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Showing papers in "IEEE Transactions on Signal Processing in 1996"


Journal ArticleDOI
TL;DR: The S transform is shown to have some desirable characteristics that are absent in the continuous wavelet transform, and provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum.
Abstract: The S transform, which is introduced in the present correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is shown to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates.

2,752 citations


Journal ArticleDOI
TL;DR: A class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called EASI, which yields algorithms with a simple structure for both real and complex mixtures.
Abstract: Source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence (EASI). The EASI algorithms are based on the idea of serial updating. This specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions, and interference rejection levels depend only on the (normalized) distributions of the source signals. Closed-form expressions of these quantities are given via an asymptotic performance analysis. The theme of equivariance is stressed throughout the paper. The source separation problem has an underlying multiplicative structure. The parameter space forms a (matrix) multiplicative group. We explore the (favorable) consequences of this fact on implementation, performance, and optimization of EASI algorithms.

1,417 citations


Journal ArticleDOI
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Abstract: An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.

1,034 citations


Journal ArticleDOI
TL;DR: The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA) providing automatically paired source azimuth and elevation angle estimates.
Abstract: The UCA-ESPRIT is a closed-form algorithm developed for use in conjunction with a uniform circular array (UCA) that provides automatically paired source azimuth and elevation angle estimates. The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA). In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two major array axes. The 2-D unitary ESPRIT offers a number of advantages over other proposed ESPRIT based closed-form 2-D angle estimation techniques. First, except for the final eigenvalue decomposition of a dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to efficient beamspace implementations that are presented. Third, it is applicable to array configurations that do not exhibit identical subarrays, e.g., two orthogonal linear arrays. Finally, the 2-D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common. Simulation results are presented verifying the efficacy of the method.

538 citations


Journal ArticleDOI
TL;DR: A decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both one-dimensional and two-dimensional data sequences corrupted by AR noise, which provides excellent estimation performance under the model assumptions and is robust to mismodeling errors.
Abstract: We present a decoupled parameter estimation (DPE) algorithm for estimating sinusoidal parameters from both 1-D and 2-D data sequences corrupted by autoregressive (AR) noise. In the first step of the DPE algorithm, we use a relaxation (RELAX) algorithm that requires simple fast Fourier transforms (FFTs) to obtain the estimates of the sinusoidal parameters. We describe how the RELAX algorithm may be used to extract radar target features from both 1-D and 2-D data sequences. In the second step of the DPE algorithm, a linear least-squares approach is used to estimate the AR noise parameters. The DPE algorithm is both conceptually and computationally simple. The algorithm not only provides excellent estimation performance under the model assumptions, in which case the estimates obtained with the DPE algorithm are asymptotically statistically efficient, but is also robust to mismodeling errors.

528 citations


Journal ArticleDOI
TL;DR: It is shown that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices.
Abstract: Iterative constant modulus algorithms such as Godard (1980) and CMA have been used to blindly separate a superposition of cochannel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. We show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, non-CM signals. Only a modest amount of samples is required. The algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set-up.

528 citations


Journal ArticleDOI
TL;DR: The CSDF paradigm is an extension of synchronous dataflow that still allows for static scheduling and, thus, a very efficient implementation of an application and it is indicated that CSDF is essential for modelling prescheduled components, like application-specific integrated circuits.
Abstract: We present cycle-static dataflow (CSDF), which is a new model for the specification and implementation of digital signal processing algorithms. The CSDF paradigm is an extension of synchronous dataflow that still allows for static scheduling and, thus, a very efficient implementation of an application. In comparison with synchronous dataflow, it is more versatile because it also supports algorithms with a cyclically changing, but predefined, behavior. Our examples show that this capability results in a higher degree of parallelism and, hence, a higher throughput, shorter delays, and less buffer memory. Moreover, they indicate that CSDF is essential for modelling prescheduled components, like application-specific integrated circuits. Besides introducing the CSDF paradigm, we also derive necessary and sufficient conditions for the schedulability of a CSDF graph. We present and compare two methods for checking the liveness of a graph. The first one checks the liveness of loops, and the second one constructs a single-processor schedule for one iteration of the graph. Once the schedulability is tested, a makespan optimal schedule on a multiprocessor can be constructed. We also introduce the heuristic scheduling method of our graphical rapid prototyping environment (GRAPE).

