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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]

This paper proposes a low complexity n-dimensional (nD) FastICA algorithm and architecture by introducing the concept of coordinate rotation where n\geq 2. The proposed algorithm can merge the two key steps of conventional FastICA—preprocessing and update and is therefore capable of reducing the hardware complexity of the conventional FastICA significantly as demonstrated in this paper. Hardware implementation can further be simplified due to the recursive nature of the proposed algorithm where the same 2D hardware module can be used as the fundamental core to implement nD architecture. Together with the algorithm formulation, its functionality is also validated and hardware complexity is analyzed and compared with the conventional nD FastICA. [ABSTRACT FROM PUBLISHER]

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with “Big Data” analytics. However, increasingly noisy, heterogeneous, and incomplete datasets, as well as the need for real-time processing of streaming data, pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from incomplete streaming data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially weighted least-squares criterion regularized with the nuclear norm. After recasting the nonseparable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed, and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the batch nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of low-rank tensors with missing entries and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives. [ABSTRACT FROM PUBLISHER]

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random variables are unknown and/or the computational complexity is prohibitive). Classical stochastic gradient methods for solving this problem may suffer from slow convergence. In this paper, we propose a stochastic parallel Successive Convex Approximation-based (best-response) algorithm for general nonconvex stochastic sum-utility optimization problems, which arise naturally in the design of multi-agent networks. The proposed novel decomposition approach enables all users to update their optimization variables in parallel by solving a sequence of strongly convex subproblems, one for each user. Almost sure convergence to stationary points is proved. We then customize the algorithmic framework to solve the stochastic sum rate maximization problem over single-input-single-output (SISO) frequency-selective interference channels, multiple-input-multiple-output (MIMO) interference channels, and MIMO multiple-access channels. Numerical results corroborate that the proposed algorithms can converge faster than state-of-the-art stochastic gradient schemes while achieving the same (or better) sum-rates. [ABSTRACT FROM AUTHOR]

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

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for this purpose. It is designed to enable the convex formulation of ill-conditioned linear inverse problems with quadratic data fidelity terms. The new penalty overcomes limitations of separable regularization. We show how the penalty parameters should be set to ensure that the objective function is convex, and provide an explicit condition to verify the optimality of a prospective solution. We present an algorithm (an instance of forward-backward splitting) for sparse deconvolution using the new penalty. [ABSTRACT FROM PUBLISHER]

This paper considers linear downlink transceiver design for the sum power minimization problem with per-user rate constraints in a multi-cell multi-user MIMO system. This non-convex problem is divided into transmit and receive beamforming optimization steps which are iteratively repeated such that the sum power converges. The transmit beamformers are solved using a successive convex approximation method (SCA), whereas the receive beamformers are computed via the linear minimum mean square error (MMSE) criterion. In addition to centralized design, we propose two decentralized algorithms where the transmit and receive beamforming designs are facilitated by a combination of pilot and backhaul signaling. In the first algorithm, sum power is minimized by computing the transmit beamformers at each base station (BS) and the receive beamformers at each user via iterative over-the-air optimization process. BS side processing requires local effective channel state information (CSI) acquired from precoded uplink pilots. In the second algorithm, the transmit and receive beamformers are iteratively optimized at each BS requiring only local CSI obtained from antenna-specific uplink pilots. In both algorithms, transmit beamforming optimization is decoupled among the BSs via primal decomposition method, which requires scalar backhaul information exchange for decentralized processing. The performance of the proposed algorithms is evaluated via numerical examples under different system settings in static and time-correlated channel conditions. [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]

