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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]

In this paper, a novel augmented complex-valued least-mean kurtosis (ACLMK) algorithm is proposed for processing complex-valued signals. The negated kurtosis of the complex-valued error signal is defined as a cost function by using augmented statistics. As a result of the minimization of this cost function, the ACLMK algorithm containing all second-order statistical properties is obtained for processing noncircular complex-valued signals. Moreover, in this paper, convergence and misadjustment conditions of the proposed ACLMK algorithm are derived from the steady-state analysis. The simulation results on complex-valued system identification, prediction, and adaptive noise cancelling problems show that the use of the cost function defined by the negated kurtosis of the complex-valued error signal based on augmented statistics enables the processing of the noncircular complex-valued signals, and significantly improves the performance of the proposed ACLMK algorithm in terms of the mean square deviation, the mean square error, the prediction gain and the convergence rate when compared to other algorithms. [ABSTRACT FROM AUTHOR]

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multitarget tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a Second-Order PHD (SO-PHD) filter, propagating the second-order moment (i.e., variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modeling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. This paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multiobject filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters. [ABSTRACT FROM PUBLISHER]

We propose a novel adaptive kernel-based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by the authors. This paper shows that in the adaptive version of the kernel regression for complex-valued signals we need to include another kernel term, the so-called pseudo-kernel. This new solution is endowed with better representation capabilities in complex-valued fields since it can efficiently decouple the learning of the real and the imaginary part. Also, we review previous realizations of the complex KLMS algorithm and its augmented version to prove that they can be rewritten as particular cases of the gCKLMS. Furthermore, important conclusions on the design of the kernels are drawn that help to greatly improve the convergence of the algorithms. In the experiments, we revisit the nonlinear channel equalization problem to highlight the better convergence of the gCKLMS compared to previous solutions. Also, the flexibility of the proposed generalized approach is tested in a second experiment with non-independent real and imaginary parts. The results illustrate the significant performance improvements of the gCKLMS approach when the complex-valued signals have different properties for the real and imaginary parts. [ABSTRACT FROM AUTHOR]

We deal with the classical problem of testing two simple statistical hypotheses but, as a new element, it is assumed that the data vector is observed after an unknown permutation of its entries. What is the fundamental limit for the detection performance in this case? How much information for detection is contained in the entry values and how much in their positions? In the first part of this paper, we answer these questions. In the second part, we focus on practical algorithms. A low-complexity detector solves the detection problem without attempting to estimate the permutation. A modified version of the auction algorithm is then considered, and two greedy algorithms with affordable worst case complexity are presented. The detection operational characteristics of these detectors are investigated by computer experiments. The problem we address is referred to as unlabeled detection and is motivated by large sensor network applications, but applications are also foreseen in different fields, including image processing, social sensing, genome research, and molecular communication. [ABSTRACT FROM AUTHOR]

This paper proposes a new method for impulsive source separation (deinterleaving) in multi-input single-output systems based purely on impulse spacing. The impulse spacing for each source is modeled as a renewal process. To classify sources, an algorithm is developed to maximize the likelihood of impulse assignment based on the impulse spacing distributions. A theoretical lower bound on performance is derived and the algorithm is shown to get reasonably close to the bound. The algorithm is extended for use when the impulse spacing distribution parameters are unknown. Performance is evaluated on multiple application examples. [ABSTRACT FROM AUTHOR]

Next generation wireless networks will exploit the large amount of spectrum available at millimeter wave (mmWave) frequencies. The design of mmWave systems, however, is challenging due to the strict power, cost, and hardware constraints at higher bandwidths. To achieve a good SNR for communication, mmWave systems use large antenna arrays. Beamforming with highly directional beams is one way to use the antennas. As the channel changes over time, the beams that maximize the SNR have to be estimated quickly to reduce the training overhead. Prior research has exploited the observation that mmWave channels are sparse to perform compressed sensing (CS) based beam alignment with few channel measurements. Most of the existing CS-based algorithms, however, assume perfect synchronization and fail in the presence of carrier frequency offset (CFO). This paper presents Swift-Link, a fast beam alignment algorithm that is robust against the offset. Swift-Link includes a novel randomized beam training sequence that minimizes the beam alignment errors due to CFO and a low-complexity algorithm that corrects these errors. Even with strict hardware constraints, our algorithm uses fewer channel measurements than comparable CS algorithms and has analytical guarantees. Swift-Link requires a small output dynamic range at the analog-to-digital converter compared to beam-scanning techniques. [ABSTRACT FROM AUTHOR]

Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical estimation of the multifractal spectrum fundamentally relies on exploiting the scale dependence of statistical properties of appropriate multiscale quantities, such as wavelet leaders, that can be robustly computed from discrete data. Despite successes of multifractal analysis in various real-world applications, current estimation procedures remain essentially limited to providing concave upper-bound estimates, while there is a priori no reason for the multifractal spectrum to be a concave function. This paper addresses this severe practical limitation and proposes a novel formalism for multifractal analysis that enables nonconcave multifractal spectra to be estimated in a stable way. The key contributions reside in the development and theoretical study of a generalized multifractal formalism to assess the multiscale statistics of wavelet leaders, and in devising a practical algorithm that permits this formalism to be applied to real-world data, allowing for the estimation of nonconcave multifractal spectra. Numerical experiments are conducted on several synthetic multifractal processes as well as on a real-world remote-sensing image and demonstrate the benefits of the proposed multifractal formalism over the state of the art. [ABSTRACT FROM AUTHOR]

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication-efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our simulation results on both synthetic and real-world datasets show that our strategies achieve a desired accuracy in inferring the underlying structure while spending a small budget on communication. [ABSTRACT FROM AUTHOR]

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large—making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems. [ABSTRACT FROM AUTHOR]

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. As a benchmark for these NC methods, we derive the closed-form deterministic $R$ -D NC Cramér-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources in this paper. Assuming a separable centro-symmetric $R$-D array, we show that in some special cases, the deterministic $R$-D NC CRB reduces to the existing deterministic $R$-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved under the deterministic data assumption in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain. Our analysis is supported by extensive simulation results. [ABSTRACT FROM PUBLISHER]

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]

Classification with a sparsity constraint on the solution plays a central role in many high dimensional signal processing applications. In some cases, the features can be grouped together, so that entire subsets of features can be selected or discarded. In many applications, however, this can be too restrictive. In this paper, we are interested in a less restrictive form of structured sparse feature selection: We assume that while features can be grouped according to some notion of similarity, not all features in a group need be selected for the task at hand. The Sparse Group Lasso (SGL) was proposed to solve problems of this form. The main contributions of this paper are a new procedure called Sparse Overlapping Group (SOG) lasso, an extension to the SGL to overlapping groups and theoretical sample complexity bounds for the same. We establish model selection error bounds that specializes to many other cases. We experimentally validate our proposed method on both real and toy datasets. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized algorithm for solving a consensus optimization problem defined in a static networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form. Examples of such problems include decentralized constrained quadratic programming and compressed sensing problems, as well as many regularization problems arising in inverse problems, signal processing, and machine learning, which have decentralized applications. This paper addresses the need for efficient decentralized algorithms that take advantages of proximal operations for the nonsmooth terms. We propose a proximal gradient exact first-order algorithm (PG-EXTRA) that utilizes the composite structure and has the best known convergence rate. It is a nontrivial extension to the recent algorithm EXTRA. At each iteration, each agent locally computes a gradient of the smooth part of its objective and a proximal map of the nonsmooth part, as well as exchanges information with its neighbors. The algorithm is “exact” in the sense that an exact consensus minimizer can be obtained with a fixed step size, whereas most previous methods must use diminishing step sizes. When the smooth part has Lipschitz gradients, PG-EXTRA has an ergodic convergence rate of O\left(1\over k\right) in terms of the first-order optimality residual. When the smooth part vanishes, PG-EXTRA reduces to P-EXTRA, an algorithm without the gradients (so no “G” in the name), which has a slightly improved convergence rate at o\left(1\over k\right) in a standard (non-ergodic) sense. Numerical experiments demonstrate effectiveness of PG-EXTRA and validate our convergence results [ABSTRACT FROM PUBLISHER]

