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In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm. [ABSTRACT FROM AUTHOR]

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

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]

Equal allocation of bandwidth and/or power may not be efficient for wireless multi-user networks with limited bandwidth and power resources. Optimal joint bandwidth and power allocation strategies for wireless multi-user networks with and without relaying are proposed in this paper for 1) the maximization of the sum capacity of all users; 2) the maximization of the worst user capacity; and 3) the minimization of the total power consumption of all users. It is shown that the proposed allocation problems are convex and, therefore, can be solved efficiently. Moreover, joint bandwidth and power allocation for admission control is considered. A suboptimal greedy search algorithm is developed to solve the admission control problem efficiently. Instructive analysis of the greedy search shows that it can achieve good performance, and the condition under which the greedy search is optimal is derived. The formal and in-depth analysis of the greedy search algorithm presented in this paper can serve as a benchmark for analyzing similar algorithms in other applications. The performance improvements offered by the proposed optimal joint bandwidth and power allocation are demonstrated by simulations. The advantages of the suboptimal greedy search algorithm for admission control are also shown in numerical results. [ABSTRACT FROM PUBLISHER]

In this paper, we study the invertibility of M-variate Laurent polynomial N x P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N x P Laurent polynomial matrix H( z1,.. . , ZM) of degree at most k, we want to find a P x N Laurent polynomial left inverse matrix G(z) of H(z) such that G(z)H(z) = I. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse. The main result of this paper is to prove that H(z) is generically invertible when N P ⩾ M; whereas when N P < M, then H(z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us. [ABSTRACT FROM AUTHOR]

An algorithm that is capable not only of tracking multiple targets but also of "track management"-meaning that it does not need to know the number of targets as a user input-is of considerable interest. In this paper we devise a recursive track-managed filter via a quantized state-space ("bin") model. In the limit, as the discretization implied by the bins becomes as refined as possible (infinitesimal bins) we find that the filter equations are identical to Mahier's probability hypothesis density (PHD) filter, a novel trackmanaged filtering scheme that is attracting increasing attention. Thus, one contribution of this paper is an interpretation of, if not the PHD itself, at least what the PHD is doing. This does offer some intuitive appeal, but has some practical use as well: with this model it is possible to identify the PHD's "target-death" problem, and also the statistical inference structures of the PHD filters. To obviate the target death problem, PHD originator Mahler developed a new "cardinalized" version of PHD (CPHD). The second contribution of this paper is to extend the "bin-occupancy" model such that the resulting recursive filter is identical to the cardinalized PHD filter. [ABSTRACT FROM AUTHOR]

The paper presents two formulations of causal cubic splines with equidistant knots. Both are based on a causal direct B-spline filter with parallel or cascade implementation. In either implementation, the causal part of the impulse response is realized with an efficient infinite-impulse-response (HR) structure, while only the anticausal part is approximated with a finite-order finite-impulse-response (FIR) filter. Resulting cubic coefficients are computed from the causal B-spline coefficients by using a third-order output FIR filter with either single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) structure, depending on the chosen formulation of the cubic spline. The paper demonstrates and proves that the properties of the resulting causal splines are quite different, whether they are based on a more popular B-spline formulation, or a bit neglected tridiagonal matrix formulation. It is shown that the proposed low-complexity but accurate causal interpolators can be realized for many practical applications with the delay of only a few samples. [ABSTRACT FROM AUTHOR]

Recent results have underlined the importance of incoherence in redundant dictionaries for a good behavior of decomposition algorithms like matching and basis pursuit. However, appropriate dictionaries for a given application may not be able to meet the incoherence condition. In such a case, decomposition algorithms may completely fail in the retrieval of the sparsest approximation. This paper studies the effect of introducing a priori knowledge when recovering sparse approximations over redundant dictionaries. Theoretical results show how the use of reliable a priori information (which in this paper appears under the form of weights) can improve the performances of standard approaches such as greedy algorithms and relaxation methods. Our results reduce to the classical case when no prior information is available. Examples validate and illustrate our theoretical statements. [ABSTRACT FROM AUTHOR]

Interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper [21], a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper. [ABSTRACT FROM AUTHOR]