This paper presents an extension of the integrated time-chirp rate analysis technique, known as the parameterized centroid frequency-chirp rate distribution (PCFCRD), for noisy multicomponent linear frequency modulated signals analysis. The PCFCRD is based on a newly defined correlation function and its auto term accumulation is two-dimensionally coherent. The principle, cross term characteristic, implementation, properties, parameter selection criterion, antinoise performance, and estimation accuracy are analyzed for the PCFCRD. In this paper, comparisons with the coherently integrated cubic phase function, maximum likelihood method, and Lv's distribution are performed. With mathematic analyses and numerical simulations, we demonstrate that the PCFCRD outperforms these three representative counterparts. Further, by combining with analyses of the PCFCRD, several unclear mechanisms of the constant delay introduction are mathematically interpreted, especially quantitative influences on the chirp rate resolution and theoretical antinoise performance. [ABSTRACT FROM AUTHOR]

Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of Gerchberg and Saxton and Fienup is still the popular choice for solving many variants of this problem. The algorithm is based on alternating minimization; i.e., it alternates between estimating the missing phase information, and the candidate solution. Despite its wide usage in practice, no global convergence guarantees for this algorithm are known. In this paper, we show that a (resampling) variant of this approach converges geometrically to the solution of one such problem—finding a vector \bf x from \bf y, \bf A, where \bf y = \vert \bf A^T\bf x\vert and \vert\bf z\vert denotes a vector of element-wise magnitudes of \bf z—under the assumption that \bf A is Gaussian. Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on “lifting” to a convex matrix problem) in sample complexity and robustness to noise. However, it is much more efficient and can scale to large problems. Analytically, for a resampling version of alternating minimization, we show geometric convergence to the solution, and sample complexity that is off by log factors from obvious lower bounds. We also establish close to optimal scaling for the case when the unknown vector is sparse. Our work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting. [ABSTRACT FROM AUTHOR]

The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due to intense computation and communication requirements. An adaptation of the FP algorithm, designated as the empirical centroid fictitious play (ECFP), is presented. In ECFP players respond to the centroid of all players’ actions rather than track and respond to the individual actions of every player. Convergence of the ECFP algorithm in terms of average empirical frequency (a notion made precise in the paper) to a subset of the Nash equilibria is proven under the assumption that the game is a potential game with permutation invariant potential function. A more general formulation of ECFP is then given (which subsumes FP as a special case) and convergence results are given for the class of potential games. Furthermore, a distributed formulation of the ECFP algorithm is presented, in which, players endowed with a (possibly sparse) preassigned communication graph, engage in local, non-strategic information exchange to eventually agree on a common equilibrium. Convergence results are proven for the distributed ECFP algorithm. [ABSTRACT FROM PUBLISHER]

Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources. [ABSTRACT FROM PUBLISHER]

Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse signals based on the sparse Bayesian learning (SBL) framework. The key idea underlying the algorithm, termed SBL-DF, is the incorporation of a signal prediction generated from a dynamics model and estimates of previous time steps into the hyperpriors of the SBL probability model. The proposed algorithm is online, robust to imperfect dynamics models (due to the propagation of dynamics information through higher-order statistics), robust to certain undesirable dictionary properties such as coherence (due to properties of the SBL framework), allows the use of arbitrary dynamics models, and requires the tuning of fewer parameters than many other dynamic filtering algorithms do. We also extend the fast marginal likelihood SBL inference procedure to the informative hyperprior setting to create a particularly efficient version of the SBL-DF algorithm. Numerical simulations show that SBL-DF converges much faster and to more accurate solutions than standard SBL and other dynamical filtering algorithms. In particular, we show that SBL-DF outperforms state of the art algorithms when the dictionary contains the challenging coherence and column scaling structure found in many practical applications. [ABSTRACT FROM AUTHOR]

The stability of sparse signal reconstruction with respect to measurement noise is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique \ell1 sparse recovery. One of our algorithms produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the \ell1-constrained minimal singular value (\ell1-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of \ell1-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared to performance analysis involving the Restricted Isometry Constant, the arguments in this paper are much less complicated and provide more intuition on the stability of sparse signal recovery. We show also that, with high probability, the subgaussian ensemble generates measurement matrices with \ell1-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the \ell1-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semidefinite relaxation. [ABSTRACT FROM AUTHOR]

