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The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF converts a continuous-time high-dynamic-range (HDR) signal into folded, low-dynamic-range, modulo samples and allows the recovery of the HDR signal via algorithmic unfolding. In hardware, however, implementing ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and practice, this paper explores a computational sampling strategy that relaxes strict hardware requirements via a novel, mathematically guaranteed reconstruction. We start with a generalized model for USF with two new parameters modeling hysteresis and folding transients in addition to the modulo threshold. Hysteresis accounts for mismatches between the reset threshold and the amplitude displacement at the folding time and the folding transient is a continuous transition period in the implementation of a reset. Both these effects are motivated by our hardware experiments and also occur in previous, domain-specific applications. We show that hysteresis is beneficial for USF and leverage it to derive the first recovery guarantees in the context of our generalized USF model for a certain sampling rate regime. Additionally, we show how the sampling rate requirement can be greatly reduced via a direct generalization of the proposed recovery. Our theoretical work is corroborated by hardware experiments with a hysteresis enabled, modulo ADC testbed comprising off-the-shelf electronic components. Thus, by capitalizing on a collaboration between hardware and algorithms, our paper enables an end-to-end pipeline for HDR sampling allowing more flexible hardware implementations. [ABSTRACT FROM AUTHOR]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finite-dimensional (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that “better” explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Computer simulations and tests on real data corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced. [ABSTRACT FROM PUBLISHER]

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]

This paper considers the noncooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for the more general multiple-input multiple-output (MIMO) case, for which the state-of-the art results are valid only for nonsingular square channel matrices. Surprisingly, these results do not hold true when the channel matrices are rectangular and/or rank deficient matrices. The goal of this paper is to provide a complete characterization of the MIMO game for arbitrary channel matrices, in terms of conditions guaranteeing both the uniqueness of the Nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms. Our analysis hinges on new technical intermediate results, such as a new expression for the MIMO waterfilling projection valid (also) for singular matrices, a mean-value theorem for complex matrix-valued functions, and a general contraction theorem for the multiuser MIMO watefilling mapping valid for arbitrary channel matrices. The quite surprising result is that uniqueness/convergence conditions in the case of tall (possibly singular) channel matrices are more restrictive than those required in the case of (full rank) fat channel matrices. We also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and con- vergence, and virtually the same performance (in terms of Nash equilibria) of the original game. [ABSTRACT FROM AUTHOR]

This paper presents a way to access both the multiple-order and parameters of a multidimensional complex number autoregressive (AR) model through matrix factorization. The principle of this technique consists of the transformation of the multidimensional model to a pseudo simple-input simple-output AR model, then performing factorization of the covariance matrix of the data. This factorization then leads- to a recursive form of the parameter and order estimation. This paper makes two principal contributions. The first is a generalization of one dimensional factored form algorithm, and the second is that it makes it possible to access all the possible different orders and parameters of a multidimensional complex number AR model of any dimension, whereas classical approaches are limited to at most four-dimensional models. Computer simulation results are provided to illustrate the behavior of this method. [ABSTRACT FROM AUTHOR]

Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This paper presents an adaptive notch filter (ANF) to achieve both these objectives. For noise reduction purpose, the proposed adaptive filter successfully extracts a single sinusoid of a possibly time-varying nature from a noise-corrupted signal. The paper proceeds with introducing a chain of filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids, and of decomposing it into its constituent components. The order of differential equations governing this algorithm is 2n + 1, where n is the number of constituent sinusoids that should be extracted. Stability analysis of the proposed algorithm is carried out based on the application of the local averaging theory under the assumption of slow adaptation. When compared with the conventional Fourier analysis, the proposed method provides instantaneous values of the constituting components. Moreover, it is adaptive with respect to the fundamental frequency of the signal. Simulation results verify the validity of the presented algorithm and confirm its desirable transient and steady-state performances as well as its desirable noise characteristics. [ABSTRACT FROM AUTHOR]

