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Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data. [ABSTRACT FROM AUTHOR]

We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications. In this framework, we show that under a minimum separation between the time-frequency shifts, all the unknowns that characterize the system can be recovered precisely and with high probability provided that a lower bound on the number of the observed samples is satisfied. The proposed framework is based on a 2D atomic norm minimization problem, which is shown to be reformulated and solved via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided. [ABSTRACT FROM AUTHOR]

Parameter uncertainties and measurement outliers unavoidably exist in a real linear system. Such uncertainties and outliers make the true joint state-measurement distributions (induced by the true system model) deviate from the nominal ones (induced by the nominal system model) so that the performance of the optimal state estimator designed for the nominal model becomes unsatisfactory or even unacceptable in practice. The challenges are to quantitatively describe the uncertainties in the model and the outliers in the measurements, and then robustify the estimator in a right way. This article studies a distributionally robust state estimation framework for linear systems subject to parameter uncertainties and measurement outliers. It utilizes a family of distributions near the nominal one to implicitly describe the uncertainties and outliers, and the robust state estimation in the worst case is made over the least-favorable distribution. The advantages of the presented framework include: 1) it only uses a few scalars to parameterize the method and does not require the structural information of uncertainties; 2) it generalizes several classical filters (e.g., the fading Kalman filter, risk-sensitive Kalman filter, relative-entropy Kalman filter, outlier-insensitive Kalman filters) into a unified framework. We show that the distributionally robust state estimation problem can be reformulated into a linear semi-definite program and in some special cases it can be analytically solved. Comprehensive comparisons with existing state estimation frameworks that are insensitive to parameter uncertainties and measurement outliers are also conducted. [ABSTRACT FROM AUTHOR]

This work studies the field prediction and smoothing problems, where the spatio-temporal field in 2-D is described by a stochastic dynamical system and observed by a number of spatially deployed sensors. We adopt a finite-element technique to approximate the field dynamics with piece-wise Gaussian functions, leading to a high-dimensional linear stochastic system. By exploiting its sparsity, a local covariance intersection-based filter and smoother are developed in each sensor only for a moderate number of state variables via communications with nearby sensors. Such a cooperative scheme is both communication and computation efficient. We prove the uniform stability of the local filter and smoother under mild conditions, and validate their effectiveness on two application examples: the temperature prediction of a metal rod and the source localization of a PM2.5 field with a real dataset in a city of China. [ABSTRACT FROM AUTHOR]

Recently, a novel method for developing filtering algorithms, based on the interconnection of two Bayesian filters and called double Bayesian filtering, has been proposed. In this manuscript we show that the same conceptual approach can be exploited to devise a new smoothing method, called double Bayesian smoothing. A double Bayesian smoother combines a double Bayesian filter, employed in its forward pass, with the interconnection of two backward information filters used in its backward pass. As a specific application of our general method, a detailed derivation of double Bayesian smoothing algorithms for conditionally linear Gaussian systems is illustrated. Numerical results for two specific dynamic systems evidence that these algorithms can achieve a better complexity-accuracy tradeoff and tracking capability than other smoothing techniques recently appeared in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a different interpretation of the cyclic Wiener filter (CWF) for digital (in-phase/quadrature) IQ-modulated signals, such as phase-shift keying (PSK) or quadrature amplitude modulations (QAM). We demonstrate that the CWF can be implemented as a multirate filter instead of the frequency-shift (FRESH) filter implementation found in the literature. The multirate implementation consists of a fractionally spaced equalizer (FSE) followed by a pulse shaping filter, thus establishing a direct relationship between the CWF and FSEs. Afterwards, the results from the study are applied to develop a simple blind adaptive algorithms for signal estimation, which are benchmarked against the most common CWF implementation based on FRESH filters. [ABSTRACT FROM AUTHOR]

