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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]

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

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

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 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]

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]

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]

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]

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]

Index tracking is a popular passive portfolio management strategy that aims at constructing a portfolio that replicates or tracks the performance of a financial index. The tracking error can be minimized by purchasing all the assets of the index in appropriate amounts. However, to avoid small and illiquid positions and large transaction costs, it is desired that the tracking portfolio consists of a small number of assets, i.e., a sparse portfolio. The optimal asset selection and capital allocation can be formulated as a combinatorial problem. A commonly used approach is to use mixed-integer programming (MIP) to solve small sized problems. Nevertheless, MIP solvers can fail for high-dimensional problems while the running time can be prohibiting for practical use. In this paper, we propose efficient and fast index tracking algorithms that automatically perform asset selection and capital allocation under a set of general convex constraints. A special consideration is given to the case of the nonconvex holding constraints and to the downside risk tracking measure. Furthermore, we derive specialized algorithms with closed-form updates for particular sets of constraints. Numerical simulations show that the proposed algorithms match or outperform existing methods in terms of performance, while their running time is lower by many orders of magnitude. [ABSTRACT FROM PUBLISHER]

Bounded component analysis (BCA) is a recently introduced approach including independent component analysis as a special case under the assumption of source boundedness. In this paper, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as well as independent sources from their mixtures. The stationary points are identified and characterized as either perfect separators, which are the global maxima of the proposed optimization scheme or saddle points. The important result emerging from the analysis is that there are no local optima that can prevent the proposed BCA algorithms from converging to perfect separators. [ABSTRACT FROM PUBLISHER]

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g., a sparsity promoting function), Majorize-Minimize (MM) methods have recently attracted much interest since they are fast, highly flexible, and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the data fidelity term corresponds to a least squares criterion and the cost function is replaced by a sequence of stochastic approximations of it. In this context, we propose an online version of an MM subspace algorithm and we study its convergence by using suitable probabilistic tools. Simulation results illustrate the good practical performance of the proposed algorithm associated with a memory gradient subspace, when applied to both nonadaptive and adaptive filter identification problems. [ABSTRACT FROM PUBLISHER]

Detection of the number of transmit antennas plays an important role in the design of adaptive multiantenna wireless communication systems. This paper develops a detection algorithm based on second- and fourth-order statistics of the received signal and time-varying nature of the wireless channel. In contrast to existing feature-based algorithms, the proposed algorithm does not require a priori information about the transmitted signals, such as coding scheme, modulation type, and pilot patterns. Unlike information-theoretic algorithms, it does not require the number of receive antennas to be larger than that of transmit antennas. In fact, the proposed algorithm is capable of operating with a single receive antenna even for large numbers of transmit antennas. The performance analysis of the proposed algorithm is provided, and the results are verified through simulations. The algorithm exhibits a good performance over a wide range of signal-to-noise ratios, and is robust to the carrier frequency and timing offsets. [ABSTRACT FROM PUBLISHER]

The multiple-input multiple-output (MIMO) system makes efficient use of spectrum and increases the transmission throughput in wireless communications. The sphere decoding (SD) is an efficient algorithm that enables the maximum-likelihood (ML) detection for the MIMO system. However, the SD algorithm has variable complexity, and its complexity increases rapidly with decreasing signal-to-noise ratio (SNR). In this paper, we propose a novel ML detection algorithm for the MIMO system based on differential metrics. We define the differential metrics and derive the associated recursive calculation. We then give the indicative functions, which can be used to possibly find some ML-detected bits of the initial sequence. The indicative functions are further applied to implement an efficient tree search for ML detection. The proposed algorithm does not need QR decomposition and matrix inversion. The tree search process needs only the additive operation, while the number of multiplications before the tree search is constant. Our algorithm can achieve the exact ML detection as the SD algorithm. Unlike the SD algorithm, the complexity of our algorithm reduces with decreasing SNR, whereas at high SNR, the complexity is nearly constant. We also give the convergence analysis for the SD and proposed algorithms, and the simulation verifies our analysis. For the proposed algorithm, the number of necessary memory is constant during the tree search, and the implementation by parallel processing is possible. The soft output of ML-detected bits can also be generated in our algorithm. [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]

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method, which is required for computing the mean square error (MSE) of subspace-based estimators, is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations. [ABSTRACT FROM PUBLISHER]