509 citations


Journal ArticleDOI
TL;DR: This work addresses the time-invariance problem for orthonormal wavelet transforms and proposes an extension to wavelet packet decompositions to achieve time invariance and preserve the orthonormality.
Abstract: A simple construction of an orthonormal basis starting with a so-called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. We address the time-invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions. We show that it,is possible to achieve time invariance and preserve the orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.

443 citations


Journal ArticleDOI
TL;DR: It is shown via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approach.
Abstract: We present an adaptive FIR filtering approach, which is referred to as the amplitude and phase estimation of a sinusoid (APES), for complex spectral estimation. We compare the APES algorithm with other FIR filtering approaches including the Welch (1967) and Capon (1969) methods. We also describe how to apply the FIR filtering approaches to target range signature estimation and synthetic aperture radar (SAR) imaging. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approach. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method.

439 citations


Journal ArticleDOI
TL;DR: A maximum-likelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site and a signal detection technique based on the finite alphabet property that is different from a standard linear combiner are introduced.
Abstract: We propose a maximum-likelihood (ML) approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for BPSK signals. We introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful In wireless communication systems. Simulation results demonstrate its promising performance.

379 citations


Journal ArticleDOI
TL;DR: Some of the properties of the relation matrix are analyzed and used to express the probability density function of normal complex vectors.
Abstract: Complex random vectors are usually described by their covariance matrix. This is insufficient for a complete description of second-order statistics, and another matrix called the relation matrix is necessary. Some of its properties are analyzed and used to express the probability density function of normal complex vectors. Various consequences are presented.

Journal ArticleDOI
TL;DR: This work proposes a method to choose the initial state to obtain uniqueness and to remove transients at both ends in forward-backward filtering.
Abstract: Forward-backward filtering is a common tool in off-line filtering for implementing noncausal filters. Filtering first forward and then backward or the other way around does not generally give the same result. Here, we propose a method to choose the initial state to obtain uniqueness and to remove transients at both ends.

Journal ArticleDOI
TL;DR: High flexibility of simulated annealing is applied to the synthesis of arrays in order to reduce the peaks of side lobes by acting on the elements' positions and weight coefficients.
Abstract: Simulated annealing is applied to the synthesis of arrays in order to reduce the peaks of side lobes by acting on the elements' positions and weight coefficients. In the case considered, the number of array elements and the spatial aperture of an unequally spaced array are a priori fixed. Thanks to the high flexibility of simulated annealing, the results obtained for a 25-element array over an aperture of 50/spl lambda/ improve those reported in the literature.

Journal ArticleDOI
TL;DR: The authors propose a general algorithm to compute multi wavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms.
Abstract: The pyramid algorithm for computing single wavelet transform coefficients is well known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. The authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be thought of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete-time signals. The authors then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms.

Journal ArticleDOI
TL;DR: The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the Cramer-Rao lower bound (CRB) at high SNR and a novel orthogonal complement matrix of the generalized Sylvester matrix is exploited.
Abstract: This paper develops a fast maximum likelihood method for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the Cramer-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML, method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established.

Journal ArticleDOI
TL;DR: It is shown that separability is an intrinsic property of the measured signals and can be described by the concept of m-row decomposability introduced in this paper, and that separation principles can be developed by using the structure characterization theory of random variables.
Abstract: This paper identifies and studies two major issues in the blind source separation problem: separability and separation principles. We show that separability is an intrinsic property of the measured signals and can be described by the concept of m-row decomposability introduced in this paper; we also show that separation principles can be developed by using the structure characterization theory of random variables. In particular, we show that these principles can be derived concisely and intuitively by applying the Darmois-Skitovich theorem, which is well known in statistical inference theory and psychology. Some new insights are gained for designing blind source separation filters.

