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Signal Processing, IEEE Transactions on

Issue 7 • Date Jul 1997

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Displaying Results 1 - 25 of 26
  • Asymptotically optimal blind fractionally spaced channel estimation and performance analysis

    Page(s): 1815 - 1830
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    When the received data are fractionally sampled, the magnitude and phase of most linear time-invariant FIR communications channels can be estimated from second-order output only statistics. We present a general cyclic correlation matching algorithm for known order FIR blind channel identification that has closed-form expressions for calculating the asymptotic variance of the channel estimates. We show that for a particular choice of weights, the weighted matching estimator yields (at least for large samples) the minimum variance channel estimator among all unbiased estimators based on second-order statistics. Furthermore, the matching approach, unlike existing methods, provides a useful estimate even when the channel is not uniquely identifiable from second-order statistics View full abstract»

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  • Parametric cumulant based phase estimation of 1-D and 2-D nonminimum phase systems by allpass filtering

    Page(s): 1742 - 1762
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    This paper proposes a parametric cumulant-based phase-estimation method for one-dimensional (1-D) and two-dimensional (2-D) linear time-invariant (LTI) systems with only non-Gaussian measurements corrupted by additive Gaussian noise. The given measurements are processed by an optimum allpass filter such that a single Mth-order (M⩾3) cumulant of the allpass filter output is maximum in absolute value. It can be shown that the phase of the unknown system of interest is equal to the negative of the phase of the optimum allpass filter except for a linear phase term (a time delay). For the phase estimation of 1-D LTI systems, an iterative 1-D algorithm is proposed to find the optimum allpass filter modeled either by an autoregressive moving average (ARMA) model or by a Fourier series-based model. For the phase estimation of 2-D LTI systems, an iterative 2-D algorithm is proposed that only uses the Fourier series-based allpass model. A performance analysis is then presented for the proposed cumulant-based 1-D and 2-D phase estimation algorithms followed by some simulation results and experimental results with real speech data to justify their efficacy and the analytic results on their performance. Finally, the paper concludes with a discussion and some conclusions View full abstract»

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  • A nonlinear adaptive estimation method based on local approximation

    Page(s): 1831 - 1841
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    One of the most important problems in signal processing is to estimate the output for a query from the input/output (I/O) data seen so far. This paper presents a nonlinear adaptive estimation method based on the n-nearest neighbor approach. In this method, observed I/O data are stored in a database in the form of a X-dimensional binary digital search trie (k-D trie), and a nonlinear local model to answer each query is derived based on regularization theory. The database contents are efficiently time updated to follow nonstationary data. A storage procedure allowing a simple and efficient update is developed for reduction in processing time and storage requirement. The effectiveness of the proposed method is demonstrated with both simulation data and real speech signals View full abstract»

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  • Maximum likelihood estimation of constellation vectors for blind separation of co-channel BPSK signals and its performance analysis

    Page(s): 1736 - 1741
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    In this paper, we present a method for blind separation of co-channel BPSK signals arriving at an antenna array. This method consists of two parts: the maximum likelihood constellation estimation and assignment. We show that at high SNR, the maximum likelihood constellation estimation is well approximated by the smallest distance clustering algorithm, which we proposed earlier on heuristic grounds. We observe that both these methods for estimating the constellation vectors perform very well at high SNR and nearly attain Cramer-Rao bounds. Using this fact and noting that the assignment algorithm causes negligible error at high SNR, we derive upper bounds on the probability of bit error for the above method at high SNR. These upper bounds fall very rapidly with increasing SNR, showing that our constellation estimation-assignment approach is very efficient. Simulation results are given to demonstrate the usefulness of the bounds View full abstract»

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  • Transmitter induced cyclostationarity for blind channel equalization

    Page(s): 1785 - 1794
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    Fractional sampling has received considerable interest recently as a means of developing blind equalization techniques without resorting to higher order statistics. Instead, cyclostationarity introduced at the receiver by fractional sampling is exploited. We show that simpler solutions are possible if cyclostationarity is introduced at the transmitter instead of the receiver. We propose specific coding and interleaving strategies at the transmitter that induce cyclostationarity and facilitate the equalization task. Novel batch and adaptive equalization algorithms are derived that make no assumptions on the channel zeros locations. Subspace methods are also proposed and, in the absence of noise, guarantee perfect estimation from finite data. Synchronization issues and bandwidth considerations are briefly discussed, and simulation examples are presented View full abstract»