Channel order estimation is a critical step in most blind single-input multiple-output (SIMO) channel identification/equalization algorithms. Several methods for estimating either the true channel order or its most significant part (the so-called effective channel order) have been recently proposed, but a solution able to work in practical scenarios (low or moderate signal-to-noise ratios (SNR5) and channels with small leading and/or trailing coefficients) has not been found yet. In this paper, a new criterion for effective channel order detection of SIMO channels is presented. The method is based on the fact that the cost function typically used in blind identification algorithms decreases monotonically with the estimated channel order, whereas for blind equalization algorithms, the cost function increases monotonically. In this paper, it is shown that a straightforward combination of both cost functions attains its minimum at the correct channel order even for moderate SNRS. The proposed method is able to work with small data sets, colored signals, and channels with small head and tail taps, which is a common problem in communication applications. The improvement of the proposed criterion over a number of existing algorithms is demonstrated through simulations. [ABSTRACT FROM AUTHOR]

We study the problem of power efficient multiuser beamforming transmission for both uplink and downlink. The base station is equipped with multiple antennas, whereas the mobile units have single antennas. In the uplink, interference is canced by successive decoding. in the downlink, ideal "dirty paper" precoding is assumed. The design goal is to minimize the total transmit power while maintaining individual SINR constraints. In the uplink, the optimization problem is solved by a recursive formula with low computational complexity. The downlink problem is solved by exploiting the duality between uplink and downlink; thus, the uplink solution carries over to the downlink. In the second part of the paper, we show how the solution can be applied to the problem of rate balancing in Gaussian multiuser channels. We propose a strategy for throughput-wise optimal transmission for broadcast and multiple access channels under a sum power constraint. Finally, we show that single-user transmission achieves the sum capacity in the low-SNR regime. We completely characterize the SNR-range where single-user transmission is optimal. [ABSTRACT FROM AUTHOR]

In this paper, algorithms for joint high-resolution direction-of-arrival (DoA) and polarization estimation using real-world arrays with imperfections are proposed. Both azimuth and elevation angles are considered. Partially correlated and coherent signals may be handled as well. Unlike most of the work available in the open literature, we consider the case when polarization sensitive antenna arrays, which may be disposed on a conformal surface, may have unknown (but fixed) geometries, be composed of elements with individual beampatterns and be subject to cross-polarization as well as mounting platform effects. Herein, recent results on steering vector modeling from noise-corrupted array calibration measurements are employed. This allows for incorporating all nonidealities of an antenna array into the estimation algorithms in a general and convenient manner. The proposed estimators can be implemented using the fast Fourier transform or polynomial rooting techniques regardless of the array configuration. The stochastic Cramér–Rao lower bound for the estimation problem at hand is established using the results from array steering vector modeling as well. The proposed expression takes into account array nonidealities, making such a bound tight even for real-world arrays. Extensive simulation results are provided using several real-world antenna arrays. The proposed algorithms outperform conventional algorithms available in the literature and have a performance close to the stochastic Cramér–Rao lower bound. [ABSTRACT FROM AUTHOR]

The goal of this paper is to propose a bio-inspired radio access mechanism for cognitive networks mimicking the behavior of a flock of birds swarming in search for food in a cohesive fashion without colliding with each other. The equivalence between swarming and radio resource allocation is established by modeling the interference distribution in the resource domain, e.g., frequency and time, as the spatial distribution of food, while the position of the single bird represents the radio resource chosen by each radio node. The swarming mechanism is enforced by letting every node allocate its resources (power/bits) in the time-frequency regions where the interference is minimum (the food density is maximum), avoiding collisions with other nodes (birds), yet limiting the spread in the time-frequency domain (i.e., maintaining the swarm cohesion). The solution is given as the distributed minimization of a functional, borrowed from social foraging swarming models, containing the average interference plus repulsion and attraction terms that help to avoid conflicts and maintain cohesiveness, respectively. [ABSTRACT FROM AUTHOR]