This paper proposes a new framework for the design of transmit and receive beamformers for interference alignment (IA) without symbol extensions in multi-antenna cellular networks. We consider IA in a G cell network with K users/cell, N antennas at each base station (BS) and M antennas at each user. The proposed framework is developed by recasting the conditions for IA as two sets of rank constraints, one on the rank of interference matrices, and the other on the transmit beamformers in the uplink. The interference matrix consists of all the interfering vectors received at a BS from the out-of-cell users in the uplink. Using these conditions and the crucial observation that the rank of interference matrices under alignment can be determined beforehand, this paper develops two sets of algorithms for IA. The first part of this paper develops rank minimization algorithms for IA by iteratively minimizing a weighted matrix norm of the interference matrix. Different choices of matrix norms lead to reweighted nuclear norm minimization (RNNM) or reweighted Frobenius norm minimization (RFNM) algorithms with significantly different per-iteration complexities. Alternately, the second part of this paper devises an alternating minimization (AM) algorithm where the rank-deficient interference matrices are expressed as a product of two lower-dimensional matrices that are then alternately optimized. Simulation results indicate that RNNM, which has a per-iteration complexity of a semidefinite program, is effective in designing aligned beamformers for proper-feasible systems with or without redundant antennas, while RFNM and AM, which have a per-iteration complexity of a quadratic program, are better suited for systems with redundant antennas. [ABSTRACT FROM PUBLISHER]

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]

The linear canonical transform (LCT) has been shown to be one of the most powerful tools in signal processing, and in this paper, we propose an adaptive approach for the computation of the discrete LCT (DLCT), termed the sliding discrete linear canonical transform (SDLCT). First, we introduce a scheme for the single-point DLCT, which can effectively calculate a single or a few linear canonical spectra. Second, the SDLCT is proposed based on an iterative algorithm to meet the requirements of online spectral analysis when only a subset of $N$ frequencies are required from an $\tilde{N}\hbox{--}$ point discrete LCT ($N\leq \tilde{N}$). The additivity and reversibility properties of the proposed algorithms are also discussed in detail. Third, the DLCT convolution operation is obtained to reduce the spectral leakage of the proposed algorithm, and time-domain windowing is implemented via frequency-domain convolution. Finally, we present two methods to assess performance with regard to computational complexity and precision and to show the correctness of the derived results. [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]

A set-membership affine projection algorithm is proposed that can estimate a complex-valued channel matrix using a set of complex-valued pilots in the presence of additive white Gaussian noise. It is shown that the algorithm converges faster than the well-known set-membership normalized least mean square algorithm (SM-NLMS) while it resolves the high steady-state error value and the complexity issues in the regular affine projection algorithm. The fast convergence of the proposed algorithm means that a shorter training sequence inside each data block is required, which in turn improves the effective bit rate. This fast convergence is more pronounced when the pilot vectors are highly correlated. We incorporated the set-membership filtering framework into our study to reduce the computational complexity of the algorithm and preserve energy in the WSNs. Other studies have shown the superiority of the adaptive filtering algorithms, and in particular the NLMS algorithm, over other alternatives in various signal processing areas in WSNs, therefore, our proposed algorithm is a powerful substitute for a variety of algorithms. In other words, the implementation of various signal processing algorithms for different purposes can be replaced with the implementation of the proposed multipurpose algorithm. In this paper, we combine the results of our previous studies and prove the convergence of the algorithm. Furthermore, the steady-state analysis in the output mean square error is presented for two cases of pilot signals, and in the conducted simulations, the MSE performance of the algorithm is compared with the regular affine projection algorithm and the SM-NLMS algorithm. [ABSTRACT FROM AUTHOR]

A fundamental problem in multimodal signal processing is to quantify relations between two different signals with respect to a certain phenomenon. In this paper, we address this problem from a kernel-based perspective and propose a measure that is based on affinity kernels constructed separately in each modality. This measure is motivated from both a kernel density estimation point of view of predicting the signal in one modality based on the other, as well as from a statistical model, which implies that high values of the proposed measure are expected when signals highly correspond to each other. Considering an online setting, we propose an efficient algorithm for the sequential update of the proposed measure, and demonstrate its application to eye-fixation prediction in audio-visual recordings. The goal is to predict locations within a video recording at which people gaze when watching the video. As studies in psychology imply, people tend to gaze at the location of the audio source, so that their prediction becomes equivalent to locating the audio source within the video. Therefore, we propose to predict eye-fixations as regions within the video with the highest correspondence to the audio signal, thereby demonstrating the improved performance of the proposed method. [ABSTRACT FROM AUTHOR]