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

The hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for bidden Markov tree models and called it the "upward-downward algorithm." This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new "upward-downward" algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of blind separation of an instantaneous mixture of sources (BSS), which has been addressed in many ways. When power spectral densities of the sources are different, methods using second-order statistics are sufficient to solve this problem. Otherwise, these methods fail and others (higher order statistics, etc.) must be used. In this paper, we propose an iterative method to process the case of sources with the same power spectral density. This method is based on an evaluation of conditional first and second-order statistics only. Restrictions on characteristics of sources are given to reach a solution, and proofs of convergence of the algorithm are provided for particular cases of probability density functions. Robustness of this algorithm with respect to the number of sources is shown through computer simulations. A particular case of sources that have a probability density function with unbounded domain of definition is described; here, the algorithm does not lead directly to a separation state but to an a priori known mixture state. Finally, prospects of links with contrast functions are mentioned, with a possible generalization of them based on results obtained with particular sources. [ABSTRACT FROM AUTHOR]

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]

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have focused on minimizing the absolute value off-diagonal entries of the Gram matrix of these structures. Recently, a method based on convex optimization that operates directly on the vectors of the frame has been shown to produce promising results. This paper gives a detailed analysis of the optimization problem at the heart of this approach and, based on these insights, proposes a new method that substantially outperforms the initial approach and all current methods in the literature for all types of frames, with low and high redundancy. We give extensive experimental results that show the effectiveness of the proposed method and its application to optimized compressed sensing. [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]

In this paper, an optimal unbiased finite impulse response (OUFIR) filter is proposed as a linking solution between the unbiased FIR (UFIR) filter and the Kalman filter (KF). We first derive the batch OUFIR estimator to minimize the mean square error (MSE) subject to the unbiasedness constraint and then find its fast iterative form. It is shown that the OUFIR filter is full horizon (FH) and that its estimate converges to the KF estimate by increasing the horizon length N. As a special feature, we note that the FH OUFIR filter operates almost as fast as the KF. Several other critical properties of the OUFIR filter are illustrated based on simulations and practical applications. Similar to the UFIR filter, and contrary to the KF, the OUFIR filter is highly insensitive to the initial conditions. It has much better robustness than KF against temporary model uncertainties. Finally, the OUFIR filter allows for ignoring system noise, which is typically not well known to the engineer. [ABSTRACT FROM PUBLISHER]

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

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]

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 signal processing, data analysis and scientific computing, one often encounters the problem of decomposing a tensor into a sum of contributions. To solve such problems, both the search direction and the step size are two crucial elements in numerical algorithms, such as alternating least squares algorithm (ALS). Owing to the nonlinearity of the problem, the often used linear search direction is not always powerful enough. In this paper, we propose two higher-order search directions. The first one, geometric search direction, is constructed via a combination of two successive linear directions. The second one, algebraic search direction, is constructed via a quadratic approximation of three successive iterates. Then, in an enhanced line search along these directions, the optimal complex step size contains two arguments: modulus and phase. A current strategy is ELSCS that finds these two arguments alternately. So it may suffer from a local optimum. We broach a direct method, which determines these two arguments simultaneously, so as to obtain the global optimum. Finally, numerical comparisons on various search direction and step size schemes are reported in the context of blind separation-equalization of convolutive DS-CDMA mixtures. The results show that the new search directions have greatly improve the efficiency of ALS and the new step size strategy is competitive. [ABSTRACT FROM AUTHOR]

Source localization especially direction-of-arrival (DOA) estimation using sensor arrays is of considerable interest in both classical array signal processing and radar applications. Most radar systems are designed under the line-of-sight (LOS) assumption with multipath echos treated as undesired clutter noise. Strong multipath, therefore, has a negative impact on the resolution of the radar systems and their ability in accurately localizing the target. Rather than treating multipath as a detrimental effect, the paper introduces time reversal (TR) to exploit spatial/multipath diversity in improving the capability of the existing localization algorithms. In particular, we design TR based range and DOA estimators that adaptively adjust the probing radar waveforms to the multipath characteristics of the environment. The benefits of the spatial/multipath diversity in the proposed DOA and range estimators are quantified by deriving the respective Cramér–Rao bounds (CRB) and comparing them with the analytical expressions for their conventional counterparts. Numerical simulations also confirm the benefit of applying TR to source localization algorithms especially at low signal-to-noise ratios below -5 dB. [ABSTRACT FROM AUTHOR]