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

This paper introduces a tensor framework to solve the problem of nonunitary joint block diagonalization (JBD) of a set of real or complex valued matrices. We show that JBD can be seen as a particular case of the block-component-decomposition (BCD) of a third-order tensor. The resulting tensor model fitting problem does not require the block-diagonalizer to be a square matrix: the over- and underdetermined cases can be handled. To compute the tensor decomposition, we build an efficient nonlinear conjugate gradient (NCG) algorithm. In the over- and exactly determined cases, we show that exact JBD can be computed by a closed-form solution based on eigenvalue analysis. In approximate JBD problems, this solution can be used to efficiently initialize any iterative JBD algorithm such as NCG. Finally, we illustrate the performance of our technique in the context of independent subspace analysis (ISA) based on second-order statistics (SOS). [ABSTRACT FROM PUBLISHER]

Compressive sensing (CS) is a new technique for the efficient acquisition of signals, images and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis representation has just K\ll N significant coefficients; in this case, the CS theory maintains that just M = \cal O\left ( K \log N\right ) random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K=SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naïve bound based on the total signal sparsity K=SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed. It means that the number of sources exceeds the number of channels of the available data. The separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block. It proceeds in two steps: 1) estimating the mixing matrix, and 2) computing the optimum beamformer in each block to maximize the signal-to-interference ratio of each separated signal with respect to the remaining signals. Estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block. It utilizes optimum weighting, which allows statistically efficient (CRB attaining) estimation provided that the data obey the assumed Gaussian piecewise stationary model. In simulations, performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals. [ABSTRACT FROM AUTHOR]

Multidimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross-product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross-product is proposed based on this algorithm. Secondly, we show that if 4D cross-product is used as the fundamental operation for formulating nD cross-product problem, then exploiting the inherent mathematical symmetry of 4D cross-product it is possible to reduce the total hardware cost of nD cross-product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new maximum-likelihood (ML) target localization approach which uses quantized sensor data as well as wireless channel statistics in a wireless sensor network. The novelty of our approach comes from the fact that statistics of imperfect wireless channels between sensors and the fusion center along with some physical layer design parameters are incorporated in the localization algorithm. We call this approach "channel-aware target localization." ML target location estimators are derived for different wireless channel models and receiver architectures. Furthermore, we derive the Cramér-Rao lower bounds (CRLBs) for our proposed channel-aware ML location estimators. Simulation results are presented to show that the performance of the channel-aware ML location estimators are quite close to their theoretical performance bounds even with relatively small number of sensors and their performance is superior compared to that of the channel-unaware ML estimators. [ABSTRACT FROM AUTHOR]

Finding computationally efficient spectrum optimization methods for a multiuser digital subscriber line (DSL) environment is a key objective of dynamic spectrum management for DSL systems. For synchronous discrete multitone (DMT) based DSL systems, the computational complexity issue can be partially addressed using a dual optimization approach that decomposes the problem in the frequency domain. However, the decomposition approach fails whenever the DMT system is asynchronous, in which case the power allocations in adjacent frequency tones interfere with each other. This paper provides a mathematical model for intercarrier interference due to symbol misalignment and proposes ways to modify the dual method for spectrum optimization of asynchronous DSL systems. The main ingredient of the algorithm is an efficient method to evaluate the minimum power required to support a given bit-allocation using a power series approximation, combined with a local gradient search. [ABSTRACT FROM AUTHOR]

This paper considers the problem of piecewise linear prediction from a competitive algorithm approach. In prior work, prediction algorithms have been developed that are "universal" with respect to the class of all linear predictors, such that they perform nearly as well, in terms of total squared prediction error, as the best linear predictor that is able to observe the entire sequence in advance. In this paper, we introduce the use of a "context tree, to compete against a doubly exponential number of piecewise linear (affine) models. We use the context tree to achieve the total squared prediction error performance of the best piecewise linear model that can choose both its partitioning of the regressor space and its real-valued prediction parameters within each region of the partition, based on observing the entire sequence in advance, uniformly, for every bounded individual sequence. This performance is achieved with a prediction algorithm whose complexity is only linear in the depth of the context tree per prediction. Upper bounds on the regret with respect to the best piecewise linear predictor are given for both the scalar and higher order case, and lower bounds on the regret are given for the scalar case. An explicit algorithmic description and examples demonstrating the performance of the algorithm are given. [ABSTRACT FROM AUTHOR]