Detecting periodicity in a short sequence is an important problem, with many applications across science and engineering. Several efficient algorithms have been proposed for this over the years. There is a wide choice available today in terms of the tradeoff between algorithmic complexity and estimation accuracy. In spite of such a rich history, one particular aspect of period estimation has received very little attention from a fundamental perspective. Namely, given a discrete time periodic signal and a list of candidate integer periods, what is the absolute minimum datalength required to estimate its integer period? Notice that the answer we seek must be a fundamental bound, i.e., independent of any particular period estimation technique. Common intuition suggests the minimum datalength as twice the largest expected period. However, this is true only under some special contexts. This paper derives the exact necessary and sufficient bounds to this problem. The above-mentioned question is also extended to the case of mixtures of periodic signals. First, a careful mathematical formulation discussing the unique identifiability of the component periods (hidden integer periods) is presented. Once again, a rigorous theoretical framework in this regard is missing in the existing literature but is a necessary platform to derive precise bounds on the minimum necessary datalength. The bounds given here are generic, that is, independent of the algorithms used. Specific algorithm-dependent bounds are also presented in the end for the case of dictionary-based integer period estimation reported in recent years. [ABSTRACT FROM AUTHOR]

One-bit quantization can significantly reduce the massive multiple-input and multiple-output (MIMO) system hardware complexity, but at the same time it also brings great challenges to the system algorithm design. Specifically, it is difficult to recover information from the highly distorted samples as well as to obtain accurate channel estimation without increasing the number of pilots. In this paper, a novel inference algorithm called variational approximate message passing (VAMP) for one-bit quantized massive MIMO receiver is developed, which attempts to exploit the advantages of both the variational Bayesian inference algorithm and the bilinear generalized approximated message passing algorithm to accomplish joint channel estimation and data detection in a closed form with first-order complexity. Asymptotic state evolution analysis indicates the fast convergence rate of VAMP and also provides a lower bound for the data detection error. Moreover, through extensive simulations, we show that VAMP can achieve excellent detection performance with low pilot overhead in a wide range of scenarios. [ABSTRACT FROM AUTHOR]

BigBand is a technique for wideband spectrum sensing (WSS) that can capture gigahertz of sparse spectrum in real time by using shifted multiple channels without sampling the signal at GS/s. In this paper, we focus on enforcing BigBand with the proposed improved algorithm, namely, AD-BigBand, for efficient and robust computation. AD-BigBand converts the nonlinear process (locating frequency and computing the spectrum value) of sparse WSS into two steps of solving linear equations. In particular, we define an r -degree frequency locator polynomial to rapidly locate nonzero frequencies. The computing complexity of the proposed method decreases from O(K{\log ^2}K ({{{n\log K} \over K}})^{\log K}) of shifted sampling based BigBand to O(K{\log ^2}K)$, where the $K$-sparse signals of bandwitdth $n$ are subsampled with arithmetic time-shifted sensing channels. We implement AD-BigBand on a commercial four-channel acquisition card. Experimental results show that AD-BigBand improves the WSS capabilities and exhibits higher processing speed and lower error spectrum construction rate than BigBand, especially in the case of relative low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In this paper, we present new algorithms and analysis for the linear inverse sensor placement and scheduling problems over multiple time instances with power and communications constraints. The proposed algorithms, which deal directly with minimizing the mean squared error (MSE), are based on the convex relaxation approach to address the binary optimization scheduling problems that are formulated in sensor network scenarios. We propose to balance the energy and communications demands of operating a network of sensors over time while we still guarantee a minimum level of estimation accuracy. We measure this accuracy by the MSE for which we provide average case and lower bounds analyses that hold in general, irrespective of the scheduling algorithm used. We show experimentally how the proposed algorithms perform against state-of-the-art methods previously described 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]

In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which, in the noiseless scenario with sufficiently many measurements, guarantees invertability of the transformation between the SOI and the observations, up to an inherent phase ambiguity. However, in many practical applications, the measurement matrix corresponds to an underlying physical setup, and is therefore deterministic, possibly with structural constraints. In this paper, we study the design of deterministic measurement matrices, based on maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimality of a measurement matrix, and analytically obtain the optimal matrix in the low signal-to-noise ratio regime. Practical methods for designing general measurement matrices and masked Fourier measurements are proposed. Simulation tests demonstrate the performance gain achieved by the suggested techniques compared to random Gaussian measurements for various phase recovery algorithms. [ABSTRACT FROM AUTHOR]

This paper examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gradient vector. The selection of coordinates varies randomly from iteration to iteration and from agent to agent across the network. Such schemes are useful in reducing computational complexity at each iteration in power-intensive large data applications. They are also useful in modeling situations where some partial gradient information may be missing at random. Interestingly, the results show that the steady-state performance of the learning strategy is not always degraded, while the convergence rate suffers some degradation. The results provide yet another indication of the resilience and robustness of adaptive distributed strategies. [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]