We consider the design of a linear sensing system with a fixed energy budget assuming that the sampling noise is the dominant noise source. The energy constraint implies that the signal energy per measurement decreases linearly with the number of measurements. When the maximum sampling rate of the sampling circuit is chosen to match the designed sampling rate, the assumption on the noise implies that its variance increases approximately linearly with the sampling rate (number of measurements). Therefore, the overall SNR per measurement decreases quadratically in the number of measurements. Our analysis shows that, in this setting there is an optimal number of measurements. This is in contrast to the standard case, where noise variance remains unchanged with sampling rate, in which case more measurements imply better performance. Our results are based on a state evolution technique of the well-known approximate message passing algorithm. We consider both the sparse (e.g. Bernoulli-Gaussian and least-favorable distributions) and the non-sparse (e.g. Gaussian distribution) settings in both the real and complex domains. Numerical results corroborate our analysis. [ABSTRACT FROM AUTHOR]

Convolution sum system representations are commonly used in signal processing. It is known that the convolution sum, treated as the limit of its partial sums, can be divergent for certain continuous signals and stable linear time-invariant (LTI) systems, even when the convergence of the partial sums is treated in a distributional setting. In this paper, we ask a far more general question: is it at all possible to define a generalized convolution sum with natural properties that works for all absolutely integrable continuous signals that vanish at infinity and all stable LTI systems? We prove that the answer is “no.” Further, for certain subspaces, we give a sufficient and necessary condition for uniform convergence. Finally, we discuss the implications of our results on the effectiveness of window functions in the convolution sum. [ABSTRACT FROM AUTHOR]

This paper addresses the use of the $Z$ transform to synthesize radiation patterns with prescribed nulls from a phased array of electronically reconfigurable leaky-wave antennas (LWAs). This approach provides the relationship between such antennas and linear and time invariant (LTI) systems. Using this signal processing perspective, the proper locations of the poles and zeros of the $Z$ transform of the associated LTI system provide a radiation pattern with prescribed specifications (mainly main lobes’ directions and surrounding radiation nulls). Then, these poles and zeros’ positions can be transformed into particular values of the LWA array control coefficients. The effectiveness of the proposed technique is demonstrated with the synthesis of various radiation patterns, with application to reconfigurable smart antennas. A comparison with more conventional uniform linear array architecture is also performed to evaluate the synthesis flexibility and system complexity of the proposed approach. [ABSTRACT FROM AUTHOR]

Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be both effective and easily optimizable. Motivated by the entropy concept from information theory, in this paper we propose the generalized Shannon entropy function and Rényi entropy function of the signal as the sparsity promoting regularizers. Both entropy functions are nonconvex, non-separable. Their local minimums only occur on the boundaries of the orthants in the Euclidean space. Compared to other popular objective functions, minimizing the generalized entropy functions adaptively promotes multiple high-energy coefficients while suppressing the rest low-energy coefficients. The corresponding optimization problems can be recasted into a series of reweighted $l_1$ -norm minimization problems and then solved efficiently by adapting the FISTA. Sparse signal recovery experiments on both the simulated and real data show that the proposed entropy functions minimization approaches perform better than other popular approaches and achieve state-of-the-art performances. [ABSTRACT FROM AUTHOR]

In this paper, we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were suggested only for the Gaussian denoising task, leaving more complicated restoration problems without a generally constructive approach. Here, we present practical methods for complexity-regularized restoration of signals, accommodating deteriorations caused by a known linear degradation operator of an arbitrary form. Our iterative procedure, obtained using the alternating direction method of multipliers (ADMM) approach, addresses the restoration task as a sequence of simpler problems involving $ \ell _2$ -regularized estimations and rate-distortion optimizations (considering the squared-error criterion). We replace the rate-distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression. Additionally, we propose a shift-invariant complexity regularizer, measuring the bit-cost of all the shifted forms of the estimate, extending our method to use averaging of decompressed outputs gathered from compression of shifted signals. On the theoretical side, we present an analysis of complexity-regularized restoration of a cyclo-stationary Gaussian signal from deterioration by a linear shift-invariant operator and an additive white Gaussian noise. The theory shows that optimal complexity-regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter. These ideas are realized also in the proposed practical methods. Finally, we present experiments showing good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards. [ABSTRACT FROM AUTHOR]