Sets of sequences with good correlation properties are desired in many active sensing and communication systems, e.g., multiple-input-multiple-output (MIMO) radar systems and code-division multiple-access (CDMA) cellular systems. In this paper, we consider the problems of designing complementary sets of sequences (CSS) and also sequence sets with both good auto- and cross-correlation properties. Algorithms based on the general majorization-minimization method are developed to tackle the optimization problems arising from the sequence set design problems. All the proposed algorithms can be implemented by means of the fast Fourier transform (FFT) and thus are computationally efficient and capable of designing sets of very long sequences. A number of numerical examples are provided to demonstrate the performance of the proposed algorithms. [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]

In this paper, we develop online learning algorithms that enable the agents to cooperatively learn how to maximize the overall reward in scenarios where only noisy global feedback is available without exchanging any information among themselves. We prove that our algorithms' learning regrets—the losses incurred by the algorithms due to uncertainty—are logarithmically increasing in time and thus the time average reward converges to the optimal average reward. Moreover, we also illustrate how the regret depends on the size of the action space, and we show that this relationship is influenced by the informativeness of the reward structure with regard to each agent's individual action. When the overall reward is fully informative, regret is shown to be linear in the total number of actions of all the agents. When the reward function is not informative, regret is linear in the number of joint actions. Our analytic and numerical results show that the proposed learning algorithms significantly outperform existing online learning solutions in terms of regret and learning speed. We illustrate how our theoretical framework can be used in practice by applying it to online Big Data mining using distributed classifiers. [ABSTRACT FROM PUBLISHER]

This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same time their relatively good performance in estimating sparse parameter vectors/signals. The paper reports two new algorithms in the context of sparsity-aware learning. In both cases, the goal is first to identify the support set of the unknown signal and then to estimate the nonzero values restricted to the active support set. First, an iterative greedy multistep procedure is developed, based on a neighborhood cooperation strategy, using batch processing on the observed data. Next, an extension of the algorithm to the online setting, based on the diffusion LMS rationale for adaptivity, is derived. Theoretical analysis of the algorithms is provided, where it is shown that the batch algorithm converges to the unknown vector if a Restricted Isometry Property (RIP) holds. Moreover, the online version converges in the mean to the solution vector under some general assumptions. Finally, the proposed schemes are tested against recently developed sparsity-promoting algorithms and their enhanced performance is verified via simulation examples. [ABSTRACT FROM PUBLISHER]

The discrete fractional Fourier transform is a powerful signal processing tool with broad applications for nonstationary signals. In this paper, we propose a sparse discrete fractional Fourier transform (SDFrFT) algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional Fourier domain. The proposed technique achieves multicomponent resolution in addition to its low computational complexity and robustness against noise. In addition, we apply the SDFrFT to the synchronization of high dynamic direct-sequence spread-spectrum signals. Furthermore, a sparse fractional cross ambiguity function (SFrCAF) is developed, and the application of SFrCAF to a passive coherent location system is presented. The experiment results confirm that the proposed approach can substantially reduce the computation complexity without degrading the precision. [ABSTRACT FROM PUBLISHER]

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 considers the problem of the distributed fusion of multiobject posteriors in the labeled random finite set filtering framework, using a generalized covariance intersection (GCI) method. Our analysis shows that GCI fusion with labeled multiobject densities strongly relies on label consistencies between local multiobject posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of the principle of minimum discrimination information and the so-called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multiobject densities that is robust to label inconsistencies between sensors. Specifically, the labeled multiobject posteriors are first marginalized to their unlabeled posteriors, which are then fused using the GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including δ-GLMB, marginalized δ-GLMB, and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze the performance of multidimensional ESPRIT ( $N$-D ESPRIT) method for estimating parameters of $N$-D superimposed damped and/or undamped exponentials. $N$-D ESPRIT algorithm is based on low-rank decomposition of multilevel Hankel matrices formed by the $N$ -D data. In order to reduce the computational complexity for large signals, we propose a fast $N$-D ESPRIT using truncated singular value decomposition (SVD). Then, through a first-order perturbation analysis, we derive simple expressions of the variance of the estimates in $N$-D multiple-tones case. These expressions do not involve the factors of the SVD. We also derive closed-form expressions of the variances of the complex modes, frequencies, and damping factors estimates in the $N$-D single-tone case. Computer results are presented to show effectiveness of the fast version of $N$-D ESPRIT and verify theoretical expressions. [ABSTRACT FROM PUBLISHER]

This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level. The problem is formulated as a biobjective Pareto optimization forcing either a continuous or a discrete phase constraint at the design stage. An iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and NP-hard in general. Each iteration of the devised method requires the solution of a nonconvex min–max problem. It is handled either through a novel bisection or an FFT-based method respectively for the continuous and the discrete phase constraint. Additionally, a heuristic approach to initialize the procedures employing the $l_p$-norm minimization technique is proposed. Simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase/binary case. [ABSTRACT FROM PUBLISHER]

Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL) decoding provides a reasonable tradeoff between the error-correction performance and hardware implementation complexity when used to decode polar codes, at the cost of limited throughput. The simplified SCL (SSCL) and its extension SSCL-SPC increase the speed of decoding by removing redundant calculations when encountering particular information and frozen bit patterns (rate one and single parity check codes), while keeping the error-correction performance unaltered. In this paper, we improve SSCL and SSCL-SPC by proving that the list size imposes a specific number of path splitting required to decode rate one and single parity check codes. Thus, the number of splitting can be limited while guaranteeing exactly the same error-correction performance as if the paths were forked at each bit estimation. We call the new decoding algorithms Fast-SSCL and Fast-SSCL-SPC. Moreover, we show that the number of path forks in a practical application can be tuned to achieve desirable speed, while keeping the error-correction performance almost unchanged. Hardware architectures implementing both algorithms are then described and implemented: It is shown that our design can achieve \mathbf 1.86 Gb/s throughput, higher than the best state-of-the-art decoders. [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]

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multi-layer graph, where the common vertex set represents the entities and the edges on different layers capture the similarities of the entities in term of the different modalities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. To this end, we propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse relationships between entities. As an illustrative application of our framework, we use our algorithm in clustering methods and test its performance on several synthetic and real world datasets where it is shown to be superior to baseline schemes and competitive to state-of-the-art techniques. Our generic framework further extends to numerous analysis and learning problems that involve different types of information on graphs. [ABSTRACT FROM PUBLISHER]

In this paper we present a novel approach to the solution of a sequence of SMV problems with a joint support. This type of problem arises in a number of applications such as multiband signal reconstruction and source localization. The approach we present is adaptive in that it solves it as a sequence of weighted SMV problems rather than collecting the measurement vectors and solving an MMV problem. The weights are adaptively updated from one instance to the next. This approach avoids delays and large memory requirements (at the cost of increased computational load) with the added capability of tracking changes in joint signal supports. [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]

This paper investigates a new class of nonconvex optimization, which provides a unified framework for linear precoding in single/multiuser multiple-input multiple-output channels with arbitrary input distributions. The new optimization is called generalized quadratic matrix programming (GQMP). Due to the nondeterministic polynomial time hardness of GQMP problems, instead of seeking globally optimal solutions, we propose an efficient algorithm that is guaranteed to converge to a Karush-Kuhn-Tucker point. The idea behind this algorithm is to construct explicit concave lower bounds for nonconvex objective and constraint functions, and then solve a sequence of concave maximization problems until convergence. In terms of application, we consider a downlink underlay secure cognitive radio network, where each node has multiple antennas. We design linear precoders to maximize the average secrecy (sum) rate with finite-alphabet inputs and statistical channel state information at the transmitter. The precoding problems under secure multicast/broadcast scenarios are GQMP problems, and thus, they can be solved efficiently by our proposed algorithm. Several numerical examples are provided to show the efficacy of our algorithm. [ABSTRACT FROM PUBLISHER]