Linear phase is an important characteristic of digital filters in many signal processing applications. In this paper, two iterative reweighted minimax phase error algorithms are proposed to design nearly linear-phase infinite impulse response (IIR) digital filters with prescribed or simultaneously minimized magnitude errors and preset transition-band gain. In each iteration of the algorithms, a weighted minimax phase error problem with a fixed weight function is firstly solved using a modified Gauss-Newton method with a variable step length, and the weight function of the phase error is then updated using the square root of a modified envelope of the group-delay error of the filter. With the proposed methods, both very small phase error and group-delay error have been obtained while meeting the requirements on the passband and stopband magnitude errors and the transition-band gain. Design examples demonstrate the effectiveness of the proposed methods and the excellent performance of the designed filters. [ABSTRACT FROM PUBLISHER]

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]

Belief propagation (BP) is an efficient algorithm for calculating approximate marginal probability density function (PDF) in large-scale Gaussian graphical models. It is known that when BP converges, the mean calculated by BP is the exact mean of the marginal PDF, while the accuracy of the variance calculated by BP is in general poor and unpredictable. In this paper, an explicit error expression of the variance calculated by BP is derived. By novel representation of this error expression, a distributed message-passing algorithm is proposed to improve the accuracy of the variance calculated by BP. It is proved that the upper bound of the residual error in the improved variance monotonically decreases as the number of selected nodes in a particular set increases, and eventually vanishes to zero as the remaining graph becomes loop-free after removal of the selected nodes. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm. [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]

Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. We further prove that the converged solution satisfies the Karush–Kuhn–Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost. [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]

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]

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]

As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple “correct” indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K>1), provided that the sensing matrix satisfies the RIP with \deltaNK<{{\sqrt{N}}\over{\sqrt{K}+3\sqrt{N}}}. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to \ell1-minimization technique with fast processing speed and competitive computational complexity. [ABSTRACT FROM PUBLISHER]

This paper presents a novel jointly sparse signal reconstruction algorithm for the DOA estimation problem, aiming to achieve faster convergence rate and better estimation accuracy compared to existing \ell 2,1-norm minimization approaches. The proposed greedy block coordinate descent (GBCD) algorithm shares similarity with the standard block coordinate descent method for \ell 2,1-norm minimization, but adopts a greedy block selection rule which gives preference to sparsity. Although greedy, the proposed algorithm is proved to also have global convergence in this paper. Through theoretical analysis we demonstrate its stability in the sense that all nonzero supports found by the proposed algorithm are the actual ones under certain conditions. Last, we move forward to propose a weighted form of the block selection rule based on the MUSIC prior. The refinement greatly improves the estimation accuracy especially when two point sources are closely spaced. Numerical experiments show that the proposed GBCD algorithm has several notable advantages over the existing DOA estimation methods, such as fast convergence rate, accurate reconstruction, and noise resistance. [ABSTRACT FROM PUBLISHER]

Mixed-scaling-rotation (MSR) coordinate rotation digital computer (CORDIC) is an attractive approach to synthesizing complex rotators. This paper presents the fixed-point error analysis and parameter selections of MSR-CORDIC with applications to the fast Fourier transform (FFT). First, the fixed-point mean squared error of the MSR-CORDIC is analyzed by considering both the angle approximation error and signal round-off error incurred in the finite precision arithmetic. The signal to quantization noise ratio (SQNR) of the output of the FFT synthesized using MSR-CORDIC is thereafter estimated. Based on these analyses, two different parameter selection algorithms of MSR-CORDIC are proposed for general and dedicated MSR-CORDIC structures. The proposed algorithms minimize the number of adders and word-length when the SQNR of the FFT output is constrained. Design examples show that the FFT designed by the proposed method exhibits a lower hardware complexity than existing methods. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of estimating the maximal value over a sensor network using wireless links between them. We introduce two heuristic algorithms and analyze their theoretical performance. More precisely, i) we prove that their convergence time is finite with probability one, ii) we derive an upper-bound on their mean convergence time, and iii) we exhibit a bound on their convergence time dispersion. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an iterative interference alignment (IA) algorithm for MIMO cellular networks with partial connectivity, which is induced by heterogeneous path losses and spatial correlation. Such systems impose several key technical challenges in the IA algorithm design, namely the overlapping between the direct and interfering links due to the MIMO cellular topology as well as how to exploit the partial connectivity. We shall address these challenges and propose a three stage IA algorithm. As illustration, we analyze the achievable degree of freedom (DoF) of the proposed algorithm for a symmetric partially connected MIMO cellular network. We show that there is significant DoF gain compared with conventional IA algorithms due to partial connectivity. The derived DoF bound is also backward compatible with that achieved on fully connected K-pair MIMO interference channels. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the joint blind source separation (JBSS) problem and introduce a number of algorithms to solve the JBSS problem using the independent vector analysis (IVA) framework. Source separation of multiple datasets simultaneously is possible when the sources within each and every dataset are independent of one another and each source is dependent on at most one source within each of the other datasets. In addition to source separation, the IVA framework solves an essential problem of JBSS, namely the identification of the dependent sources across the datasets. We propose to use the multivariate Gaussian source prior to achieve JBSS of sources that are linearly dependent across datasets. Analysis within the paper yields the local stability conditions, nonidentifiability conditions, and induced Cramér-Rao lower bound on the achievable interference to source ratio for IVA with multivariate Gaussian source priors. Additionally, by exploiting a novel nonorthogonal decoupling of the IVA cost function we introduce both Newton and quasi-Newton optimization algorithms for the general IVA framework. [ABSTRACT FROM PUBLISHER]