In this paper, we study the validity of the usual convolution sum sampling representation of linear time-invariant (LTI) systems. We consider continuous input signals with finite energy that are absolutely integrable and vanish at infinity. Even for these benign signals, the convolution sum does not always converge. There exist LTI systems and signals such that the convolution sum diverges even in a distributional sense. This result shows that the practice of multiplying a signal with a Dirac comb and convolving subsequently with the impulse response of the LTI system is not valid for this signal space. We further fully characterize the LTI systems for which we have convergence for all signals in the space, and establish a connection between the pointwise, uniform, and distributional convergence. In particular, we show that the convolution sum converges in a distributional sense if and only it converges in a classical pointwise sense. Hence, for this signal space, nothing can be gained by treating the convergence in a distributional sense. [ABSTRACT FROM AUTHOR]

A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties enabling compact calculus and physically interpretable filtering relations in the frequency domain. The design of filters exhibiting fundamental properties of polarization optics (birefringence and diattenuation) is straightforward. It yields an efficient spectral synthesis method and new insights on Wiener filtering for bivariate signals with prescribed frequency-dependent polarization properties. This generic framework facilitates original descriptions of bivariate signals in two components with specific geometric or statistical properties. Numerical experiments support our theoretical analysis and illustrate the relevance of the approach on synthetic data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven to be more versatile than linear systems for dealing with complex-value signals. To be able to use the WL concept in kernel methods, we need to introduce a pseudo-kernel to complement the standard kernel in RKHS, which is not defined in previous RKHS approaches in the existing literature. In this paper, we present WL-RKHS, its properties, and the kernel and pseudo-kernel designs. We illustrate the need of the pseudo-kernel with simply verifiable examples that allow understanding the intuitions behind this kernel. We conclude this paper, showing that in the all-relevant nonlinear equalization problem the pseudo-kernel plays a significant role and previous approaches that do not rely on this kernel clearly underperform. [ABSTRACT FROM PUBLISHER]

Noncontact estimation of respiratory pattern (RP) and respiratory rate (RR) has multiple applications. Existing methods for RP and RR measurement fall into one of the three categories—1) estimation through nasal air flow measurement, 2) estimation from video-based remote photoplethysmography, and 2) estimation by measurement of motion induced by respiration using motion detectors. However, these methods require specialized sensors, are computationally expensive, and/or critically depend on selection of a region of interest (ROI) for processing. In this paper, a general framework is described for estimating a periodic signal driving noisy linear time-invariant (LTI) channels connected in parallel with unknown dynamics. The method is then applied to derive a computationally inexpensive method for estimating RP using two-dimensional cameras that does not critically depend on ROI. Specifically, RP is estimated by imaging changes in the reflected light caused by respiration-induced motion. Each spatial location in the field of view of the camera is modeled as a noise-corrupted LTI measurement channel with unknown system dynamics, driven by a single generating respiratory signal. Estimation of RP is cast as a blind deconvolution problem and is solved through a method comprising subspace projection and statistical aggregation. Experiments are carried out on 31 healthy human subjects by generating multiple RPs and comparing the proposed estimates with simultaneously acquired ground truth from an impedance pneumograph device. The proposed estimator agrees well with the ground truth in terms of correlation measures, despite variability in clothing pattern, camera angle, and ROI. [ABSTRACT FROM PUBLISHER]

The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization. [ABSTRACT FROM PUBLISHER]

Signal processing on graphs finds applications in many areas. In recent years, renewed interest on this topic was kindled by two groups of researchers. Narang and Ortega constructed two-channel filter banks on bipartitie graphs described by Laplacians. Sandryhaila and Moura developed the theory of linear systems, filtering, and frequency responses for the case of graphs with arbitrary adjacency matrices, and showed applications in signal compression, prediction, etc. Inspired by these contributions, this paper extends classical multirate signal processing ideas to graphs. The graphs are assumed to be general with a possibly nonsymmetric and complex adjacency matrix. The paper revisits ideas, such as noble identities, aliasing, and polyphase decompositions in graph multirate systems. Drawing such a parallel to classical systems allows one to design filter banks with polynomial filters, with lower complexity than arbitrary graph filters. It is shown that the extension of classical multirate theory to graphs is nontrivial, and requires certain mathematical restrictions on the graph. Thus, classical noble identities cannot be taken for granted. Similarly, one cannot claim that the so-called delay chain system is a perfect reconstruction system (as in classical filter banks). It will also be shown that $M$ -partite extensions of the bipartite filter bank results will not work for $M$-channel filter banks, but a more restrictive condition called $M$-block cyclic property should be imposed. Such graphs are studied in detail. A detailed theory for $M$ -channel filter banks is developed in a companion paper. [ABSTRACT FROM PUBLISHER]