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean-square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs. [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]

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]

This paper studies a distributed resource allocation problem for a multiagent network with a time-varying digraph. Each agent in the network is associated with a local variable (resource) and a convex cost function. The goal is to collectively minimize the total cost in a distributed fashion, subject to individual resource constraints, and collective equality constraints. The main challenge of the problem is due to the local information structure imposed by the time-varying digraph that should be considered as part of the problem formulation. This paper develops a nonnegative surplus-based distributed optimization algorithm. It is shown that the proposed distributed algorithm converges to the global minimizer provided that the time-varying digraph is jointly strongly connected. Also, all the parameters used in the proposed algorithm rely only on local knowledge. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of compressively sampling wide sense stationary random vectors with a low rank Toeplitz covariance matrix. Certain families of structured deterministic samplers are shown to efficiently compress a high-dimensional Toeplitz matrix of size N\times N , producing a compressed sketch of size O(\sqrt{r})\times O(\sqrt{r}).The reconstruction problem can be cast as that of line spectrum estimation, whereby, in absence of noise, Toeplitz matrices of any size N can be exactly recovered from compressive sketches of size O(\sqrtr)\times O(\sqrtr), no matter how large N is. In the presence of noise and finite data, the line spectrum estimation algorithm is combined with a novel denoising technique that only exploits a positive semidefinite (PSD) Toeplitz constraint to denoise the compressed sketch using a simple least-squares minimization framework. A major advantage of the algorithm is that it does not require any regularization parameter. It also enjoys lower computational complexity owing to its ability to predict the unobserved entries of the low-rank Toeplitz matrix. Explicit bounds on the reconstruction error are established and it is shown that the PSD constraint on the denoiser is sufficient to ensure stable reconstruction from a sketch of size O(\sqrtr)\times O(\sqrtr). Extensive simulations demonstrate that the proposed algorithm provides better performance over random samplers and algorithms that use nuclear-norm-based regularizers. [ABSTRACT FROM PUBLISHER]

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center which obtains an estimate of a parameter related to the observations of all terminals. It is well known that if the transmission rates are in the Slepian–Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian–Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator that has the same performance as that of the optimal estimator in the centralized case while using information rates less than the conditions required in the Slepian–Wolf rate region. The key idea is that, instead of aiming to recover the observations at the fusion center, we design universal schemes enabling the fusion center to compute a sufficient statistic using rates outside of the Selpian–Wolf region. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the problem of low-rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems with complexity that scales with the dimension of the data, which limits their scalability. Furthermore, existing randomized approaches mostly rely on uniform random sampling, which is quite inefficient for many real world data matrices that exhibit additional structures (e.g., clustering). In this paper, a scalable subspace-pursuit approach that transforms the decomposition problem to a subspace learning problem is proposed. The decomposition is carried out by using a small data sketch formed from sampled columns/rows. Even when the data are sampled uniformly at random, it is shown that the sufficient number of sampled columns/rows is roughly \mathcal O(r \mu), where $\mu$ is the coherency parameter and $r$ is the rank of the low-rank component. In addition, adaptive sampling algorithms are proposed to address the problem of columns/rows sampling from structured data. We provide an analysis of the proposed method with adaptive sampling and show that adaptive sampling makes the required number of sampled columns/rows invariant to the distribution of the data. The proposed approach is amenable to online implementation and an online scheme is proposed. [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, the joint support recovery of several sparse signals whose supports exhibit similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analyzed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results. [ABSTRACT FROM PUBLISHER]