In this paper we study two fourth-order cumulant-based techniques for the estimation of the mixing matrix in underdetermined independent component analysis. The first method is based on a simultaneous matrix diagonalization. The second is based on a simultaneous off-diagonalization. The number of sources that can be allowed is roughly quadratic in the number of observations. For both methods, explicit expressions for the maximum number of sources are given. Simulations illustrate the performance of the techniques. [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]

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]

The adaptive nonlinear predistorter is an effective technique to compensate for the nonlinear distortion existing in digital communication and control systems. However, available adaptive nonlinear predistorters using indirect learning are sensitive to measurement noise and do not perform optimally. Other available types are either slow to converge, complicated in structure and computationally expensive, or do not consider the memory effects in nonlinear systems such as a high power amplifier (HPA). In this paper, we first propose several novel adaptive nonlinear predistorters based on direct learning algorithms--the nonlinear filtered-x RLS (NFXRLS) algorithm, the nonlinear adjoint LMS (NALMS) algorithm, and the nonlinear adjoint RLS (NARLS) algorithm. Using these new learning algorithms, we design adaptive nonlinear predistorters for an HPA with memory effects or for an HPA following a linear system. Because of the direct learning algorithm, these novel adaptive predistorters outperform nonlinear predistorters that are based on the indirect learning method in the sense of normalized mean square error (NMSE), bit error rate (BER), and spectral regrowth. Moreover, our developed adaptive nonlinear predistorters are computationally efficient and/or converge rapidly when compared to other adaptive nonlinear predistorters that use direct learning, and furthermore can be easily implemented. We further simplify our proposed algorithms by exploring the robustness of our proposed algorithm as well as by examining the statistical properties of what we call the ‘instantaneous equivalent linear’ (IEL) filter. Simulation results confirm the effectiveness of our proposed algorithms. [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 we study the problem of pruning a binary tree by minimizing, over all pruned subtrees of the given tree, an objective function that combines an additive cost term with a penalty term that depends only on tree size. We present algorithms for general size-based penalties, although our focus is on subadditive penalties (roughly, penalties that grow more slowly than linear penalties with increasing tree size). Such penalties are motivated by recent results in statistical learning theory for decision trees, but may have wider application as well. We show that the family of pruned subtrees induced by a subadditive penalty is a subset of the family induced by an additive penalty. This implies (by known results about additive penalties) that the family induced by a subadditive penalty 1) is nested; 2) is unique; and 3) can be computed efficiently. It also implies that, when a single tree is to be selected by cross-validation from the family of prunings, subadditive penalties will never present a richer set of options than an additive penalty. [ABSTRACT FROM AUTHOR]

This paper is concerned with optimal filtering in a distributed multiple sensor system with the so-called out-of-sequence measurements (OOSM). Based on best linear unbiased estimation (BLUE) fusion, we present two algorithms for updating with OOSM that are optimal for the information available at the time of update. Different minimum storages of information concerning the occurrence time of OOSMs are given for both algorithms. It is shown by analysis and simulation results that the two proposed algorithms are flexible and simple. [ABSTRACT FROM AUTHOR]