Linear Gaussian state-space models are ubiquitous in signal processing, and an important procedure is that of estimating system parameters from observed data. Rather than making a single point estimate, it is often desirable to conduct Bayesian learning, in which the entire posterior distribution of the unknown parameters is sought. This can be achieved using Markov chain Monte Carlo. On some occasions it is possible to deduce the form of the unknown system matrices in terms of a small number of scalar parameters, by considering the underlying physical processes involved. Here we study the case where this is not possible, and the entire matrices must be treated as unknowns. An efficient Gibbs sampling algorithm exists for the basic formulation of linear model. We extend this to the more challenging situation where the transition model is possibly degenerate, i.e., the transition covariance matrix is singular. Appropriate Markov kernels are devised and demonstrated with simulations. [ABSTRACT FROM PUBLISHER]

This paper considers parameter estimation of linear systems under sensor-to-estimator communication constraint. Due to the limited battery power and the traffic congestion over a large sensor network, each sensor is required to reduce the rate of communication between the estimator and itself. We propose an observation-driven sensor scheduling policy such that the sensor transmits only the important measurements to the estimator. Unlike the existing deterministic scheduler, our stochastic scheduling is smartly designed to well compensate for the loss of the Gaussianity of the system. This results in a nice feature that the maximum-likelihood estimator (MLE) is still able to be recursively computed in a closed form, and the resulting estimation performance can be explicitly evaluated. Moreover, an optimization problem is formulated and solved to obtain the best parameters of the scheduling policy under which the estimation performance becomes comparable to the standard MLE with full measurements under a moderate transmission rate. Finally, simulations are included to validate the theoretical results. [ABSTRACT FROM AUTHOR]

We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being stable in the mean. We also find a lower bound for the forgetting factor that ensures mean-square stability of the algorithm and calculate the theoretical steady-state mean-square deviation (MSD). We verify the effectiveness of the proposed algorithm and the accuracy of the predicted steady-state MSD via simulations. [ABSTRACT FROM PUBLISHER]

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage, while maintaining the theoretical convergence of the sampler. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost per effective sample. The connection between this algorithm and some existing strategies is given and its performance is illustrated on a linear inverse problem of image resolution enhancement. [ABSTRACT FROM PUBLISHER]

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics. It has been shown recently that, locally, the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint. In this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications. These analytical tools can also be applied to other algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem. [ABSTRACT FROM PUBLISHER]

Toeplitz-structured linear systems arise often in practical engineering problems. Correspondingly, a number of algorithms have been developed that exploit Toeplitz structure to gain computational efficiency when solving these systems. Early “fast” algorithms required \cal O(n^2) operations, but recent “superfast” algorithms are more efficient. In this work, we present a superfast algorithm for Tikhonov regularization of Toeplitz systems. Using an “extension-and-transformation” technique, our algorithm translates a Tikhonov-regularized Toeplitz system into a type of specialized polynomial problem known as tangential interpolation. Under this formulation, we can compute the solution in only \cal O(KN\log ^2 N) operations, where K is the number of regularizers and N is on the order of the number of parameters defining the system matrix. Our algorithm is further improved with displacement structure, which reduces the complexity when solving the system for multiple input vectors. We use numerical simulations to demonstrate our algorithm's complexity and accuracy. [ABSTRACT FROM PUBLISHER]

The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gamma chirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates consideration of the use the PSP on non-asymptotic integrals and leads to the introduction of a test for phase rate dominance. Regions of the TF plane that pass the test and do not contain stationary phase points contribute little or nothing to the final output. Analysis values that lie in these regions can thus be set to zero, i.e., sparsity. In regions of the TF plane that fail the test or are in the vicinity of stationary phase points, synthesis is performed in the usual way. A new interpretation of the location parameters associated with the synthesis filters leads to: i) a new method for locating stationary phase points in the TF plane and ii) a test for phase rate dominance in that plane. Together this is a TF stationary phase approximation (TFSPA) for both analysis and synthesis. The stationary phase regions of several elementary signals are identified theoretically and examples of reconstruction given. An analysis of the TF phase rate characteristics for the case of two simultaneous tones predicts and quantifies a form of simultaneous masking similar to that which characterizes the auditory system. [ABSTRACT FROM AUTHOR]