The present paper is a continuing work on the recently established adaptive Fourier decomposition (AFD) mainly stressing on the algorithm aspect, including algorithm analysis and numerical examples. AFD is a variation and realization of greedy algorithm (matching pursuit) suitable for the Hardy H^2 and the L^2 spaces. Applying AFD to a given signal, one obtains a series expansion in the basic signals, called mono-components, that possess non-negative analytic phase derivatives (functions), or, equivalently, meaningful analytic instantaneous frequencies. AFD is shown to be robust with computational complexity comparable with DFT. Consistent to the greedy algorithm principle experiments show that AFD produces (pre-) mono-component series with efficient energy decay that also leads to efficient pointwise convergence, both in terms of computer running time. [ABSTRACT FROM AUTHOR]

In this paper, an optimal amplitude weight expression is derived and presented in closed form. The minimal error variance for location estimation of a near-field source signal that has a low time-bandwidth product is also presented. A noniterative method to calculate and apply weights is proposed to yield more robust estimation results at a lower calculational cost when compared to the traditional iterative method. Besides a theoretical evaluation, the proposed algorithm is also verified through Monte Carlo simulation. The weight expression derived also optimizes the system signal-to-noise ratio (SNR), hence it can be applied to improve the performance of any estimator/detector that utilizes the energy in the sum of sensor output signals. [ABSTRACT FROM AUTHOR]

Dynamic system modeling plays a crucial role in the development of techniques for stationary and nonstationary signal processing. Due to the inherent physical characteristics of systems under investigation, nonnegativity is a desired constraint that can usually be imposed on the parameters to estimate. In this paper, we propose a general method for system identification under nonnegativity constraints. We derive the so-called nonnegative least-mean-square algorithm (NNLMS) based on stochastic gradient descent, and we analyze its convergence. Experiments are conducted to illustrate the performance of this approach and consistency with the analysis. [ABSTRACT FROM AUTHOR]

Consider the multiple-input multiple-output (MIMO) interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper, we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean-square error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, the algorithm and its convergence can be extended to a general class of sum-utility maximization problem. The effectiveness of the proposed algorithm is validated by numerical experiments. [ABSTRACT FROM AUTHOR]

It is well known that the complex-valued nonunitary joint diagonalization (NUJD) problem in blind source separation (BSS) can be linked to the trilinear models. In this paper, by exploring the special structure of the NUJD problem in BSS, we introduce a novel symmetric tri-quadratic cost function and then derive a simultaneous bi-iterative algorithm (s-BIA) for solving the NUJD problem. Finally, three experiments are conducted in order to show the comparatively good performance of the proposed BSS algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a wireless amplify-and-forward relay network with one relay node and multiple source-destination pairs/users and propose a pricing framework that enables the relay to set prices to maximize either its revenue or any desirable system utility. Specifically, depending on the quality of the received signals, the relay sets prices and correspondingly charges the users utilizing its resources for their transmissions. The price is determined in such a way that the relay's revenue or system utility is maximized. Given the specified price, the users competitively employ the relay node to forward their signals. We model each user as a rational player, which aims at maximizing its own net utility through power allocation, and analyze the competition among the users within the framework of noncooperative game theory. It is shown that, in the game played by the users, there always exists a unique pure Nash equilibrium point that can be achieved through distributed iterations. Next, subject to the availability of complete information about the users at the relay, we propose a low-complexity uniform pricing algorithm and an optimal differentiated pricing algorithm, in which the relay either charges the users at a suboptimal uniform price or charges different users at different prices. We also show that, by applying the differentiated pricing algorithm that enforces the users to transmit at certain power levels, any system utility can be maximized. Extensive simulations are conducted to quantify the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multicommodity flow control and multicarrier power allocation problem in multihop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by \cal O\left(\bar T/\bar N\right), where \bar T and \bar N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm. [ABSTRACT FROM AUTHOR]