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  • On spatial smoothing for two-dimensional direction-of-arrival estimation of coherent signals

    Page(s): 1689 - 1696
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    We present an analysis of a spatial smoothing scheme extended for the estimation of two-dimensional (2-D) directions of arrival (DOAs) of coherent signals using a uniform rectangular array. The uniform rectangular array is divided into overlapping rectangular subarrays by the extended scheme, which is referred to as the 2-D spatial smoothing scheme. The analysis shows that when the extended preprocessing scheme is used in conjunction with the eigenstructure technique, the size of the subarrays should be at least (K+1)×(K+1), and the number of the subarrays must be no less than K×K in order to guarantee the “decorrelation” of κ coherent signals for all possible scenarios. The minimum size of the total uniform rectangular array is thus shown to be 2K×2K. Instead of using a uniform rectangular array, a minimal subarray structure incorporated with a minimal subarray grouping is also devised for resolving the 2-D DOAs of K coherent signals. The number of sensor elements of the minimal total array is then (K2+4K-2) instead of 4K2 View full abstract»

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  • A penalty approach to iterative algorithms for envelope constrained filter design

    Page(s): 1869 - 1873
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    The discrete-time envelope-constrained (EC) filtering problem can be formulated as a quadratic programming (QP) problem with affine inequality constraints. This QP problem is approximated by an unconstrained minimization problem with two parameters. Descent direction-based algorithms are applied to solve the unconstrained problem iteratively. It is shown that these algorithms converge View full abstract»

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  • A novel blind estimation algorithm

    Page(s): 1763 - 1769
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    In this paper, we propose a cumulant-based blind signal estimation algorithm for estimating the channel matrix in an n-sensor m-source system. The only available information is the output of the n sensors. The algorithm first deduces the number of sources, which may be greater than or equal to the number of sensors, from the output cumulant matrix. Then, by suitably arranging the elements within that matrix, the entries of the original channel matrix are estimated row by row. Simulations results are given to illustrate the performance of the algorithm View full abstract»

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  • Threshold parameter estimation in nonadditive non-Gaussian noise

    Page(s): 1681 - 1688
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    Threshold or weak-signal locally optimum Bayes estimators (LOBEs) of signal parameters, where the observations are an arbitrary mixture of signal and noise, the latter being independent, are first derived for “simple” as well as quadratic cost functions under the assumption that the signal is present a priori. It is shown that the desired LOBEs are either a linear (simple cost function) or a nonlinear (quadratic cost function) functional of an associated locally optimum and asymptotically optimum Bayes detector. Second, explicit classes of (threshold) optimum estimators are obtained for both cost functions in the coherent as well as in the incoherent reception modes. Third, the general results are applied to amplitude estimation, where two examples are considered: (1) coherent amplitude estimation in multiplicative noise with simple cost function (SCF) and (2) incoherent amplitude estimation with quadratic cost function (QFC) of a narrowband signal arbitrarily mixed with noise. Moreover, explicit estimator structures are given together with desired properties (i.e. efficiency of the unconditional maximum likelihood (ML) estimator) and Bayes' risks. These properties are obtained by employing contiguity-a powerful concept in modern statistics-implied by the locally asymptotically normal character of the detection algorithms View full abstract»

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  • On the achievable localization accuracy of multiple sources at high SNR

    Page(s): 1795 - 1799
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    The Cramer-Rao bound (CRB) for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated. It is shown that unlike in the case where the number of samples grows, wherein the CRB for the localization error always converges to zero, in the case where the number of snapshots is kept fixed and the signal-to-noise ratio (SNR) grows, the CRB converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension View full abstract»

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  • On the approximation power of convolution-based least squares versus interpolation

    Page(s): 1697 - 1711
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (704 KB)  