When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was a priori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery. In practice, however, the distribution is unknown, motivating the use of robust algorithms like LASSO—which is nearly minimax optimal—at the cost of significantly larger MSE for non-least-favorable distributions. As an alternative, we propose an empirical-Bayesian technique that simultaneously learns the signal distribution while MMSE-recovering the signal—according to the learned distribution—using AMP. In particular, we model the non-zero distribution as a Gaussian mixture and learn its parameters through expectation maximization, using AMP to implement the expectation step. Numerical experiments on a wide range of signal classes confirm the state-of-the-art performance of our approach, in both reconstruction error and runtime, in the high-dimensional regime, for most (but not all) sensing operators. [ABSTRACT FROM PUBLISHER]

To reduce the communication cost of a sensor node, this paper is concerned with an estimation framework with scheduled measurements for a linear system. A scheduler is designed to control the transmission of measurements from sensor to estimator, which results in that only a subset of measurements is transmitted to the estimator. We propose an innovation based scheduler and derive an analytical expression for the Cramér–Rao lower bound (CRLB) for the given scheduling strategy. Under a communication constraint, an adaptive scheduler and a corresponding recursive estimator are jointly designed to asymptotically attain the CRLB. The structure of the estimator bears close resemblance to the standard least square estimator (LSE) with the full set of sensor measurements. Moreover, we prove that the estimation performance in terms of mean-square estimation error is comparable to the standard LSE even under a moderate communication cost. The theoretical results are verified by simulations. [ABSTRACT FROM PUBLISHER]

The problem of modeling and estimation for linear equality constrained (LEC) systems is considered. The exact constrained dynamic model usually is not readily available or is too complicated, and hence in many studies an auxiliary dynamic model is employed in which the state does not necessarily obey the constraint strictly. Based on the understanding that the constraints, as prior information about the state, should be incorporated into the dynamics modeling, an LEC dynamic model (LECDM) is constructed first. The model optimally fuses the linear equality constraint (LEC) and the auxiliary dynamics. Some of its superior properties are presented. Next, the linear minimum mean squared error (LMMSE) estimate of the LEC state is proved to satisfy the constraint. The LMMSE estimator for linear systems, called the LEC Kalman filter (LECKF), and two approximate LMMSE estimators for nonlinear systems are presented. The LECKF is compared with other constrained estimators, and a sufficient condition is also provided under which the estimate projection method mathematically equals the LECKF. Furthermore, extensions of the LECDM for the LEC systems with uncertain or unknown constraint parameters are discussed. Finally, illustrative examples are provided to show the effectiveness and efficiency of the LECKF and to verify the theoretical results given in the paper. [ABSTRACT FROM PUBLISHER]

In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility. [ABSTRACT FROM AUTHOR]

We consider the problem of blind identification and equalization of single-input multiple-output (SIMO) nonlinear channels. Specifically, the nonlinear model consists of multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on a well-known blind identification technique for linear SIMO systems. By transforming the output signals into a reproducing kernel Hilbert space (RKHS), a linear identification problem is obtained, which we propose to solve through an iterative procedure that alternates between canonical correlation analysis (CCA) to estimate the linear parts, and kernel canonical correlation (KCCA) to estimate the memoryless nonlinearities. The proposed algorithm is able to operate on systems with as few as two output channels, on relatively small data sets and on colored signals. Simulations are included to demonstrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied. [ABSTRACT FROM PUBLISHER]