This paper studies the achievable rate region for an amplify-and-forward (AF)-based two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed-form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the nonreciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms by solving a sequence of semi-definite programming (SDP) problems after semi-definite relaxation(SDR), where the optimal beamformer can be obtained under the sum-power constraint and approximate optimal solutions can be obtained under the individual power constraints. [ABSTRACT FROM AUTHOR]

Group Lasso is a mixed l1/l2-regularization method for a block-wise sparse model that has attracted a lot of interests in statistics, machine learning, and data mining. This paper establishes the possibility of stably recovering original signals from the noisy data using the adaptive group Lasso with a combination of sufficient block-sparsity and favorable block structure of the overcomplete dictionary. The corresponding theoretical results about the solution uniqueness, support recovery and representation error bound are derived based on the properties of block-coherence and subcoherence. Compared with the theoretical results on the parametrized quadratic program of conventional sparse representation, our stability results are more general. A comparison with block-based orthogonal greedy algorithm is also presented. Numerical experiments demonstrate the validity and correctness of theoretical derivation and also show that in case of noisy situation, the adaptive group Lasso has a better reconstruction performance than the quadratic program approach if the observed sparse signals have a natural block structure. [ABSTRACT FROM PUBLISHER]

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]

A new family of cumulant-based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources. These algorithms perform a joint canonical decomposition (CAND) of several higher order cumulants through a CAND of a three-way array with special symmetries. These techniques are studied in terms of identifiability, performance and numerical complexity. From a signal processing viewpoint, the proposed methods are shown i) to have a better estimation resolution and ii) to be able to process more sources than the other classical cumulant-based techniques. Second, from a numerical analysis viewpoint, we deal with the convergence speed of several procedures for three-way array decomposition, such as the ACDC scheme. We also show how to accelerate the iterative CAND algorithms by using differently the symmetries of the considered three-way array. Next, from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint CAND of several Hermitian multiway arrays compared to the CAND of only one array. This allows us, as a result, to extend the concept of virtual array (VA) to the case of combination of several VAs. [ABSTRACT FROM AUTHOR]

The S transform is a useful linear time-frequency distribution with a progressive resolution. Since it is linear, it filters efficiently in a time-frequency domain by multiplying a mask function. Several different inverse algorithms exist, which may result in different filtering effects. The conventional inverse S transform (IST) proposed by Stockwell et a!. is efficient but suffers from time leakage during filtering. The recent algorithm proposed by Schimmel and Gallart has better time localization during filtering but suffers from a reconstruction error and the frequency leakage during filtering. In this paper, two new IST algorithms are proposed that have better time.frequency localization in filtering than the previous two methods. [ABSTRACT FROM AUTHOR]

The problem of minimizing the sum of a number of component functions is of great importance in the real world. In .this paper, a new incremental optimization algorithm, named normalized incremental subgradient (NIS) algorithm, is proposed for a class of such problems where the component functions have common local minima. The NIS algorithm is performed incrementally just as the general incremental subgradient (IS) algorithm and thus can be implemented in a distributed way. In the NIS algorithm, the update of each subiteration is based on a search direction obtained by individually normalizing each component of subgradients of component functions, resulting in much better convergence performance as compared to the IS algorithm and other traditional optimization methods (e.g., Gauss-Newton method). The convergence of the NIS algorithm with both diminishing stepsizes and constant stepsizes is proved and analyzed theoretically. Two important applications are presented. One is to solve a class of convex feasibility problems in a distributed way and the other is distributed maximum likelihood estimation. Numerical examples, arising from two important topics in the area of wireless sensor networks-source localization and node localization-demonstrate the effectiveness and efficiency of the NIS algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider distributed estimation of a noise-corrupted deterministic parameter in energy-constrained wireless sensor networks from energy-distortion perspective. Given a total energy budget allowable to be used by all sensors, there exists a tradeoff between the subset of active sensors and the energy used by each active sensor in order to minimize the estimation MSE. To determine the optimal quantization bit rate and transmission energy of each sensor, a concept of equivalent unit-energy MSE function is introduced. Based on this concept, an optimal energy-constrained distributed estimation algorithm for homogeneous sensor networks and a quasi-optimal energy-constrained distributed estimation algorithm for heterogeneous sensor networks are proposed. Moreover, the theoretical energy-distortion performance bound for distributed estimation is addressed and it is shown that the proposed algorithm is quasi-optimal within a factor 2 of the theoretical lower bound. Simulation results also show that the proposed method can achieve a significant reduction in the estimation MSE when compared with other uniform schemes. Finally, the proposed algorithm is easy to implement in a distributed manner and it adapts well to the dynamic sensor environments. [ABSTRACT FROM AUTHOR]

