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In this paper, the problem of adaptive distributed learning in diffusion networks is considered. The algorithms are developed within the convex set theoretic framework. More specifically, they are based on computationally simple geometric projections onto closed convex sets. The paper suggests a novel combine-project-adapt protocol for cooperation among the nodes of the network; such a protocol fits naturally with the philosophy that underlies the projection-based rationale. Moreover, the possibility that some of the nodes may fail is also considered and it is addressed by employing robust statistics loss functions. Such loss functions can easily be accommodated in the adopted algorithmic framework; all that is required from a loss function is convexity. Under some mild assumptions, the proposed algorithms enjoy monotonicity, asymptotic optimality, asymptotic consensus, strong convergence and linear complexity with respect to the number of unknown parameters. Finally, experiments in the context of the system-identification task verify the validity of the proposed algorithmic schemes, which are compared to other recent algorithms that have been developed for adaptive distributed learning. [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]

Low-rank matrix approximation has applications in many fields, such as 2-D filter design and 3-D reconstruction from an image sequence. In this paper, one issue with low-rank matrix approximation is investigated: heteroscedastic noise. In most of previous research, the covariance matrix of the heteroscedastic noise is assumed to be positive definite. This requirement restricts the usefulness of results derived from such research. In this paper, we extend the Wiberg algorithm, which originally deals with the missing data problem with low-rank approximation, to the cases, where the heteroscedastic noise has a singular covariance matrix. Experiments show that the proposed Wiberg algorithm converges much faster than the bilinear approach, and consequently avoids many nonconvergent cases in the bilinear approach. Experiments also show that, to some extent, the Wiberg algorithm can tolerate outliers and is not sensitive to parameter variation. [ABSTRACT FROM AUTHOR]

Linear dispersion (LD) codes are a good candidate for high-data-rate multiple-input multple-ouput (MIMO) signaling. Traditionally LD codes were designed by maximizing the average mutual information, which cannot guarantee good error performance. This paper presents a new design scheme for LD codes that directly minimizes the block error rate (BLER) in MIMO channels with arbitrary fading statistics and various detection algorithms. For MIMO systems employing LD codes, the error rate does not admit an explicit form. Therefore, we cannot use deterministic optimization methods to design the minimum-error-rate LD codes. In this paper, we propose a simulation-based optimization methodology for the design of LD codes through stochastic approximation and simulation-based gradient estimation. The gradient estimation is done using the score function method originally developed in the discrete-event-system community. The proposed method can be applied to design the minimum-error-rate LD codes for a variety of detector structures including the maximum-likelihood (ML) detector and several sub-optimal detectors. It can also design optimal codes under arbitrary fading channel statistics; in particular, it can take into account the knowledge of spatial fading correlation at the transmitter and receiver ends. Simulation results show that codes generated by the proposed new design paradigm generally outperform the codes designed based on algebraic number theory. [ABSTRACT FROM AUTHOR]

This paper proposes, analyzes, and illustrates several best basis search algorithms for dictionaries consisting of lapped orthogonal bases. It improves upon the best local cosine basis selection based on a dyadic tree [10], [11] by considering larger dictionaries of bases. It is shown that this can result in sparser representations and approximate shift invariance. An algorithm that is strictly shift invariant is also provided. The experiments in this paper suggest that the new dictionaries can be advantageous for time-frequency analysis, compression, and noise removal. Accelerated versions of the basic algorithm are provided that explore various tradeoffs between computational efficiency and adaptability. It is shown that the proposed algorithms are in fact applicable to any finite dictionary comprised of lapped orthogonal bases. One such novel dictionary is proposed that constructs the best local cosine representation in the frequency domain, and it is shown that the new dictionary is better suited for representing certain types of signals. [ABSTRACT FROM AUTHOR]

In this paper, a method for approximating a multi- input multi-output (MIMO) transfer function by a causal finite-im- pulse response (FIR) paraunitary (PU) system in a weighted least- squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase- type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmul- tiplexers. [ABSTRACT FROM AUTHOR]

CANDECOMP/PARAFAC (CP) approximates multiway data by sum of rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-R tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper, we propose a novel deflation method for the problem. When one factor matrix of a rank-R CP decomposition is of full column rank, the decomposition can be performed through (R-1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank. For decomposition of order-3 tensors of size R\times R\times R and rank-R, estimation of one rank-1 tensor has a computational cost of \cal O(R^3) per iteration which is lower than the cost \cal O(R^4) of the ALS algorithm for the overall CP decomposition. The method can be extended to tracking one or a few rank-one tensors of slow changes, or inspect variations of common patterns in individual datasets. [ABSTRACT FROM PUBLISHER]