Given a U-invariant sampling scheme on a Hilbert space \cal H. This paper characterizes atomic subspaces \cal A of \cal H such that every signal x\in\cal A can be reconstructed from its generalized samples acquired with the U-invariant sampling scheme. If signal recovery is possible a linear filter is derived which reconstructs the signal from the samples. Moreover, the paper gives necessary and sufficient conditions on a sequence of sampling functions such that it forms a pseudoframe or pseudo-Riesz basis for a given atomic subspace \cal A. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the parametric version of Wiener systems where both the linear and nonlinear parts are identified with clipped observations in the presence of internal and external noises. Also the static functions are allowed noninvertible. We propose a classification based support vector machine (SVM) and formulate the identification problem as a convex optimization. The solution to the optimization problem converges to the true parameters of the linear system if it is an finite-impulse-resposne (FIR) system, even though clipping reduces a great deal of information about the system characteristics. In identifying a Wiener system with a stable infinite-impulse-response (IIR) system, an FIR system is used to approximate it and the problem is converted to identifying the FIR system together with solving a set of nonlinear equations. This leads to biased estimates of parameters in the IIR system while the bias can be controlled by choosing the order of the approximated FIR system. [ABSTRACT FROM PUBLISHER]

This paper is concerned with quantifying shift-variance of linear systems with continuous-time input and discrete-time output. We first introduce a notion of \mbi \mu-shift-invariance for the system. It specifies how the system should respond when the input signal is shifted. For generalized sampling processes, the property is characterized by the sampling kernel, and is shown to be equivalent to lack of aliasing and to shiftability. We then define a shift-variance level which describes how far the system can be possibly away from the set of systems that are \mbi \mu-shift-invariant. The level is defined to be the maximum of the induced norms of the commutators of the system and the shift-operators (both continuous-time or discrete-time are necessarily involved). A shift-variance measure is then defined to be the ratio of the shift-variance level to the system norm, further divided by two so that the measure is between zero and unity. For generalized sampling, we obtain analytical formulas for the shift-variance level and the shift-variance measure. The results allow us to analyze the shift-variance of, among others, the discrete-time wavelet transform (DWT) and the short-time Fourier transform (STFT). We obtain a simple relation between the shift-variance levels at all scales of the DWT, and show that the shift-variance measures are identical at all scales. We calculate the shift-variance level and the shift-variance measure of some typical DWTs and the STFTs. [ABSTRACT FROM AUTHOR]

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least \mbi \ell\bf 1-norm solution of the underdetermined linear system \mbi A\mbi x = \mbi b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix \mbi A at any time. We consider two scenarios in which either the columns or the rows of \mbi A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

Modeling natural and artificial systems has played a key role in various applications and has long been a task that has drawn enormous efforts. In this work, instead of exploring predefined models, we aim to identify implicitly the system degrees of freedom. This approach circumvents the dependency of a specific predefined model for a specific task or system and enables a generic data-driven method to characterize a system based solely on its output observations. We claim that each system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic model for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and practical examples has shown accurate recovery of parameters. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of designing compact-support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an nonlinear infinite dimensional problem to a linear finite dimensional case, and then find the optimum compact-support function that best approximates a given filter in the least square sense (\ell2 norm). The benefit of compact-support interpolants is the low computational complexity in the interpolation process while the optimum compact-support interpolant guarantees the highest achievable signal-to-noise ratio (SNR). Our simulation results confirm the superior performance of the proposed kernel compared to other conventional compact-support interpolants such as cubic spline. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random sensor delays, packet dropouts and uncertain observations. We develop a unified model to describe the mixed uncertainties of random delays, packet dropouts and uncertain observations by three Bernoulli distributed random variables with known distributions. Based on the proposed model, the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach. Their solutions are given in terms of a Riccati equation and a Lyapunov equation. They can deal with the optimal linear filtering, prediction and smoothing for systems with random sensor delays, packet dropouts and uncertain observations in a unified framework. Simulation results show the effectiveness of the proposed optimal linear estimators. [ABSTRACT FROM AUTHOR]

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rather limited model for many applications. Here we generalize conventional TV in 1-D by extending the derivative operator, which is within the regularization term, to any linear differential operator. This provides flexibility for tailoring the approach to the presence of nontrivial linear systems and for different types of driving signals such as spike-like, piecewise-constant, and so on. Conventional TV remains a special case of this general framework. We illustrate the feasibility of the method by considering a nontrivial linear system and different types of driving signals. [ABSTRACT FROM AUTHOR]