Distributed power control over interference limited network has received an increasing intensity of interest over the past few years. Distributed solutions (like the iterative water-filling, gradient projection, etc.) have been intensively investigated under quasi-static channels. However, as such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the distributed scaled gradient projection algorithm (DSGPA) in a K pairs multicarrier interference network under a finite-state Markov channel (FSMC) model. We shall analyze the convergence property as well as tracking performance of the proposed DSGPA. Our analysis shows that the proposed DSGPA converges to a limit region rather than a single point under the FSMC model. We also show that the order of growth of the tracking errors is given by \cal O(1 / \barN), where \barN is the average sojourn time of the FSMC. Based on the analysis, we shall derive the tracking error optimal scaling matrices via Markov decision process modeling. We shall show that the tracking error optimal scaling matrices can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed DSGPA over three baseline schemes, such as the gradient projection algorithm with a constant stepsize. [ABSTRACT FROM PUBLISHER]

In this paper, we develop a unified framework for beamforming designs in non-regenerative multiuser two-way relaying (TWR). The core of our framework is the solution to the max-min signal-to-interference-plus-noise-ratio (SINR) problem for multiuser TWR. We solve this problem using a Dinkelbach-type algorithm with near-optimal performance and superlinear convergence. We show that, using the max-min SINR solution as a corner stone, the beamforming designs under various important criteria, such as weighted sum-rate maximization, weighted sum mean-square-error (MSE) minimization, and average bit-error-rate (BER) or symbol-error-rate (SER) minimization, etc, can be reformulated into a monotonic program. A polyblock outer approximation algorithm is then used to find the desired solutions with guaranteed convergence and optimal performance (provided that the core max-min SINR solver is optimal). Furthermore, the proposed unified approach can provide important insights for tackling the optimal beamforming designs in other emerging network models and settings. For instances, we extend the proposed framework to address the beamforming design in collaborative TWR and multi-pair MIMO TWR. Extensive numerical results are presented to demonstrate the merits of the proposed beamforming solutions. [ABSTRACT FROM AUTHOR]

Lattice Reduction aided soft output MIMO detectors (LR-SOMD) have been demonstrated to offer a promising gain. This work explores the potential of implementing a LR-SOMD on a parallel programmable baseband processor. In this paper, first a LR algorithm called the Data Regularized Parallel Lattice Reduction algorithm (DRP-LR) is proposed. Afterwards, a low-complexity LR-SOMD, Radius Constrained Multi-Tree Selective Spanning (RC-MTSS) is presented. RC-MTSS uses a novel multiple-tree search approach for LR-SOMD, while combining the benefits of Sphere Detection (SD) and Selective Spanning with Fast Enumeration (SSFE). A fixed complexity LR-SOMD, Multi-Tree Selective Spanning (MTSS) is also proposed for implementation. Both the algorithms, DRP-LR and MTSS, are enabled to exploit data level parallelism (DLP) and instruction level parallelism (ILP). In order to evaluate performance, the proposed DRP-LR and MTSS are implemented on the ADRES baseband processor for a 4 \times 4 LTE system using QAM-64. DRP-LR achieves an average throughput of 33.33 M LR per second, which is comparable to recently reported ASIC implementations, while MTSS shows an average throughput of 730 Mbps on the same processor. To the best of authors' knowledge, this is the first reported implementation of a LR-SOMD algorithm on a parallel programmable baseband processor. [ABSTRACT FROM AUTHOR]

A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the change in distribution as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and distributed algorithms are proposed in which on-off observation control and censoring is used at each sensor to meet the constraints on data. It is shown that the proposed algorithms are asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. The asymptotic optimality of the proposed algorithms implies that an arbitrary but fixed fraction of data can be skipped without any loss in asymptotic performance as compared to the scheme where all the observations are used for decision making. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by skipping a fixed fraction of observations either deterministically or randomly, independent of the observation process. [ABSTRACT FROM PUBLISHER]