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]

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation. [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 presents a novel accurate array response control algorithm, abbreviated as \text A^2\text RC, and its application to array pattern synthesis. The proposed \text A^2\text RC algorithm deals with the problem of how to accurately control the array response at a given direction. Starting from the adaptive array theory, a deep analysis of the optimal weight vector is carried out. It is found that the normalized response at a given direction can be accurately adjusted to an arbitrary level, by means of making some simple modification to the initial weight vector. On this basis, all possible weight vectors, which have a specific form and can make the normalized response at the given direction equal to the prescribed value, are first figured out. Then, an effective approach to selecting the most appropriate one, which would cause the least pattern distortion, is devised. By applying the \text A^2\text RC algorithm, a new pattern synthesis approach for arbitrary arrays is developed. In this approach, the array pattern is adjusted in a point-by-point manner by successively modifying the weight vector. Contrary to the conventional approaches that assign artificial interferences in an ad hoc way, our approach is able to obtain the weight vector without iteratively determining the powers of the artificial interferences. Extensive simulation results are provided to demonstrate the performance of the \text A^2\text RC algorithm in array response control and the effectiveness of this algorithm in pattern synthesis under various situations. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with a known mean. In applications where the covariance matrix naturally possesses a certain structure, taking the prior structure information into account in the estimation procedure is beneficial to improving the estimation accuracy. We propose incorporating the prior structure information into Tyler's M-estimator and formulating the problem as minimizing the cost function of Tyler's estimator under the prior structural constraint. First, the estimation under a general convex structural constraint is introduced with an efficient algorithm for finding the estimator derived based on the majorization-minimization (MM) algorithm framework. Then, the algorithm is tailored to several special structures that enjoy a wide range of applications in signal processing related fields, namely, sum of rank-one matrices, Toeplitz, and banded Toeplitz structure. In addition, two types of non-convex structures, i.e., the Kronecker structure and the spiked covariance structure, are also discussed, where it is shown that simple algorithms can be derived under the guidelines of MM. The algorithms are guaranteed to converge to a stationary point of the problems. Furthermore, if the constraint set is geodesically convex, such as the Kronecker structure set, then the algorithm converges to a global minimum. Numerical results show that the proposed estimator achieves a smaller estimation error than the benchmark estimators at a lower computational cost. [ABSTRACT FROM AUTHOR]

A multiband-structured subband adaptive filter (MSAF) algorithm was introduced to achieve a fast convergence rate for the correlated input signal. The convergence analysis of the adaptive filter algorithm is an important concept because it provides a guideline to design the adaptive filter. However, the convergence analysis of the MSAF algorithm has not been researched as extensively as that of the normalized least-mean-square algorithm. Therefore, it needs to be researched. In this paper, we present a new approach to the mean-square deviation (MSD) analysis of the MSAF algorithm by using the persistently exciting input and the practical assumption that the stopband attenuation of the prototype filter is high. Unlike the previous analysis, the proposed analysis is possible to be applied to the long-length adaptive filter such as the acoustic echo cancellation. The proposed analysis is also applied to a non-stationary model with a random walk of the optimal weight vector. The simulation results match with the theoretical results in both the transient-state and steady-state MSD. [ABSTRACT FROM AUTHOR]

To increase efficacy in traditional classroom courses as well as in Massive Open Online Courses (MOOCs), automated systems supporting the instructor are needed. One important problem is to automatically detect students that are going to do poorly in a course early enough to be able to take remedial actions. Existing grade prediction systems focus on maximizing the accuracy of the prediction while overseeing the importance of issuing timely and personalized predictions. This paper proposes an algorithm that predicts the final grade of each student in a class. It issues a prediction for each student individually, when the expected accuracy of the prediction is sufficient. The algorithm learns online what is the optimal prediction and time to issue a prediction based on past history of students’ performance in a course. We derive a confidence estimate for the prediction accuracy and demonstrate the performance of our algorithm on a dataset obtained based on the performance of approximately 700 UCLA undergraduate students who have taken an introductory digital signal processing over the past seven years. We demonstrate that for 85% of the students we can predict with 76% accuracy whether they are going do well or poorly in the class after the fourth course week. Using data obtained from a pilot course, our methodology suggests that it is effective to perform early in-class assessments such as quizzes, which result in timely performance prediction for each student, thereby enabling timely interventions by the instructor (at the student or class level) when necessary. [ABSTRACT FROM AUTHOR]

Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coherence, which provides a “bridge” between the well known mutual coherence and the restricted isometry constant, the performance of orthogonal matching pursuit with thresholding is analyzed and more general results for sparse signal reconstruction are obtained. It is also shown that given the same assumption on the coherence index and the restricted isometry constant as required for orthogonal matching pursuit, the thresholding variation gives exactly the same reconstruction performance with significantly less complexity. [ABSTRACT FROM PUBLISHER]

This paper considers the coherent integration problem for a maneuvering target with complex motions, where the velocity, acceleration, and jerk result in respectively the first-order range migration (FRM), second-order range migration (SRM), and third-order range migration (TRM) within the coherent pulse interval. A new coherent integration algorithm based on generalized keystone transform (KT) and second-order dechirp process is proposed, which employs the third-order KT, six-order KT, second-order KT, and fold factor searching to correct the TRM, SRM, and FRM, respectively. The range migration change during each step and computational complexity are also theoretically analyzed. Compared with the generalized Radon Fourier transform (GRFT) algorithm, the presented method can avoid the blind speed sidelobe (BSSL) and acquire close integration performance but with much lower computational cost. Simulations are provided to demonstrate the effectiveness. Finally, a generalized method, named generalized KT and generalized dechirp process (GKTGDP), is also introduced for the maneuvering target with arbitrary high-order range migration. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a method to localize a wireless and stationary blind node based on received signal strength measurements; the positioning scheme relies on the statistical path loss model. The operating environment is either non-homogeneous, i.e., the attenuation factors of the various links are different, or homogeneous, i.e., all links share one and the same attenuation factor. We introduce a cognitive procedure to circumvent the a priori uncertainty on the actual scenario being in force: the first stage is a properly designed hypothesis test, fed by measurements between anchors, moving along known trajectories, to decide whether or not the environment is homogeneous. Based upon the output of the test, a model-dependent maximum-likelihood localization algorithm is adopted using the measurements made by the blind node and the parameters estimated by the anchors at previous stage. The performance assessment shows that the proposed approach could be a viable means to handle localization in uncertain scenarios. [ABSTRACT FROM PUBLISHER]

In Part II of this paper, also in this issue, we carried out a detailed mean-square-error analysis of the performance of asynchronous adaptation and learning over networks under a fairly general model for asynchronous events including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. In this Part III, we compare the performance of synchronous and asynchronous networks. We also compare the performance of decentralized adaptation against centralized stochastic-gradient (batch) solutions. Two interesting conclusions stand out. First, the results establish that the performance of adaptive networks is largely immune to the effect of asynchronous events: the mean and mean-square convergence rates and the asymptotic bias values are not degraded relative to synchronous or centralized implementations. Only the steady-state mean-square-deviation suffers a degradation in the order of \nu, which represents the small step-size parameters used for adaptation. Second, the results show that the adaptive distributed network matches the performance of the centralized solution. These conclusions highlight another critical benefit of cooperation by networked agents: cooperation does not only enhance performance in comparison to stand-alone single-agent processing, but it also endows the network with remarkable resilience to various forms of random failure events and is able to deliver performance that is as powerful as batch solutions. [ABSTRACT FROM PUBLISHER]

This paper investigates pilot-aided channel estimation for two-way relay networks (TWRNs) in the presence of synchronization errors between the two sources. The unpredictable synchronization error leads to time domain offset and signal arriving order (SAO) ambiguity when two signals sent from two sources are superimposed at the relay. A two-step channel estimation algorithm is first proposed, in which the linear minimum mean-square-error (LMMSE) estimator is used to obtain initial channel estimates based on pilot symbols and a linear minimum error probability (LMEP) estimator is then developed to update these estimates. Optimal training sequences and power allocation at the relay are designed to further improve the performance for LMMSE based initial channel estimation. To tackle the SAO ambiguity problem, the generalized likelihood ratio testing method is applied and an upper bound on the SAO detection error probability is derived. By using the SAO information, a scaled LMEP estimation algorithm is proposed to compensate for the performance degradation caused by SAO detection error. Simulation results show that the proposed estimation algorithms can effectively mitigate the negative effects caused by asynchronous transmissions in TWRNs, thus significantly outperforming the existing channel estimation algorithms. [ABSTRACT FROM AUTHOR]