High resolution radars (HRRs) transmit a wideband signal to achieve a high range resolution. A target is considered as composed of multiple scatterers, which occupy or spread in multiple radar range cells with several scatterers in each cell. Therefore, the refection of a target spreads in multiple range cells in the received signal, which contains more information of target than that obtained from low resolution radars. The target in high resolution radar systems is a range-spread target. The range-spreading or echo features of target are utilized for target detection and identification. The echoes of target are convolutions of transmitted signals with target range-scattering functions dependent on the gesture of target to the line of radar sight. A single echo is used in the conventional detection. It is difficult for target detection and identification in low signal-to-noise ratio (SNR) condition. In this paper, we propose a new range-spread target detection scheme exploiting the image features of cross time-frequency distribution (TFD) of a pair of adjacent received signals. After dechirping, the received signal reflected from target consists of multiple sinusoidal components due to its multiple scatterers when a linear frequency modulated (LFM) signal is transmitted from radar. Some regular image patterns or features of target appear in the cross TFD of two adjacent received signals, while the cross TFD of two independent Gaussian noises does not show such patterns. The cross TFD features are exploited in the proposed scheme. Three steps are composed in the proposed scheme. Firstly, a cross smoothed-pseudo Wigner-Ville distribution (CSPWVD) is made for two adjacent received signals to generate a two-dimensional (2-D) TF image. Then, some regular geometric patterns are detected and extracted from the image. At last, two features of the extracted geometric patterns are jointly utilized to detect target. The proposed algorithm is verified by using raw radar data. It outperforms the conventional detection methods. [ABSTRACT FROM AUTHOR]

Nuclear quadrupole resonance (NQR) is a radio-frequency (RF) spectroscopic technique, able to detect the presence of many high explosives and narcotics. In practice, the weak NQR signal is often corrupted by strong RF interference (RFI); therefore, various multichannel detection algorithms have recently been proposed for NQR. However, these algorithms allow for only a single compound/polymorph, whose associated amplitudes are assumed to be known to within a scaling. Regrettably, these amplitudes are typically prone to some level of uncertainty; and, in several cases of interest, signals from a mixture of NQR compounds/polymorphs may be present, leading to performance degradation in the aforementioned algorithms. In this paper, we develop a robust multisensor hybrid algorithm able to process NQR signals from mixtures while also allowing for errors in the assumed amplitudes. Numerical investigations indicate that the proposed algorithm provides significant performance gains as compared to existing algorithms in the case when there are multiple polymorphs present and/or when uncertainties in the amplitudes exist. [ABSTRACT FROM AUTHOR]

The rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of non-adaptive linear measurements, under appropriate conditions on the measurement matrix. The vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern. In this paper, we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors. Extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set. Instead, we prove that the entire infinite set of sparse vectors can be recovered by solving a single, reduced-size finite-dimensional problem, corresponding to recovery of a finite set of sparse vectors. We then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements. Our approach is exact for both countable and uncountable sets, as it does not rely on discretization or heuristic techniques. To efficiently find the single sparse vector produced by the last reduction step, we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector. Numerical experiments on random data demonstrate that, when applied to infinite sets, our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate. In the finite model, our boosting algorithm has fast run time and much higher recovery rate than known popular methods. [ABSTRACT FROM AUTHOR]

Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and direction-of-arrival (DOA) estimation. This paper presents a procedure for multiple-input multiple-output instantaneous blind identification based on second-order temporal properties of the signals, such as coloredness and nonstationarity. The procedure consists of two stages. First, based on assumptions on the second-order temporal structure (SOTS) of the source and noise signals, and using subspace techniques, the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations. Then, this nonlinear system of equations is solved by means of a so-called homotopy method, which provides a general tool for solving (possibly nonexact) systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system. Our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions, something that is often believed to be impossible when using only second-order statistics. In addition, since our algorithm does not require any assumption on the mixing matrix, also mixing matrices that are rank-deficient or even have identical columns can be identified. Finally, we give examples and performance results for speech source signals. [ABSTRACT FROM AUTHOR]