It is usually assumed that all state metric values are necessary in the maximum a posteriori (MAP) algorithm in order to compute the a posteriori probability (APP) values. This paper extends the mathematical derivation of the original MAP algorithm and shows that the log likelihood values can be computed using only partial state metric values. By processing N stages in a trellis concurrently, the proposed algorithm results in savings in the required memory size and leads to a power efficient implementation of the MAP algorithm in channel decoding. The computational complexity analysis for the proposed algorithm is presented. Especially for the N = 2 case, we show that the proposed algorithm halves the memory requirement without increasing the computational complexity. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the performance and behavior of a blind adaptive carrier phase offset recovery scheme based on dispersion minimization (DM). The algorithm, called the DM-derotator, is a kind of simple equalizer that attempts to correct the carrier phase offset by minimizing the dispersion of the projection of the real part of the (complex) data signal. The recent application of this algorithm to digital broadcasting signals motivates our analysis. This paper classifies the stationary points of the DM-derotator for a variety of source signals including digital vestigial side band (VSB) and quadrature amplitude modulation (QAM) and discusses initialization strategies. The analysis is extended to a variety of situations including i) its behavior in the presence of intersymbol interference, ii) its behavior when there is statistical dependence between the in-phase and quadrature components, and iii) its tracking ability. [ABSTRACT FROM AUTHOR]

Markovian jump systems (MJSs) evolve in a jump-wise manner by switching among simpler models, according to a finite Markov chain, whose parameters are commonly assumed known. This paper addresses the problem of state estimation of MJS with unknown transition probability matrix (TPM) of the embedded Markov chain governing the jumps. Under the assumption of a time-invariant but random TPM, an approximate recursion for the TPMs posterior probability density function (PDF) within the Bayesian framework is obtained. Based on this recursion, four algorithms for online minimum mean-square error (MMSE) estimation of the TPM are derived. The first algorithm (for the case of a two-state Markov chain) computes the MMSE estimate exactly, if the likelihood of the TPM is linear in the transition probabilities. Its computational load is, however, increasing with the data length. To limit the computational cost, three alternative algorithms are further developed based on different approximation techniques-truncation of high order moments, quasi-Bayesian approximation, and numerical integration, respectively. The proposed TPM estimation is naturally incorporable into a typical online Bayesian estimation scheme for M.JS [e.g., generalized pseudo-Bayesian (GPB) or interacting multiple model (IMM)]. Thus, adaptive versions of MJS state estimators with unknown TPM are provided. Simulation results of TPM-adaptive IMM algorithms for a system with failures and maneuvering target tracking are presented. [ABSTRACT FROM AUTHOR]

The objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions, suppress the noises and the interfering signals from other directions, and/or simultaneously provide the focalization of the associated sources. In this paper, we present a higher order cumulant-based beamforming algorithm, namely, the super-exponential blind adaptive beamforming algorithm, which is extended from the super-exponential algorithm (SEA) and the inverse filter criteria (IFC). While both SEA and IFC assume noise-free conditions, this requirement is no longer needed, and all the noise components are taken into account in the proposed algorithm. Two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error (MMSE). Simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors; its performance with the use of the fourth-order cumulants is close to that of the nonblind optimal MMSE beamformer. [ABSTRACT FROM AUTHOR]

Abstract-Subspace-based estimation of multiple real-valued sine wave frequencies is considered in this paper. A novel data covariance model is proposed. In the proposed model, the dimension of the signal subspace equals the number of frequencies present in the data, which is half of the signal. subspace dimension for the conventional model. Consequently, an ESPRIT-like algorithm using the proposed data model is presented. The proposed algorithm is then extended for the case of complex-valued sine waves. Performance analysis of the proposed algorithms are also carried out. The algorithms are tested in numerical simulations. When compared with ESPRIT, the newly proposed algorithm results in a significant reduction in computational burden without any compromise in the accuracy. [ABSTRACT FROM AUTHOR]

This paper introduces a new framework to construct fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we prerandomize the sensing signal by scrambling its sample locations or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the resulting transform coefficients to obtain the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable to that of completely random sensing matrices. Numerical simulation results verify the validity of the theory and illustrate the promising potentials of the proposed sensing framework. [ABSTRACT FROM PUBLISHER]

In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available. The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios. [ABSTRACT FROM AUTHOR]

