tailored global algorithm for the single-group multicast beamforming problem. Simulation results show that our proposed algorithm is computationally efficient (albeit its theoretical worst-case iteration complexity is exponential with respect to the number of receivers) and it significantly outperforms a state-of-the-art general-purpose global optimization solver called Baron. Our proposed algorithm provides an important benchmark for performance evaluation of existing algorithms for the same problem. By using it as the benchmark, we show that two state-of-the-art algorithms, semidefinite relaxation algorithm and successive linear approximation algorithm, work well when the problem dimension (i.e., the number of antennas at the transmitter and the number of receivers) is small but their performance deteriorates quickly as the problem dimension increases. [ABSTRACT FROM PUBLISHER]

The low-rank matrix completion problem is fundamental to a number of tasks in data mining, machine learning, and signal processing. This paper considers the problem of adaptive matrix completion in time-varying scenarios. Given a sequence of incomplete and noise-corrupted matrices, the goal is to recover and track the underlying low rank matrices. Motivated from the classical least-mean square (LMS) algorithms for adaptive filtering, three LMS-like algorithms are proposed for estimating and tracking low-rank matrices. Performance of the proposed algorithms is provided in form of nonasymptotic bounds on the tracking mean-square error. Tracking performance of the algorithms is also studied via detailed simulations over real-world datasets. [ABSTRACT FROM PUBLISHER]

Based on the minimum noise subspace (MNS) method previously introduced in the context of blind channel identification, generalized minimum noise subspace (GMNS) is proposed in this paper for array processing that generalizes MNS with respect to the availability of only a fixed number of parallel computing units. Different batch and adaptive algorithms are then introduced for fast and parallel computation of signal (principal) and noise (minor) subspaces. The computational complexity of GMNS and its related estimation accuracy are investigated by simulated experiments and a real-life experiment in radio astronomy. It is shown that GMNS represents an excellent tradeoff between the computational gain and the subspace estimation accuracy, as compared to several standard subspace methods. [ABSTRACT FROM PUBLISHER]

Time synchronization is crucial for wireless sensor networks (WSNs) since it maintains data consistency, coordination, and enables other fundamental operations. Over the last decade, a number of powerful time synchronization algorithms have been proposed for clock accuracy optimization by using signal processing techniques. However, most of these algorithms attempt to estimate the clock phase offset and skew and do not correct the node's local clock at every timing packet exchange before the clock parameters are jointly estimated, which reduces the network synchronization accuracy during the estimation of clock parameters and limits the applicability of the synchronization algorithms for some practical sensor networks where a global time scale is consistently required. Motivated by this, this paper investigates the synchronization scheme of having inactive nodes overhearing the pairwise sender-receiver time synchronization based on acknowledgement with clock correction at every synchronization. Assuming exponential random delays, the maximum likelihood estimators (MLEs) of clock skew and the corresponding approximate Cramer-Rao lower bounds (CRLBs) for active and overhearing nodes are derived. In addition, we also consider a linear synchronization model that the clock skew is directly estimated. Simulation results verify the efficiency of the clock skew estimators. [ABSTRACT FROM PUBLISHER]

This paper studies the stochastic behavior of the signed variants of the LMS algorithm for a system identification framework when the input signal is a cyclostationary white Gaussian process. Three algorithms are studied: the signed regressor, the signed error, and the sign–sign algorithms. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights with the input cyclostationarity. These models are used to derive new results concerning the performance of the algorithms. Some of these results are surprising. Monte Carlo simulations of the three algorithms provide strong support for the theory. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce. [ABSTRACT FROM PUBLISHER]

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters in an online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz 63 system. [ABSTRACT FROM PUBLISHER]

In this paper, we present a novel approach for achieving phase desynchronization in a pulse-coupled oscillator network. Ensuring phase desynchronization is a difficult problem, and existing results are constrained to a completely interconnected network and a fixed number of nodes. Our approach is more robust than previous approaches, removing the constraint of a fixed number of nodes. The removal of this constraint is significant because it allows the network to receive and drop nodes freely without any change to the phase update strategy. Also, to our knowledge, our approach is the first to prove the convergence to the desynchronized state for a topology that is more general than the all-to-all topology. More specifically, our approach is applicable to any circulant, symmetric network topology, including the circulant symmetric ring topology. Rigorous mathematical proofs are provided to support the result that any circulant, symmetric network with ordered phases under our proposed algorithm will converge to uniform phase desynchronization. Simulation results are also presented to demonstrate the algorithm's performance. [ABSTRACT FROM PUBLISHER]