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

In this paper, we provide a thorough stability analysis of two well known adaptive algorithms for equalization based on a novel least squares reference model that allows to treat the equalizer problem equivalently as system identification problem. While not surprising the adaptive minimum mean-square error (MMSE) equalizer algorithm behaves l2–stable for a wide range of step-sizes, the even older zero-forcing (ZF) algorithm however behaves very differently. We prove that the ZF algorithm generally does not belong to the class of robust algorithms but can be convergent in the mean square sense. We furthermore provide conditions on the upper step-size bound to guarantee such mean squares convergence. We specifically show how noise variance of added channel noise and the channel impulse response influences this bound. Simulation examples validate our findings. [ABSTRACT FROM AUTHOR]

In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments. [ABSTRACT FROM AUTHOR]

This paper deals with detection algorithms for impulse-radio ultrawideband transmitted-reference systems. For binary modulation schemes, we propose a novel detector that operates on the partial autocorrelations of the received signal as computed over time intervals (bins) of size less than the symbol period. Assuming that the receiver has knowledge of the partial autocorrelations of the channel response over those bins, we derive the minimum error probability detector (MEPD). In doing so, we exploit some invariance properties of the detection problem under consideration. It turns out that the receiver adopting such a strategy is superior to a conventional TR system, the more so the smaller the bin size is. Also, we address the problem of estimating the partial autocorrelations of the channel response and propose a simple solution by exploiting a training sequence. The impact of the estimation errors on the receiver performance is shown to be marginal. [ABSTRACT FROM AUTHOR]

This paper addresses the independent component analysis (ICA) of quaternion random vectors. In particular, we focus on the Gaussian case and therefore only consider the quaternion second-order statistics (SOS), which are given by the covariance matrix and three complementary covariance matrices. First, we derive the necessary and sufficient conditions for the identifiability of the quaternion ICA model, which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles. Second, we show that the maximum-likelihood (ML) approach to the quaternion ICA problem reduces to the approximated joint diagonalization (AJD) of the sample-mean estimates of the covariance and complementary covariance matrices. Unlike the complex case, these four matrices cannot be simultaneously diagonalized in general, and we have to resort to a particular AJD algorithm. The proposed technique, which can be seen as a quasi-Newton method, is based on the local approximation of the nonconvex ML-ICA cost function (a measure of the entropy loss due to the residual correlation among the estimated quaternion sources), and it provides a satisfactory solution of the quaternion ICA model. The performance of the proposed quaternion ML-ICA algorithm, as well as its relationship to the identifiability conditions, are illustrated by means of several numerical examples. [ABSTRACT FROM PUBLISHER]

Dynamic spectrum management (DSM) has been recognized as a key technology to significantly improve the performance of digital subscriber line (DSL) broadband access networks. The basic concept of DSM is to coordinate transmission over multiple DSL lines so as to mitigate the impact of crosstalk interference amongst them. Many algorithms have been proposed to tackle the nonconvex optimization problems appearing in DSM, many of them relying on a standard subgradient based dual decomposition approach. In practice however, this approach is often found to lead to extremely slowconvergence or even no convergence at all, one of the reasons being the very difficult tuning of the stepsize parameters. In this paper we propose a novel improved dual decomposition approach inspired by recent advances in mathematical programming. It uses a smoothing technique for the Lagrangian combined with an optimal gradient based scheme for updating the Lagrange multipliers. The stepsize parameters are furthermore selected optimally removing the need for a tuning strategy. With this approach we show how the convergence of current state-of-the-art DSM algorithms based on iterative convex approximations (SCALE and CA-DSB)can be improvedby one order of magnitude. Furthermore we apply the improved dual decomposition approach to otherDSM algorithms (OSB, ISB, ASB, (MS)-DSB, and MIW) and propose further improvements to obtain fast and robust DSM algorithms. Finally, we demonstrate the effectiveness of the improved dual decomposition approach for a number of realistic multiuser DSL scenarios. [ABSTRACT FROM AUTHOR]