This paper presents an improved mean-square deviation (MSD) analysis of the standard affine projection algorithm (APA) based on two distinctive features. First, the propagation model of the error covariance includes the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs; such a cross-correlation has merely been considered previously. Second, the analysis based on n most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where n denotes the tap-length of the filter. Simulation results are in better agreement with the proposed theoretical results, than the previous theoretical ones, over a wide range of parameters such as tap-length, projection order, and step-size. [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]

Over the last decade, the theory of reproducing kernels has made a major breakthrough in the field of pattern recognition. It has led to new algorithms, with improved performance and lower computational cost, for nonlinear analysis in high dimensional feature spaces. Our paper is a further contribution which extends the framework of the so-called kernel learning machines to time-frequency analysis, showing that some specific reproducing kernels allow these algorithms to operate in the time-frequency domain. This link offers new perspectives in the field of non-stationary signal analysis, which can benefit from the developments of pattern recognition and Statistical Learning Theory. [ABSTRACT FROM AUTHOR]

Given a large overcomplete dictionary of basis vectors, the goal is to simultaneously represent L > 1 signal vectors using coefficient expansions marked by a common sparsity profile. This generalizes the standard sparse representation problem to the case where multiple responses exist that were putatively generated by the same small subset of features. Ideally, the associated sparse generating weights should be recovered, which can have physical significance in many applications (e.g., source localization). The generic solution to this problem is intractable and, therefore, approximate procedures are sought. Based on the concept of automatic relevance determination, this paper uses an empirical Bayesian prior to estimate a convenient posterior distribution over candidate basis vectors. This particular approximation enforces a common sparsity profile and consistently places its prominent posterior mass on the appropriate region of weight-space necessary for simultaneous sparse recovery. The resultant algorithm is then compared with multiple response extensions of matching pursuit, basis pursuit, FOCUSS, and Jeifreys prior-based Bayesian methods, finding that it often outperforms the others. Additional motivation for this particular choice of cost function is also provided, including the analysis of global and local minima and a variational derivation that highlights the similarities and differences between the proposed algorithm and previous approaches. [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]

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]

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]

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]

This paper proposes a tree-based pursuit algorithm that efficiently trades off complexity and approximation performance for overcomplete signal expansions. Finding the sparsest representation of a signal using a redundant dictionary is, in general, an NP-hard problem. Even suboptimal algorithms such as Matching Pursuit remain highly complex. We propose a structuring strategy that can be applied to any redundant set of functions, and which basically groups similar atoms together. A measure of similarity based on coherence allows for representing a highly redundant subdictionary of atoms by a unique element, called molecule. When the clustering is applied recursively on atoms and then on molecules, it naturally leads to the creation of a tree structure. We then present a new pursuit algorithm that uses the structure created by clustering as a decision tree. This tree-based algorithm offers important complexity reduction with respect to Matching Pursuit, as it prunes important parts of the dictionary when traversing the tree. Recent results on incoherent dictionaries are extended to molecules, while the true highly redundant nature of the dictionary stays hidden by the tree structure. We then derive recovery conditions on the structured dictionary, under which tree-based pursuit is guaranteed to converge. Experimental results finally show that the gain in complexity offered by tree-based pursuit does in general not have a high penalty on the approximation performance. They show that the dimensionality of the problem is reduced thanks to the tree construction, without significant loss of information. [ABSTRACT FROM AUTHOR]

There is a fundamental tradeoff between power consumption, data transmission rates, and congestion levels in a wireless network. These three elements influence the performance of rate and power control strategies, and they need to be coordinated judiciously. This paper proposes dynamic rate and power control algorithms for distributed wireless networks that also account for the congestion levels in a network. The design is pursued by formulating state-space models with and without uncertain dynamics and by determining control signals that help meet certain performance criteria (such as robustness and desired levels of signal-to-interference ratio). Simulation results illustrate the performance of the proposed control schemes. [ABSTRACT FROM AUTHOR]