The performance of full-duplex (FD) relay systems can be greatly impacted by the self-interference (SI) at relays. By exploiting multiple antennas, the spectral efficiency of FD relay systems can be enhanced through spatial SI mitigation. This paper studies joint source transmit beamforming and relay processing to achieve rate maximization for FD multiple-input–multiple-output (MIMO) amplify-and-forward (AF) relay systems with consideration of relay processing delay. The problem is difficult to solve mainly due to the SI constraint induced by the relay processing delay. In this paper, we first present a sufficient condition under which the relay amplification matrix has rank-one structure. Then, for the case of rank-one amplification matrix, the rate maximization problem is equivalently simplified into an unconstrained problem that can be locally solved using the gradient ascent method. Next, we propose a penalty-based algorithmic framework, named P-BSUM, for a class of constrained optimization problems that have difficult equality constraints in addition to some convex constraints. By rewriting the rate maximization problem with a set of auxiliary variables, we apply the P-BSUM algorithm to the rate maximization problem in the general case. Finally, numerical results validate the efficiency of the proposed algorithms and show that the joint source-relay design approach under the rank-one assumption could be strictly suboptimal as compared to the P-BSUM-based joint source-relay design approach. [ABSTRACT FROM PUBLISHER]

This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multiple-input multiple-output interference channel (MIMO-IC) with the interference treated as Gaussian noise, we show that the user's achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex Gaussian signaling in terms of the users' transmit covariance matrices, and an additional term, which is a function of both the users' transmit covariance and pseudo-covariance matrices. The additional degrees of freedom in the pseudo-covariance matrix, which is conventionally set to be zero for the case of proper Gaussian signaling, provide an opportunity to further improve the achievable rates of Gaussian MIMO-ICs by employing improper Gaussian signaling. To this end, this paper proposes widely linear precoding, which efficiently maps proper information-bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo-covariance matrices. In particular, for the case of two-user Gaussian single-input single-output interference channel (SISO-IC), we propose a joint covariance and pseudo-covariance optimization algorithm with improper Gaussian signaling to achieve the Pareto-optimal rates. By utilizing the separable structure of the achievable rate expression, an alternative algorithm with separate covariance and pseudo-covariance optimization is also proposed, which guarantees the rate improvement over conventional proper Gaussian signaling. [ABSTRACT FROM PUBLISHER]

Recent advances in neurophysiology have led to the development of complex dynamical models that describe the connections and causal interactions between different regions of the brain. These models are able to accurately mimic the event-related potentials observed by EEG/MEG measurement systems, and are considered to be key components for understanding brain functionality. In this paper, we focus on a class of nonlinear dynamic causal models (DCM) that are described by a set of connectivity parameters. In practice, the DCM parameters are inferred using data obtained by an EEG or MEG sensor array in response to a certain event or stimulus, and then used to analyze the strength and direction of the causal interactions between different brain regions. The usefulness of these parameters in this process will depend on how accurately they can be estimated, which in turn will depend on noise, the sampling rate, number of data samples collected, the accuracy of the source localization and reconstruction steps, etc. The goals of this paper are to present several algorithms for DCM parameter estimation, derive Cramér-Rao performance bounds for the estimates, and compare the accuracy of the algorithms against the theoretical performance limits under a variety of circumstances. The influence of noise and sampling rate will be explicitly investigated. [ABSTRACT FROM PUBLISHER]

Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid. [ABSTRACT FROM PUBLISHER]

This paper considers the average-consensus problem within the same framework as the companion paper [K. Topley and V. Krishnamurthy, “Average-Consensus Algorithms in a Deterministic Framework—Part I: Strong Connectivity, IEEE Trans. Signal Process., vol. 60, no. 12, Dec. 2012]. Two distributed algorithms are proposed and shown to be analogous to the algorithms presented in the Part I of the paper with respect to the communication costs and conditions sufficient for average-consensus. We provide convergence proofs, as well as numerical examples that (i) illustrate the empirical convergence rate of all four algorithms, and (ii) show that consensus algorithms in the past literature can fail to achieve average-consensus within our framework. Three applications from the literature that motivate the proposed algorithms are discussed, and also we show how all four algorithms allow each node to compute an upper bound on the error of their current local consensus estimate. [ABSTRACT FROM PUBLISHER]