Cost functions used in blind source separation are often defined in terms of expectations, i.e., an infinite number of samples is assumed. An open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case. To answer this question, we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions. In particular, we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix. The method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function. This shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function. We also answer a long-standing problem of the mean-squared error (MSE) behavior of the (finite sample) least squares constant modulus algorithm (LS-CMA), namely whether there exist LS-CMA receivers with good MSE performance. We demonstrate how the proposed techniques can be used to determine the required number of samples for LS-CMA to exceed a specified performance. The paper concludes with simulations that validate the results. [ABSTRACT FROM AUTHOR]

This paper presents methods for independently modifying the time and pitch scale of acoustic signals, with an emphasis on speech signals. The algorithms developed here use parametric (sinusoidal) modeling techniques introduced by other authors, but new perspectives on the role of vocal tract decomposition and maintaining phase relationships between sinusoidal tracks are derived that achieve improved output quality with decreased computational load. Simulation results are provided to illustrate performance, and the algorithms developed here have been demonstrated capable of implementation on simple DSP hardware. [ABSTRACT FROM AUTHOR]

Polarization diversity has proved to be a useful tool for radar detection, especially when discrimination by Doppler effect is not possible. In this paper, we address the problem of improving the performance of polarimetric detectors for targets in heavy inhomogeneous clutter. First, we introduce a new polarimetric radar model that includes the realistic dependence of the clutter reflections on the transmitted signal. Then, we develop a polarimetric detection test that is robust to inhomogeneous clutter. We run this polarimetric test against synthetic and real data to assess its performance in comparison with existing polarimetric detectors. Finally, we propose a polarimetric waveform-design algorithm to further improve the target-detection performance. A numerical analysis is presented to demonstrate the potential performance improvement that can be achieved with this algorithm. [ABSTRACT FROM AUTHOR]

The maximum-likelihood detection (MLD) algorithm is the optimal detection scheme for vertical Bell Laboratories layered space-time (V-BLAST) systems. However, it is generally infeasible to implement the MLD algorithm in practical systems because of its high computational complexity. In this paper, we used two parallel interference cancellation techniques, including precancellation and postcancellation, to simplify the MLD algorithm into a class of computationally efficient suboptimal detection algorithms, herein called the generalized parallel interference cancellation (GPIC) algorithm. Numerical analysis shows that the GPIC algorithm can approximately achieve the MLD performance with considerably low and stable computational complexity. Furthermore, it can be significantly accelerated via parallel processing methods. With near-optimal performance, low and stable complexity, and high running speed, the GPIC algorithm is very suitable for real-time communication systems. [ABSTRACT FROM AUTHOR]

This paper presents a multidimensional extension of the Schur-Cohn algorithm for testing BIBO stability in N variables. This new method only needs a unique condition to be checked, as an alternative to the set of N conditions of the well-known Huang-Jury-Anderson stability test. The proposed algorithm is based on a generalization of the Schur coefficients recently obtained by the authors. In the two-variable case a simplification to the Sturm algorithm is presented, which can also be used in the case of a polynomial with complex coefficients. This approach is illustrated on several numerical examples. [ABSTRACT FROM AUTHOR]

We consider the design and analysis of quantizers for equal gain transmission (EGT) systems with finite rate feedback-based communication in flat-fading multiple input single output (MISO) systems. EGT is a beamforming technique that maximizes the MISO channel capacity when there is an equal power-per-antenna constraint at the transmitter, and requires the feedback of t - 1 phase angles, when there are t antennas at the transmitter. In this paper, we contrast two popular approaches for quantizing the phase angles: vector quantization (VQ) and scalar quantization (SQ). On the VQ side, using the capacity loss with respect to EGT with perfect channel information at transmitter as performance metric, we develop a criterion for designing the beamforming codebook for quantized EGT (Q-EGT). We also propose an iterative algorithm based on the well-known generalized Lloyd algorithm, for computing the beamforming vector codebook. On the analytical side, we study the performance of Q-EGT and derive closed-form expressions for the performance in terms of capacity loss and outage probability in the case of i.i.d. Rayleigh flat-fading channels. On the SQ side, assuming uniform scalar quantization and i.i.d. Rayleigh flat-fading channels, we derive the high-resolution performance of quantized EGT and contrast the performance with that of VQ. We find that although both VQ and SQ achieve the same rate of convergence (to the capacity with perfect feedback) as the number of feedback bits B increases, there exists a fixed gap between the two. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of source separation in the case when the observations result from a multiple-input multiple-output convolutive mixing system. In a blind framework, higher order contrast functions have been proved to be efficient for extracting sources. Inspired by a semiblind approach, we propose new contrast functions for blind signal separation that make use of reference signals. The main advantage of this approach consists in the quadratic form of these criteria: the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available. The separation of the other sources from the mixture is then carried out by an iterative deflation method. Furthermore, these contrasts are shown to be valid for both independent identically distributed (i.i.d.) and non-i.i.d. source signals. The performance offered by these criteria is investigated through simulations: they appear as very appealing tools compared with some classical contrast functions. [ABSTRACT FROM AUTHOR]