Recently, a generalized noise reduction scheme has been proposed, called the Spatially Preprocessed, Speech Distortion Weighted, Multichannel Wiener Filter (SP-SDW-MWF). It encompasses the Generalized Sidelobe Canceller (GSC) and a multichannel Wiener filtering technique as extreme cases. Compared with the widely studied GSC with Quadratic Inequality Constraint (QICuGSC), the SP-SDW-MWF achieves a better noise reduction performance for a given maximum speech distortion level. In this paper, we develop a low-cost, stochastic gradient implementation of the SP-SDW-MWE To speed up convergence and reduce computational complexity, the algorithm is implemented in the frequency domain. Experimental results with a behind-the-ear hearing aid show that the proposed frequency-domain stochastic gradient algorithm preserves the benefit of the exact SP-SDW-MWF over the QIC-GSC, while its computational cost is comparable to the least mean square-based scaled projection algorithm for QIC-GSC. [ABSTRACT FROM AUTHOR]

In this paper, we consider a signal/parameter estimation problem that is based on a linear model structure and a given setting of statistical models with unknown hyperparameters. We consider several combinations of Gaussian and Laplacian models. We develop iterative algorithms based on two typical machine learning methods-the evidence-based method and the integration-based method-to deal with the hyperparameters. We have applied the proposed algorithms to adaptive prediction and wavelet denoising. In linear prediction, we show that the proposed algorithms are efficient tools for tackling a difficult problem of adapting simultaneously the order and the coefficients of the predictor. In wavelet denoising, we show that by using the proposed algorithms, the noisy wavelet coefficients are subject to shrinkage and thresholding. [ABSTRACT FROM AUTHOR]

A delay-dependent approach to robust H∞ filtering is proposed for linear discrete-time uncertain systems with multiple delays in the state. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed H∞ noise attenuation level. The proposed filter design methodology incorporates some recently appeared results, such as Moon's new version of the upper bound for the inner product of two vectors and de Oliveira's idea of parameter-dependent stability, which greatly reduce the overdesign introduced in the derivation process. In addition to the full-order filtering problem, the challenging reduced-order case is also addressed by using different linearization procedures. Both full- and reduced-order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies. [ABSTRACT FROM AUTHOR]

A fully decentralized sensor network, without fusion center, is deployed to estimate the position of a target. Taking advantage of the limited communication range of the nodes, and exploiting their (unknown) location inside the surveyed area, the likelihood profile is approximately reconstructed. A distributed ML-like estimator is, therefore, proposed and its asymptotic performance is investigated analytically, while computer experiments assess the behavior of the estimator in nonasymptotic regimes. The differences between one- and two-dimensional scenarios are also discussed. [ABSTRACT FROM AUTHOR]

Translation-invariant interpolation of frequency domain functions by means of Fourier transforms of Pólya frequency functions, which belong to the Bochner class of interpolation kernels, is presented. For the implementation, we use an adaptive interpolation process which is a variant of the recently introduced adaptive residual subsampling method. Moreover, it is shown that adaptive residual subsampling with Pólya interpolation kernels is an excellent preprocessing interface when used in conjunction with the well-known vector fitting (VF) rational modeling algorithm. [ABSTRACT FROM AUTHOR]

A new blind subspace-based algorithm for signature waveform estimation in binary phase-shift-keying (BPSK)-modulated direct-sequence code-division multiple-access (DS-CDMA) systems is proposed. Our approach can be viewed as a modification of the popular blind technique by Liu and Xu (LX), which additionally exploits noncircularity of the transmitted signals and circularity of noise to increase the dimension of the observation space twice while keeping the dimension of the signal subspace unchanged. This enables us to improve the performance substantially and to apply the proposed algorithm to scenarios with an increased number of active users and lengthier user channels as compared with the original LX algorithm. The theoretical analysis of the identifiability of the proposed technique is provided, which shows that it enjoys more relaxed identifiability conditions than the LX algorithm. Analytical expressions for the mean-square error (MSE) of the proposed algorithm are also derived. Numerical examples verify the advantages of the proposed algorithm over the LX technique and validate our analytical results. [ABSTRACT FROM AUTHOR]