Bounded Component Analysis (BCA) has recently been introduced as an alternative linear decomposition scheme. In this approach the boundedness property of sources is exploited to replace the usual independence assumption with a weaker assumption, which enables development of methods to separate both independent and dependent components from their mixtures. This paper positions total output range minimization based blind source separation approach as a BCA method for the separation of uncorrelated sources. It is shown that the global minimizers of the corresponding optimization problem are the perfect separators. Furthermore, a stationary point analysis for the corresponding algorithms based on symmetrical orthogonalization is provided. The main result of this analysis is that the range minimization based parallel BCA algorithm and the kurtosis maximization based Independent Component Analysis algorithm have related set of identified stationary points. [ABSTRACT FROM PUBLISHER]

This paper exemplifies that the use of multiple kernels leads to efficient adaptive filtering for nonlinear systems. Two types of multikernel adaptive filtering algorithms are proposed. One is a simple generalization of the kernel normalized least mean square (KNLMS) algorithm refid="ref2"/ , adopting a coherence criterion for dictionary designing. The other is derived by applying the adaptive proximal forward-backward splitting method to a certain squared distance function plus a weighted block \ell1 norm penalty, encouraging the sparsity of an adaptive filter at the block level for efficiency. The proposed multikernel approach enjoys a higher degree of freedom than those approaches which design a kernel as a convex combination of multiple kernels. Numerical examples show that the proposed approach achieves significant gains particularly for nonstationary data as well as insensitivity to the choice of some design-parameters. [ABSTRACT FROM PUBLISHER]

Weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance. This paper introduces a fast algorithm to compute the weighted median (WM) of N samples which has linear time and space complexity as opposed to O(N log N) which is the time complexity of traditional sorting algorithms. A popular selection algorithm often used to find the WM in large data sets is Quickselect whose performance is highly dependent on how the pivots are chosen. We introduce an optimization based pivot selection strategy which results in significantly improved performance as well as a more consistent runtime compared to traditional approaches. The selected pivots are order statistics of subsets. In order to find the optimal order statistics as well as the optimal subset sizes, a set of cost functions are derived, which when minimized lead to optimal design parameters. We compare the complexity to Floyd and Rivest's algorithm SELECT which to date has been the fastest median finding algorithm and we show that the proposed algorithm compared with SELECT requires close to 30% fewer comparisons. It is also shown that the proposed selection algorithm is asymptotically optimal for large N. [ABSTRACT FROM PUBLISHER]

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a dictionary which leads to the sparsest representation for a given set of signals. In some applications, the signals of interest can have further structure, so that they can be well approximated by a union of a small number of subspaces (e.g., face recognition and motion segmentation). This implies the existence of a dictionary which enables block-sparse representations of the input signals once its atoms are properly sorted into blocks. In this paper, we propose an algorithm for learning a block-sparsifying dictionary of a given set of signals. We do not require prior knowledge on the association of signals into groups (subspaces). Instead, we develop a method that automatically detects the underlying block structure given the maximal size of those groups. This is achieved by iteratively alternating between updating the block structure of the dictionary and updating the dictionary atoms to better fit the data. Our experiments show that for block-sparse data the proposed algorithm significantly improves the dictionary recovery ability and lowers the representation error compared to dictionary learning methods that do not employ block structure. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a computational framework based on an iterative twisted approximation (ITROX) and a set of associated algorithms for various sequence design problems. The proposed computational framework can be used to obtain sequences (or complementary sets of sequences) possessing good periodic or aperiodic correlation properties and, in an extended form, to construct zero (or low) correlation zone sequences. Furthermore, as constrained (e.g., finite) alphabets are of interest in many applications, we introduce a modified version of our general framework that can be useful in these cases. Several applications of ITROX are studied and numerical examples (focusing on the construction of real-valued and binary sequences) are provided to illustrate the performance of ITROX for each application. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition (EMD) is an adaptive and data-driven approach for analyzing multicomponent nonlinear and nonstationary signals. The stop criterion, envelope technique, and mode-mixing problem are the most important topics that need to be addressed in order to improve the EMD algorithm. In this paper, we study the envelope technique and the mode-mixing problem caused by separating multicomponent AM-FM signals with the EMD algorithm. We present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function (IMF). Then, we present a solution to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated. We experiment on several signals, including simulated signals and real-life signals, to demonstrate the efficacy of the proposed method in resolving the mode-mixing problem. [ABSTRACT FROM PUBLISHER]