This paper studies direction finding of electromagnetic energy sources using passive vector sensor arrays whose manifold is only nominally known. The problem of direction finding is studied in the context of an airborne array, thus facilitating the observation of a ground-based source from multiple look-angles. A calibration algorithm explicitly accounting for the polarization diverse nature of the vector sensor is developed. It is also shown that the direction finding performance provided by a conventional array calibration algorithm is greatly enhanced with usage of the proposed polarization diverse calibration algorithm. [ABSTRACT FROM AUTHOR]

Linear space-time block codes (STBCs) have proven their effectiveness in performance improvement of wireless multiple-input multiple-output communication systems. Their successful decoding, however, requires reliable channel knowledge at the receiver. In this paper, we present a semiblind channel estimation method for linear STBC without the usual code orthogonality condition. We provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration. We also present a simple channel estimation algorithm. Finally; we provide simulation results that illustrate the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

The polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial-phase signals (PPSs) with the maximum likelihood method. The transform converts a one-dimensional (1-D) data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated. A prohibitive computational load is generally needed for high-order polynomial-phase signals although the 1-D fast Fourier transform (FFT) algorithm can be used. Based on the split-radix concept, this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity. Comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

While the theory of estimation of monocomponent polynomial phase signals is well established, the theoretical and methodical treatment of multicomponent polynomial phase signals (mc-PPSs) is limited. In this paper, we investigate several aspects of parameter estimation for mc-PPSs and derive the Cramér-Rao bound. We show the limits of existing techniques and then propose a nonlinear least squares (NLS) approach. We also motivate the use the Nelder-Mead simplex algorithm for minimizing the nonlinear cost function. The slight increase in computational complexity is a tradeoff for improved mean square error performance, which is evidenced by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we derive a stochastic maximum-likelihood (ML) method for estimating spatio-temporal parameters for multiple-input multiple-output (M1MO) channels. Such estimators are needed in propagation studies where extensive channel measurements and sounding are required. These are seminal tasks in the process of developing advanced channel models. The proposed method employs an angular von Mises distribution model which is appropriate for angular data observed in channel measurement campaigns. The signal model is stochastic, and consequentially the method is particularly useful for estimation of the diffuse scattering component. This approach leads to lower complexity and faster convergence in comparison to deterministic models. These benefits are due to lower dimensionality of the model, leading to a simpler optimization problem. The statistical performance of the estimator is studied by establishing the Cramér-Rao lower bound (CRLB) and comparing the variances. The simulations show that the variance of the proposed estimation technique reaches the CRLB for relatively small sample size. The estimator is robust in the sense that meaningful results are obtained when applied to data generated by channel models other than the one used in its derivation. [ABSTRACT FROM AUTHOR]

In this paper, a regularized spectral estimation formula and a regularized iterative algorithm for band-limited extrapolation are presented. The ill-posedness is taken into account. First the Fredholm equation is regularized. Then it is transformed to a differential equation in the case where the time interval is R. A fast algorithm to solve the differential equation is given by the finite difference and a regularized spectral estimation formula is obtained. Then a regularized iterative extrapolation algorithm is introduced and compared with the Papoulis and Gerchberg algorithm. [ABSTRACT FROM AUTHOR]