ℓ0 norm based algorithms have numerous potential applications where a sparse signal is recovered from a small number of measurements. The direct ℓ0 norm optimization problem is NP-hard. In this paper we work with the the smoothed ℓ0 (SL0) approximation algorithm for sparse representation. We give an upper bound on the run-time estimation error. This upper bound is tighter than the previously known bound. Subsequently, we develop a reliable stopping criterion. This criterion is helpful in avoiding the problems due to the underlying discontinuities of the ℓ0 cost function. Furthermore, we propose an alternative optimization strategy, which results in a Newton like algorithm. [ABSTRACT FROM AUTHOR]

Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is, developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of "bridge" sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-LMS is also assessed. Numerical simulations: i) illustrate that D-LMS outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering; ii) highlight its tracking capabilities; and iii) corroborate the stability and performance analysis results. [ABSTRACT FROM AUTHOR]

Sparse signal approximations have become a fundamental tool in signal processing with wide-ranging applications from source separation to signal acquisition. The ever-growing number of possible applications and, in particular, the ever-increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of fast and efficient algorithms has become paramount. Recently, very fast algorithms have been developed to solve convex optimization problems that are often used to approximate the sparse approximation problem; however, it has also been shown, that in certain circumstances, greedy strategies, such as orthogonal matching pursuit, can have better performance than the convex methods. In this paper, improvements to greedy strategies are proposed and algorithms are developed that approximate orthogonal matching pursuit with computational requirements more akin to matching pursuit. Three different directional optimization schemes based on the gradient, the conjugate gradient, and an approximation to the conjugate gradient are discussed, respectively. It is shown that the conjugate gradient update leads to a novel implementation of orthogonal matching pursuit, while the gradient-based approach as well as the approximate conjugate gradient methods both lead to fast approximations to orthogonal matching pursuit, with the approximate conjugate gradient method being superior to the gradient method. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of sensing dictionaries. It presents an alteration of greedy algorithms like thresholding or (orthogonal) matching pursuit which improves their performance in finding sparse signal representations in redundant dictionaries while maintaining the same complexity. These algorithms can be split into a sensing and a reconstruction step, and the former will fail to identify correct atoms if the cumulative coherence of the dictionary is too high. We thus modify the sensing step by introducing a special sensing dictionary. The correct selection of components is then determined by the cross cumulative coherence which can be considerably lower than the cumulative coherence. We characterize the optimal sensing matrix and develop a constructive method to approximate it. Finally, we compare the performance of thresholding and OMP using the original and modified algorithms. [ABSTRACT FROM AUTHOR]

Novel low-density signature (LDS) structure is proposed for transmission and detection of symbol-synchronous communication over memoryless Gaussian channel. Given N as the processing gain, under this new arrangement, users' symbols are spread over N chips but virtually only dv < N chips that contain nonzero-values. The spread symbol is then so uniquely interleaved as the sampled, at chip rate, received signal contains the contribution from only dc < K number of users, where K denotes the total number of users in the system. Furthermore, a near-optimum chip-level iterative soft-in-soft-out (SISO) multiuser decoding (MUD), which is based on message passing algorithm (MPA) technique, is proposed to approximate optimum detection by efficiently exploiting the LDS structure. Given β = K/N as the system loading, our simulation suggested that the proposed system alongside the proposed detection technique, in AWGN channel, can achieve an overall performance that is close to single-user performance, even when the system has 200% loading, i.e., when β = 2. Its robustness against near-far effect and its performance behavior that is very similar to optimum detection are demonstrated in this paper. In addition, the complexity required for detection is now exponential to dc instead of K as in conventional code division multiple access (CDMA) structure employing optimum multiuser detector. [ABSTRACT FROM AUTHOR]

This paper examines the problem of target detection by a wireless sensor network. Sensors acquire measurements emitted from the target that are corrupted by noise, and initially make individual decisions about the presence/absence of the target. We propose the local vote decision fusion algorithm, in which sensors first correct their decisions using decisions of neighboring sensors, and then make a collective decision as a network. An explicit formula that approximates the system's decision threshold for a given false alarm rate is derived using limit theorems for random fields, which provides a theoretical performance guarantee for the algorithm. We examine both distance- and nearest-neighbor-based versions of the local vote algorithm for grid and random sensor deployments and show that, in many situations, for a fixed-system false alarm, the local vote correction achieves significantly higher target detection rate than decision fusion based on uncorrected decisions. The algorithm does not depend on the signal model and is shown to be robust to different types of signal decay. We also extend this framework to temporal fusion, where information becomes available over time. [ABSTRACT FROM AUTHOR]

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

Prefilters are generally applied to the discrete multi-wavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the pre-filter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. [ABSTRACT FROM AUTHOR]