In this correspondence, the use of superimposed training (ST) as a mean to estimate the finite impulse response (FIR) components of a widely linear (WL) system is proposed. The estimator here presented is based on the first-order statistics of the signal observed at the output of the system and its variance is independent of the channel components if suitable designed training sequences are employed. The construction of such sequences having constant magnitude both in time and frequency domains is also addressed. [ABSTRACT FROM AUTHOR]

Takens' embedding theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state space. However, Takens' theorem is fragile in the sense that even small imperfections can induce arbitrarily large errors in this attractor representation. We extend Takens' result to establish deterministic, explicit and nonasymptotic sufficient conditions for a delay coordinate map to form a stable embedding in the restricted case of linear dynamical systems and observation functions. Our work is inspired by the field of Compressive Sensing (CS), where results guarantee that low-dimensional signal families can be robustly reconstructed if they are stably embedded by a measurement operator. However, in contrast to typical CS results, i) our sufficient conditions are independent of the size of the ambient state space, and ii) some system and measurement pairs have fundamental limits on the conditioning of the embedding (i.e., how close it is to an isometry), meaning that further measurements beyond some point add no further significant value. We use several simple simulations to explore the conditions of the main results, including the tightness of the bounds and the convergence speed of the stable embedding. We also present an example task of estimating the attractor dimension from time-series data to highlight the value of stable embeddings over traditional Takens' embeddings. [ABSTRACT FROM PUBLISHER]

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]

In order to mitigate the effect of additive noises and reduce the computational burden, we propose a new computationally efficient cross-correlation based two-dimensional (2-D) direction-of-arrivals (DOAs) estimation (CODE) method for noncoherent narrowband signals impinging on the L-shaped sensor array structured by two uniform linear arrays (ULAs). By estimating the azimuth and elevation angles independently with a one-dimensional (1-D) subspace-based estimation technique without eigendecomposition, where the null spaces are obtained through a linear operation of the matrices formed from the cross-correlation matrix between the received data of two ULAs, then the pair-matching of estimated azimuth and elevation angles is accomplished by searching the minimums of a cost function of the azimuth and elevation angles, where the computationally intensive and time-consuming eigendecomposition process is avoided. Further the asymptotic mean-square-error (MSE) expressions of the azimuth and elevation estimates are derived. The effectiveness of proposed method and the theoretical analysis are verified through numerical examples, and it is shown that the proposed CODE method performs well at low signal-to-noise ratio (SNR) and with a small number of snapshots. [ABSTRACT FROM AUTHOR]

This paper introduces novel wavelet-based semiparametric centralized and distributed compression methods for a class of 1-D piecewise smooth functions. Classical centralized compression schemes are based on a relatively complex, nonlinear encoder and a simple, linear decoder. Recently, a new paradigm in compression called distributed source coding has emerged. This setup involves multiple encoders, where each one partially observes the source, and a centralized decoder. First, we focus on the dual situation of the centralized compression with a simple encoder and a complex decoder. We show that, by incorporating parametric estimation into the decoding procedure, it is possible to achieve the same rate-distortion performance as that of a conventional wavelet-based compression scheme. Second, we consider the distributed compression scenario, where each independent encoder partially observes the 1-D piecewise smooth function. We propose a new wavelet-based distributed compression scheme that uses parametric estimation to perform joint decoding. Our analysis shows that it is possible for the proposed scheme to achieve the same compression performance as that of a joint encoding scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fault detection filter design for discrete-time Markovian jump singular systems with intermittent measurements. The measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing. Our attention is focused on the design of a fault detection filter such that the residual system is stochastically Markovian jump admissible and satisfies some expected performances. A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastically Markovian jump admissible is proposed in the form of strict linear matrix inequalities. Sufficient conditions are established for the existence of the fault detection filter. Finally, a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results. [ABSTRACT FROM AUTHOR]

Blocking filters are commonly used in array processing to excise targets from data when suitable target-free training data is not available. A drawback is the reduction of the effective size of the array by the order of the filter, motivating a search for the smallest filter that meets the design specifications. Common linear-phase approaches lead to convex optimization and efficient global solutions, but can be inefficient when the phase of the blocking filter is unimportant. Although direct magnitude-response optimization is nonconvex in general, for narrowband linear arrays optimal-magnitude blocking filters can be found using constrained optimization followed by spectral factorization. This approach cannot be directly applied to wideband arrays, as finite-support spectral factors do not generally exist in higher dimensions. Instead, a procedure is presented in which an approximate multidimensional spectral factor of an optimized spectral density is used as a target response in a second optimization stage. Linear and nonlinear-phase solutions are found and compared for both narrowband and wideband notch filters, with the nonlinear phase outperforming the linear phase in both notch width and passband error. The various optimizations are performed using second-order cone programming, an efficient class of convex optimization. [ABSTRACT FROM AUTHOR]

In a previous paper, a method was introduced that used a system of linear equations to determine the frequency and the complex amplitude of a complex single tone signal. The system of linear equations was derived from the model of a complex single tone in the DFT domain and was used as parameters estimator in noisy conditions. In this paper, this approach is extended to a complex multitone signal. As for the complex single tone case, the parameters value is determine from the solution of systems of linear equations and the method is directly applied for parameters estimation in noisy conditions. An analysis of the estimators is provided, including the case of closely spaced frequencies, and criteria and procedures for the appropriate selection of the DFT samples are presented. [ABSTRACT FROM AUTHOR]

We propose a generalization of the matched subspace filter for the detection of unknown signals in a background of non-Gaussian and nonindependent noise. The generalization is based on a modification of the Rao test by including a linear transformation derived from independent component analysis (ICA). Receiver operating characteristic (ROC) curves computed for simulated examples illustrate the significant improvement achieved with the generalized solution. [ABSTRACT FROM PUBLISHER]

This paper studies the outage probability minimization problem for state estimation of linear dynamical systems using multiple sensors, where an estimation outage is defined as an event when the state estimation error exceeds a pre-determined threshold. The sensors amplify-and-forward their measurements (using uncoded analog transmission) to a remote fusion center over wireless fading channels. For stable systems, the resulting infinite horizon problem can be formulated as a constrained average cost Markov decision process (MDP) control problem. A suboptimal power allocation that is less computationally intensive is proposed and numerical results demonstrate very close performance to the power allocation obtained from the solution of the MDP based average cost optimality equation. Motivated by practical considerations, assuming that sensors can transmit with only a finite number of power levels, optimization of the values of these levels is also considered using a stochastic approximation technique. In the case of unstable systems, a finite horizon formulation of the estimation outage minization problem is presented and solved. An extension to the problem of minimization of the expected error covariance is also studied. [ABSTRACT FROM PUBLISHER]

Oversampled filter banks are at the center of essential signal processing systems, either for source coding or for transmission applications. Among this class of filter banks (FBs), the case of oversampled discrete Fourier transform (DFT) filter banks is particularly important since it leads to efficient algorithm implementations. However, up to now, no general construction algorithm has been proposed to exhaustively cover the large set of the various solutions offered by this family of FBs. The paper recalls in detail the precise features of the rectangular paraunitary matrices that are specific of this type of systems. A parametrization method is proposed involving transformations, being either rotations or shifts, that depend upon the oversampling ratio and upon the prototype filter length. This shows that several factorizations exist leading to solutions of different dimension. Orthogonal and paraunitary patterns are introduced and, using a sequence of transformations applied to a pattern (STAP), an algorithm is derived that allows us to get the exhaustive set of solutions for various values of the oversampling ratio and prototype filter length. Furthermore, for some oversampling ratios, explicit expressions of some solutions are also provided that are valid whatever the maximum length of the prototype filter. Finally, design examples for linear and nonlinear phase prototype filters are presented. [ABSTRACT FROM PUBLISHER]

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of underspread linear systems (ULSs), whose responses lie within a unit-area region in the delay-Doppler space, by probing them with a known input signal. It is shown that sufficiently-underspread parametric linear systems, described by a finite set of delays and Doppler-shifts, are identifiable from a single observation as long as the time-bandwidth product of the input signal is proportional to the square of the total number of delay-Doppler pairs in the system. In addition, an algorithm is developed that enables identification of parametric ULSs from an input train of pulses in polynomial time by exploiting recent results on sub-Nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials. Finally, application of these results to super-resolution target detection using radar is discussed. Specifically, it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay-Doppler space, resulting in a resolution that substantially exceeds that of standard matched-filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing-based radar methods. [ABSTRACT FROM AUTHOR]