Given a random vector p with a probability density function (pdf) π(p), a credible set π(p) with level α is a set that contains p with a probability α. The problem of characterizing minimal-volume credible sets (which correspond to level sets for π) is considered. It is only assumed that the expression of π(p) results from a combination of elementary operators (+, -, *, /) and elementary functions (sin, cos, abs, etc.). This paper provides an algorithm able to compute accurate inner and outer approximations of minimal-volume credible sets, in a guaranteed way. The approach is based on interval analysis and an application to nonlinear parameter estimation, in a Bayesian context, is treated. A windows solver associated with the presented algorithm is made available at http://www.ensieta.fr/e3i2/Jaulin/bayes.zip. [ABSTRACT FROM AUTHOR]

In this paper we consider the Cramer-Rao lower bound (CRB) for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols (DSs) as well as known pilot symbols (PSs). We point out that the CRB depends on the location of the PSs in the burst, the number of PSs, the number of DSs, the signal-to-noise ratio (SNR), and the data modulation scheme. Distributing the PSs symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation, making the CRB for phase estimation independent of the specific location of the PSs. At low and moderate SNR, the CRBs for both phase and frequency estimation decrease as the fraction of the PSs in the burst increases. In addition, the CRB for frequency estimation decreases as the PSs are separated with more DSs. Numerical evaluation of the CRB indicates that the carrier phase and frequency of a "hybrid" burst (i.e., containing PSs and DSs) can be estimated more accurately when exploiting both the presence of the DSs and the a priori knowledge about the PSs, instead of using only the knowledge about the PSs (and ignoring the DSs), or considering all the received symbols (PSs and DSs) as unknown (and ignoring the knowledge about the PSs). Comparison of the CRB with the performance of existing carrier synchronizers shows that the iterative soft-decision-directed (sDD) estimator with data-aided (DA) initialization performs very closely to the CRB and provides a large improvement over the classical non-data-aided (NDA) estimator at lower SNR. [ABSTRACT FROM AUTHOR]

This paper is concerned with recursive estimation using augmented data. We study two recursive procedures closely linked with the well-known expectation and maximization (EM) and space alternating generalized EM (SAGE) algorithms. Unlike iterative methods, the recursive EM and SAGE-inspired algorithms give a quick update on estimates given new data. Under mild conditions, estimates generated by these procedures are strongly consistent and asymptotically normally distributed. These mathematical properties are valid for a broad class of problems. When applied to direction of arrival (DOA) estimation, the recursive EM and SAGE-inspired algorithms lead to a very simple and fast implementation of the maximum-likelihood (ML) method. The most complicated computation in each recursion is inversion of the augmented information matrix. Through data augmentation, this matrix is diagonal and easy to invert. More importantly, there is no search in such recursive procedures. Consequently, the computational time is much less than that associated with existing numerical methods for finding ML estimates. This feature greatly increases the potential of the ML approach in real-lime processing. Numerical experiments show that both algorithms provide good results with low computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we present an entropy-directed deterministic annealing optimization algorithm and show its applicability to the problem of designing digital filters with discrete coefficients, each implemented as a sum of signed power-of-two terms and additional general hardware constraints. The algorithm is based on analogies from statistical mechanics and is related to the well-known mean field annealing algorithm. It utilizes estimates of conditional entropy to prune the problem during the optimization, thereby reducing the computational time by 30 to 50%. In conjunction with a scheme to compute the value of the objective function as a sequence of updates, this approach leads to a very fast algorithm. As an application example demonstrating the potential of the new method, we consider the design of digital filters with discrete coefficients consisting of a minimum number of signed power-of-two terms. [ABSTRACT FROM AUTHOR]

In this paper, efficient architectures for realizing the recursive discrete cosine transform (DCT) and the recursive inverse DCT (IDCT) are proposed. By respectively folding the inputs of the DCT and the outputs of the IDCT, efficient formulations of the DCT and IDCT are derived to construct a transform kernels. The data throughout per transformation is twice that of the existing methods by spending only half of the computational cycles used by the single folding algorithms. To further improve efficiency, the double folding recursive architectures of the DCT and IDCT are developed. The computational cycles of the DCT are half of the single folding method, and the data throughout of the IDCT is twice that of the single folding method. The regular and modular properties of the proposed recursive archietectures are suitable for very scale integration (VLSI) implementation. With high throughout advantage, the proposed structures could be implemented with less power consumption, which could be applied to low rate video in mobile and portable information appliances. [ABSTRACT FROM AUTHOR]