A sequential partial optimization method is presented in this paper for the minimax design of two-dimensional infinite impulse response filters with separable denominator. The method converts the minimax design problem into a sequence of smaller subproblems, each updating only one pair of second-order denominator factors. The necessary and sufficient stability triangles for one-dimensional filters are used as the stability constraints on the two-dimensional filters. The first-order Taylor expansion and a trust-region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm. By comparing with a corresponding joint optimization method, the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order. This is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method. Moreover, the limit solution of the sequential partial optimization algorithm has been proved to be a Karush–Kuhn–Tucker point of the design problem. Design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the channel estimation problem in millimeter wave (mmWave) wireless systems with large antenna arrays. By exploiting the inherent sparse nature of the mmWave channel, we first propose a fast channel estimation (FCE) algorithm based on a novel overlapped beam pattern design, which can increase the amount of information carried by each channel measurement compared to the existing nonoverlapped designs and thus reduce the required channel estimation time. We develop a maximum likelihood estimator to optimally extract the path information from the channel measurements. Then, we propose a novel rate-adaptive channel estimation (RACE) algorithm, which can dynamically adjust the number of channel measurements based on the expected probability of estimation error (PEE). The performance of both proposed algorithms is analyzed. For the FCE algorithm, an approximate closed-form expression for the PEE is derived. For the RACE algorithm, a lower bound for the minimum signal energy-to-noise ratio required for a given number of channel measurements is developed based on the Shannon–Hartley theorem. Simulation results show that the FCE algorithm significantly reduces the number of channel estimation measurements compared to the existing algorithms using nonoverlapped beam patterns. By adopting the RACE algorithm, we can achieve up to a 6 dB gain in signal energy-to-noise ratio for the same PEE compared to the existing algorithms. [ABSTRACT FROM AUTHOR]

Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide strong performance guarantees. This paper examines two algorithms for dynamic filtering of sparse signals that are based on efficient $\ell _1$ optimization methods. We first present an analysis for one simple algorithm (BPDN-DF) that works well when the system dynamics are known exactly. We then introduce a novel second algorithm (RWL1-DF) that is more computationally complex than BPDN-DF but performs better in practice, especially in the case where the system dynamics model is inaccurate. Robustness to model inaccuracy is achieved by using a hierarchical probabilistic data model and propagating higher-order statistics from the previous estimate (akin to Kalman filtering) in the sparse inference process. We demonstrate the properties of these algorithms on both simulated data as well as natural video sequences. Taken together, the algorithms presented in this paper represent the first strong performance analysis of dynamic filtering algorithms for time-varying sparse signals as well as state-of-the-art performance in this emerging application. [ABSTRACT FROM AUTHOR]

In this paper, based on a successively accuracy-increasing approximation of the $\ell _0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell _0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell _1$ and $\ell _0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed that leads to a number of weighted $\ell _1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the coordinated beamforming design problem for the multiple-input single-output (MISO) interference channel, assuming only channel distribution information (CDI) known to the transmitters. Under a given requirement on the rate outage probability for receivers, we aim to maximize the system utility (e.g., the weighted sum rate, weighted geometric mean rate, and the weighed harmonic mean rate) subject to the rate outage constraints and individual power constraints. The outage constraints, however, lead to a complicated, nonconvex structure for the considered beamforming design problem and render the optimization problem difficult to handle. Although this nonconvex optimization problem can be solved in an exhaustive search manner, this brute-force approach is only feasible when the number of transmitter-receiver pairs is small. For a system with a large number of transmitter-receiver pairs, computationally efficient alternatives are necessary. Hence, the focus of this paper is the design of such efficient approximation methods. In particular, by employing semidefinite relaxation (SDR) and first-order approximation techniques, we propose an efficient successive convex approximation (SCA) algorithm that provides high-quality approximate beamforming solutions via solving a sequence of convex approximation problems. The solution thus obtained is further shown to be a stationary point for the SDR of the original outage constrained beamforming design problem. Furthermore, we propose a distributed SCA algorithm where each transmitter optimizes its own beamformer using local CDI and information obtained from limited message exchange with the other transmitters. Our simulation results demonstrate that the proposed SCA algorithm and its distributed counterpart indeed converge, and promising performance can be achieved for all the considered system utilities. [ABSTRACT FROM PUBLISHER]