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

Recently, there has been an intense activity in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit (MP) and Basis Pursuit (BP). However, most of the theoretical results obtained so far are valid only for the restricted class of incoherent dictionaries. This paper investigates a new class of overcomplete dictionaries, called block incoherent dictionaries, where coherence can be arbitrarily big. We show that a simple greedy algorithm can correctly identify stable subdictionaries (called blocks) and demonstrate how one can use the extra coherence freedom for approximation purposes. [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]

This paper presents a study of sequential parameter estimation based on a linear non-Gaussian observation model. To develop robust algorithms, we consider a family of heavy-tailed distributions that can be expressed as the scale mixture of Gaussian and extend the development to include some robust penalty functions. We treat the problem as a Bayesian learning problem and develop an iterative algorithm by using the Laplace approximation for the posterior and the minorization-maximization (MM) algorithm as an optimization tool. We then study a one-step implementation of the iterative algorithm. This leads to a family of generalized robust RLS-type of algorithms which include several well-known algorithms as special cases. Using a further simplification that the covariance is fixed, leads to a family of generalized robust LMS-type of algorithms. Through mathematical analysis and simulations, we demonstrate the robustness of these algorithms [ABSTRACT FROM PUBLISHER]

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

In array signal processing, high-resolution direction-of-arrival (DOA) estimation algorithms are known to be sensitive to system errors. In practice, the system should be properly calibrated before DOA estimation. In this paper, a calibration method of gain and phase errors of linear equispaced arrays (LEAs) is considered. A class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed. The statistical performance analyses of the calibration algorithms due to finite data perturbations are presented. Expressions for average bias (Abias) and square root of average variance (SRAV) of the calibration algorithms are derived using first-order approximation. These statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations, the more inferior performance that may be obtained. Based on this conclusion, the simple and optimal gain and phase error calibration algorithms for such model are obtained. [ABSTRACT FROM AUTHOR]

The ESPRIT algorithm is a subspace-based high-resolution method used in source localization and spectral analysis, which provides very accurate estimates of the signal parameters. However, the underlying theory assumes a known model order, which is usually not the case in many applications. In particular, it is well known that underevaluating the model order biases the estimation. In this paper, we analyze the perturbation induced by an erroneous model order, and we present an error bound for the estimated parameters. Based on this theoretical framework, we propose a new method for selecting an appropriate modeling order, which consists in minimizing the error bound. This approach is applied to both synthetic and musical signals, and its performance is compared to that of existing methods, such as the information theoretic criteria. [ABSTRACT FROM AUTHOR]

This paper presents a general feedforward symbol-timing estimation framework based on the conditional maximum likelihood principle. The proposed timing estimator presents reduced implementation complexity and is obtained by performing an approximation on the Fourier series expansion of the conditional maximum likelihood function. The proposed algorithm is applied to linear modulations and two commonly used continuous phase modulations: minimum shift keying (MSK) and Gaussian MSK (GMSK). For the linear modulations, it is shown both analytically and via simulations that the performance of the proposed estimator is very close to the conditional CRB and modified CRB for signal-to-noise ratios (SNRs) in the range SNR ≤ 30 dB. Furthermore, the proposed estimator is shown to be asymptotically equivalent to the classic square-law nonlinearity estimator under certain conditions. In the case of MSK and GMSK modulations, although the proposed algorithm reaches the conditional CRB at certain SNRs, however, the conditional CRB is quite far away from the modified CRB, and there exists an alternative algorithm whose performance comes closer to the modified CRB. Therefore, the proposed estimator is more suitable for linear modulations than for MSK and GMSK modulations. [ABSTRACT FROM AUTHOR]

We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over R[x] or C[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9. [ABSTRACT FROM AUTHOR]

A recent paper [E. Masazade, R. Niu, P. K. Varshney, and M. Keskinoz, “Energy Aware Iterative Source Localization for Wireless Sensor Networks”, IEEE Transactions on Signal Processing, vol. 58, no. 9, pp. 4824–4835, 2010] presents an iterative source localization scheme based on the selection of sensors. An importance sampling based Monte Carlo method was employed at each iteration using the entire received data to approximate the posterior distribution of the source location in the paper. In this note, we propose an alternative sequential importance sampling and resampling algorithm to implement the iterative source localization. The proposed method provides significant performance improvement over the current method via combination of auxiliary particle filtering with kernel smoothing approximation. The superiority of the alternative algorithm is verified by Monte Carlo simulation results. [ABSTRACT FROM PUBLISHER]