Journal ArticleDOI
TL;DR: The bounded-variance filtered estimation of the state of an uncertain, linear, discrete-time system, with an unknown norm-bounded parameter matrix, is considered and an upper bound on the variance of the estimation error is found.
Abstract: The bounded-variance filtered estimation of the state of an uncertain, linear, discrete-time system, with an unknown norm-bounded parameter matrix, is considered. An upper bound on the variance of the estimation error is found for all admissible systems, and estimators are derived that minimize the latter bound. We treat the finite-horizon, time-varying case and the infinite-time case, where the nominal system model is time invariant. In the special stationary case, where it is known that the uncertain system is time invariant, we provide a robust filter for all uncertainties that still keep the system asymptotically stable.

Journal ArticleDOI
TL;DR: It is shown that the celebrated least-mean squares (LMS) adaptive algorithm is H/sup /spl infin// optimal, and it is established that it is a minimax filter, which minimizes the maximum energy gain from the disturbances to the predicted errors.
Abstract: We show that the celebrated least-mean squares (LMS) adaptive algorithm is H/sup /spl infin// optimal. The LMS algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least-squares problem, and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function. We show that the LMS can be regarded as the exact solution to a minimization problem in its own right. Namely, we establish that it is a minimax filter: it minimizes the maximum energy gain from the disturbances to the predicted errors, whereas the closely related so-called normalized LMS algorithm minimizes the maximum energy gain from the disturbances to the filtered errors. Moreover, since these algorithms are central H/sup /spl infin// filters, they minimize a certain exponential cost function and are thus also risk-sensitive optimal. We discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the LMS filter.

Journal ArticleDOI
TL;DR: The Teager-Kaiser algorithm (TKA) and other similar local methods to the analytic signal (AS) procedure is compared to show that only AS meets certain physical conditions for the amplitude, phase, and frequency (APF).
Abstract: This paper compares the Teager-Kaiser algorithm (TKA) and other similar local methods to the analytic signal (AS) procedure. The general concepts of the instantaneous amplitude and frequency are discussed. It is shown that only AS meets certain physical conditions for the amplitude, phase, and frequency (APF). The advantage of accuracy and simplicity of the AS is also demonstrated.

Journal ArticleDOI
TL;DR: A class of lapped orthogonal transforms with extended overlap (GenLOTs) is developed as a subclass of the general class of LPPUFB as a method to process finite-length signals.
Abstract: The general factorization of a linear-phase paraunitary filter bank (LPPUFB) is revisited. From this new perspective, a class of lapped orthogonal transforms with extended overlap (generalized linear-phase lapped orthogonal transforms (GenLOTs)) is developed as a subclass of the general class of LPPUFB. In this formulation, the discrete cosine transform (DCT) is the order-1 GenLOT, the lapped orthogonal transform is the order-2 GenLOT, and so on, for any filter length that is an integer multiple of the block size. The GenLOTs are based on the DCT and have fast implementation algorithms. The implementation of GenLOTs is explained, including the method to process finite-length signals. The degrees of freedom in the design of GenLOTs are described, and design examples are presented along with image compression tests.

Journal ArticleDOI
TL;DR: The design of an extended Kalman filter for tracking a time-varying frequency and the design tradeoff between balancing noise rejection and tracking at a maximal slew rate is discussed.
Abstract: The design of an extended Kalman filter for tracking a time-varying frequency is discussed. Its principal modes of failure are explained. The design tradeoff between balancing noise rejection and tracking at a maximal slew rate is discussed. The performance penalties for overdesign and underdesign of noise covariances are examined, and theoretically supported design guidelines are suggested.

Journal ArticleDOI
TL;DR: A class of adaptive filters based on sequential adaptive eigendecomposition (subspace tracking) of the data covariance matrix that can be computationally less (or even much less) demanding, depending on the order/rank ratio N/r or the compressibility of the signal.
Abstract: We introduce a class of adaptive filters based on sequential adaptive eigendecomposition (subspace tracking) of the data covariance matrix. These new algorithms are completely rank revealing, and hence, they can perfectly handle the following two relevant data cases where conventional recursive least squares (RLS) methods fail to provide satisfactory results: (1) highly oversampled "smooth" data with rank deficient of almost rank deficient covariance matrix and (2) noise-corrupted data where a signal must be separated effectively from superimposed noise. This paper contradicts the widely held belief that rank revealing algorithms must be computationally more demanding than conventional recursive least squares. A spatial RLS adaptive filter has a complexity of O(N/sup 2/) operations per time step, where N is the filter order. The corresponding low-rank adaptive filter requires only O(Nr) operations per time step, where r/spl les/N denotes the rank of the data covariance matrix. Thus, low-rank adaptive filters can be computationally less (or even much less) demanding, depending on the order/rank ratio N/r or the compressibility of the signal. Simulation results substantiate our claims. This paper is devoted to the theory and application of fast orthogonal iteration and bi-iteration subspace tracking algorithms.

Journal ArticleDOI
TL;DR: A new subspace-based method for bearing estimation in the presence of impulsive noise which can be modeled as a complex symmetric alpha-stable (S/spl alpha/S) process is presented and its asymptotic performance is studied.
Abstract: This paper presents a new subspace-based method for bearing estimation in the presence of impulsive noise which can be modeled as a complex symmetric alpha-stable (S/spl alpha/S) process. We define the covariation matrix of the array sensor outputs and show that eigendecomposition-based methods, such as the MUSIC algorithm, can be applied to the sample covariation matrix to extract the bearing information from the measurements. A consistent estimator for the marginals of the covariation matrix is presented and its asymptotic performance is studied. The improved performance of the proposed source localization method in the presence of a wide range of impulsive noise environments is demonstrated via Monte Carlo experiments.

Journal ArticleDOI
TL;DR: This paper presents discrete vector wavelet transforms for discrete-time vector-valued (or blocked) signals, which can be thought of as a family of unitary vector transforms.
Abstract: In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector filter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued wavelets, multiwavelets can be constructed from vector-valued wavelets. We show that certain linear combinations of known scalar-valued wavelets may yield multiwavelets. We then present discrete vector wavelet transforms for discrete-time vector-valued (or blocked) signals, which can be thought of as a family of unitary vector transforms.

Journal ArticleDOI
TL;DR: A new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractionAL lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay.
Abstract: New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data.

Journal ArticleDOI
TL;DR: A simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log-likelihood is presented.
Abstract: We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an "unachievable region" of the delta-sigma plane for a specified statistical model. In order to place an estimator on this plane for comparison with the delta-sigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log-likelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems.

Journal ArticleDOI
TL;DR: This paper introduces a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the Kullback-Leibner distance and derives useful forms of this criterion when only a sample from that distribution is available.
Abstract: In this paper, we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the Kullback-Leibner distance. By replacing the unknown density with a kernel estimate, we derive useful forms of this criterion when only a sample from that distribution is available. We also compute the gradient and Hessian of our criteria for use in an iterative minimization. Setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem, except that here, these functions are adapted to the observed data. Finally, some simulations are given, illustrating the good performance of the method.

Journal ArticleDOI
TL;DR: It is shown quantitatively how assumptions about the parameters can fundamentally affect the maximum number of identifiable sources in various acoustic and electromagnetic vector-sensor models.
Abstract: We present a bound on the number of sources identifiable in a class of array processing models with multiple parameters and signals per source. The bound is applied to determine the maximum number of uniquely resolvable plane-wave sources in various acoustic and electromagnetic vector-sensor models. We examine the use of a priori information about the sources, the effects of known and unknown noise characteristics, and the presence of nuisance parameters. Connections between identifiability and existence of the Cramer-Rao bound (CRB) are investigated. We show quantitatively how assumptions about the parameters can fundamentally affect the maximum number of identifiable sources.

Journal ArticleDOI
TL;DR: It is shown that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: (1) a finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and (2) the linear FSE filter length need not be longer than the channel delay spread.
Abstract: The Godard (1980) or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSEss) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. We present a convergence analysis of Godard/CMA FSEs that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: (1) a finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and (2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE.

Journal ArticleDOI
TL;DR: New estimators based on asymptotic extreme value theory, order statistics, and fractional lower order moments are proposed, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms.
Abstract: We address the problem of estimation of the parameters of the recently proposed symmetric, alpha-stable model for impulsive interference. We propose new estimators based on asymptotic extreme value theory, order statistics, and fractional lower order moments, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms. The performance of the new estimators is theoretically evaluated, verified via Monte Carlo simulation, and compared with the performance of maximum-likelihood estimators.