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the squared row norms of the effective channel matrices. [ABSTRACT FROM PUBLISHER]

Performance evaluation of multi-target tracking algorithms is of great practical importance in the design, parameter optimization and comparison of tracking systems. The goal of performance evaluation is to measure the distance between two sets of tracks: the ground truth tracks and the set of estimated tracks. This paper proposes a mathematically rigorous metric for this purpose. The basis of the proposed distance measure is the recently formulated consistent metric for performance evaluation of multi-target filters, referred to as the OSPA metric. Multi-target filters sequentially estimate the number of targets and their position in the state space. The OSPA metric is therefore defined on the space of finite sets of vectors. The distinction between filtering and tracking is that tracking algorithms output tracks and a track represents a labeled temporal sequence of state estimates, associated with the same target. The metric proposed in this paper is therefore defined on the space of finite sets of tracks and incorporates the labeling error. Numerical examples demonstrate that the proposed metric behaves in a manner consistent with our expectations. [ABSTRACT FROM PUBLISHER]

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]

This paper considers a convex optimization problem with a globally coupled linear equality constraint and local polyhedron constraints and develops efficient distributed optimization methods. The considered problem has many engineering applications. Due to the polyhedron constraints, agents in the existing methods have to deal with polyhedron constrained subproblems at each iteration. One of the key challenges is that projection onto a polyhedron set is not trivial, which prohibits the agents from solving these subproblems efficiently. In this paper, based on the alternating direction method of multipliers (ADMM), we propose a new distributed optimization method, called proximal dual consensus ADMM (PDC-ADMM). The PDC-ADMM transforms the polyhedron constraints as quadratic penalty terms in the subproblems, making the subproblems efficiently solvable and consequently reducing the overall computational overhead of the agents. In addition, we propose a randomized PDC-ADMM which can deal with time-varying networks with randomly on/off agents and communication errors, and an inexact (randomized) PDC-ADMM for low-complexity computations. We show that the proposed distributed methods converge to the optimal solution set almost surely and have a \mathcalO\left(1/k\right) ergodic convergence rate in the mean. Numerical results show that the proposed methods offer significantly lower computation time than the existing distributed ADMM method in solving a linearly constrained LASSO problem. [ABSTRACT FROM AUTHOR]

The generalized Hermitian eigenvalue problem (GHEP) is of great use in modern signal processing. Compared with other methods, neural network model based algorithms provide an efficient way to solve such problems online. Up to now, a class of neural network model based generalized feature extraction algorithms have been reported in the literature. However, most existing noncoupled algorithms suffer from the so-called speed-stability problem. In contrast, coupled learning algorithms estimate the generalized eigenvector and generalized eigenvalue simultaneously in coupled manners. Therefore they can solve the speed-stability problem and perform better than noncoupled algorithms. In this paper, we first propose a coupled generalized system, which is obtained by using the Newton’s method and a novel generalized information criterion. Then, based on this coupled generalized system, we successfully obtain two coupled algorithms with normalization steps for minor/principal generalized eigen-pairs extraction. And the technique of multiple generalized eigen-pairs extraction is also introduced in this paper. The convergence of the proposed algorithms is justified by deterministic discrete-time (DDT) approach, with the efficiency and feasibility validated by experimental results as well. Compared with similar work, the proposed algorithms have lower computational complexity, better numerical stability and higher estimation accuracy. [ABSTRACT FROM AUTHOR]

The popular least-mean-squares (LMS) algorithm for adaptive filtering is nonrobust against impulsive noise in the measurements. The presence of this type of noise degrades the transient and steady-state performance of the algorithm. Since the distribution of the impulsive noise is generally unknown, a robust semi-parametric approach to adaptive filtering is warranted, where the output error nonlinearity is adapted jointly with the parameter of interest. In this paper, a robust adaptive filtering algorithm is developed that effectively learns and tracks the output error distribution to improve estimation performance. The performance of the algorithm is analyzed mathematically and validated experimentally. [ABSTRACT FROM AUTHOR]