    There are many signal processing tasks for which convolution-based continuous signal representations such as splines and wavelets provide an interesting and practical alternative to the more traditional sine-based methods. The coefficients of the corresponding signal approximations are typically obtained by direct sampling (interpolation or quasi-interpolation) or by using least squares techniques that apply a prefilter prior to sampling. We compare the performance of these approaches and provide quantitative error estimates that can be used for the appropriate selection of the sampling step h. Specifically, we review several results in approximation theory with a special emphasis on the Strang-Fix (1971) conditions, which relate the general O(hL ) behavior of the error to the ability of the representation to reproduce polynomials of degree n=L-1. We use this theory to derive pointwise error estimates for the various algorithms and to obtain the asymptotic limit of the L2-error as h tends to zero. We also propose a new improved L2-error bound for the least squares case. In the process, we provide all the relevant bound constants for polynomial splines. Some of our results suggest the existence of an intermediate range of sampling steps where the least squares method is roughly equivalent to an interpolator with twice the order. We present experimental examples that illustrate the theory and confirm the adequacy of our various bound and limit determinations View full abstract»

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  • Scale periodicity and its sampling theorem

    Page(s): 1862 - 1865
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    The scalar transform is a new representation for signals, offering a perspective that is different from the Fourier transform. We introduce the notion of a scalar periodic function. These functions are then represented through the discrete scale series. We also define the notion of a strictly scale-limited signal. Analogous to the Shannon interpolation formula, we show that such signals can be exactly reconstructed from exponentially spaced samples of the signal in the time domain. As an interesting, practical application, we show how properties unique to the scale transform make it very useful in computing depth maps of a scene View full abstract»

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  • Bayesian estimation of parameters of a damped sinusoidal model by a Markov chain Monte Carlo method

    Page(s): 1806 - 1814
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    A dynamic Monte Carlo method is proposed to compute the posterior means and covariances of the parameters of a damped sinusoidal model when an informative prior distribution is known. The Bayesian framework provides a sound mathematical ground, which possibly allows one to overcome the approximations commonly used to cope with this difficult problem. Some simulations results are provided, which support the conclusion that the prior information can also be significantly improved when the data have a low signal-to-noise ratio View full abstract»

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  • A robust recursive least squares algorithm

    Page(s): 1726 - 1735
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    A new algorithm is developed, which guarantees the normalized bias in the weight vector due to persistent and bounded data perturbations to be bounded. Robustness analysis for this algorithm has been presented. An approximate recursive implementation is also proposed. It is termed as the robust recursive least squares (RRLS) algorithm since it resembles the RLS algorithm in its structure and is robust with respect to persistent bounded data perturbation. Simulation results are presented to illustrate the efficacy of the RRLS algorithm View full abstract»

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  • The degradation of higher order spectral detection using narrowband processing

    Page(s): 1770 - 1784
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    In certain scenarios, higher order statistic (HOS)-based detectors exploiting the Gaussian noise rejection property of HOS have been shown to have performances superior to widely used second-order (SOS) techniques. However, a crucial limitation on these detectors that has not been addressed is a constraint on the processing bandwidth. We study the effects of commonly used narrowband processing on these detectors. As the processing bandwidth is decreased, we characterize the tradeoff between HOS and SOS detectors and demonstrate that the performance of HOS detectors degrades faster than that of SOS ones. We then consider distributed wideband detection by a bank of local narrowband detectors whose decisions are fused together. Given a fixed-bandwidth input signal, we show that as the number of local detectors increases, corresponding to a decreasing amount of bandwidth for each local detector, the performance of such a scheme using HOS local detectors degrades more quickly than a scheme using SOS ones View full abstract»

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  • Finding of optimal stack filter by graphic searching methods

    Page(s): 1857 - 1862
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    An efficient process to filter noise via an optimal stack filter is proposed. The graphic search based techniques are employed to speed up the finding of the optimal stack filter. Experimental results and performance evaluation are demonstrated to show the efficiency of our proposed method View full abstract»

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  • ML estimation of time and frequency offset in OFDM systems

    Page(s): 1800 - 1805
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    We present the joint maximum likelihood (ML) symbol-time and carrier-frequency offset estimator in orthogonal frequency-division multiplexing (OFDM) systems. Redundant information contained within the cyclic prefix enables this estimation without additional pilots. Simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode View full abstract»

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  • Blind separation of mixture of independent sources through a quasi-maximum likelihood approach

    Page(s): 1712 - 1725
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    We propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution. They are obtained by considering a maximum likelihood (ML) solution corresponding to some given distributions of the sources and relaxing this assumption afterward. The first method is specially adapted to temporally independent non-Gaussian sources and is based on the use of nonlinear separating functions. The second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters. A theoretical analysis of the performance of the methods has been made. A simple procedure for optimally choosing the separating functions is proposed. Further, in the second method, a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided. Finally, some numerical and simulation results are given, illustrating the performance of the method and the good agreement between the experiments and the theory View full abstract»

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  • Observations on oblique projectors and pseudoinverses

    Page(s): 1886 - 1889
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    Oblique projectors (which were examined by Behrens and Scharf (see ibid., vol.42, no.6, p.1413-24, 1994)) are related to earlier work on oblique pseudoinverses and constrained least-squares methods and are reconsidered from the standpoint of orthogonal basis vectors and QR factorizations. Construction algorithms are presented that are numerically more stable than the normal-equations constructions previously used View full abstract»

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  • Matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts

    Page(s): 1894 - 1899
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    The performance of high-resolution direction of arrival (DOA) estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence. The original solution to this problem was proposed by Paulraj and Kailath (1988), but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture. A novel solution to this problem is proposed, which does not require a priori knowledge of the spatial coherence matrix View full abstract»

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  • Adaptive beamforming algorithms with robustness against jammer motion

    Page(s): 1878 - 1885
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    The performance of adaptive array algorithms is known to degrade in rapidly moving jammer environments. This degradation occurs due to the jammer motion that may bring the jammers out of the sharp notches of the adapted pattern. We develop the robust modifications of the sample matrix inversion (SMI) algorithm, loaded SMI (LSMI) algorithm, and eigenvector projection (EP) algorithm by means of artificial broadening of the null width in the jammer directions. For this purpose, data-dependent sidelobe derivative constraints that do not require any a priori information about the jammer directions are used View full abstract»

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  • Blind carrier phase tracking with guaranteed global convergence

    Page(s): 1889 - 1894
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    Conventional blind carrier recovery algorithms have been observed to show unstable behaviors for large constellation modulation schemes such as 64-QAM or 256-QAM. We propose a new carrier tracking approach that has guaranteed global convergence. First, we show that the carrier tracking problem is equivalent to a blind source separation problem, which involves the separation of a linear unitary mixture of two independent components that are the real and imaginary parts of the emitted signal. Then, by using a blind source separation procedure, we derive a new and robust carrier tracking algorithm with guaranteed global convergence. Some numerical simulations are provided to illustrate the effectiveness of the proposed method View full abstract»

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  • Data-adaptive algorithms for signal detection in sub-Gaussian impulsive interference

    Page(s): 1873 - 1878
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    We address the problem of coherent detection of a signal embedded in heavy-tailed noise modeled as a sub-Gaussian, alpha-stable process. We assume that the signal is a complex-valued vector of length L, known only within a multiplicative constant, while the dependence structure of the noise, i.e. the underlying matrix of the sub-Gaussian process, is not known. We implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength. The performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses Gaussian estimates of the noise-underlying matrix and the signal strength and is found to be clearly superior. The proposed new algorithms are theoretically analyzed and illustrated in a Monte-Carlo simulation View full abstract»

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  • On the efficient prediction of fractal signals

    Page(s): 1865 - 1868
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    A novel prediction scheme for self-affine fractal signals is presented. The signal is modeled by self-affine linear mappings, whose contraction factors are assumed to follow an auto-regressive (AR) process. In this way, the highly nonlinear time evolution of the fractal signal is captured by the linear AR process of the contraction factors, thereby exploiting the simplicity and ease of computation inherent in the AR model. An adaptive version of the proposed scheme is applied in simulations using the Weierstrass-Mandelbrot cosine fractal, as well as, in practice, using real radar sea clutter data View full abstract»

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  • Resolution of overlapping echoes and constrained matched filter

    Page(s): 1854 - 1857
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    An algorithm for the resolution of overlapping echoes is proposed based on the constrained matched filters (CMF) that maximize the signal to noise ratio (SNR) for a desired signal-and cancel out other unwanted signals. The CMP is equivalent to the maximum likelihood detection and asymptotically identical to the optimum detector of signal from interference. The resolution capability of the algorithm breaks the classical resolution limit in the time domain View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota