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Signal Processing, IEEE Transactions on

Issue 9 • Date Sept. 2003

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Displaying Results 1 - 18 of 18
  • Nonminimum-phase FIR channel estimation using cumulant matrix pencils

    Page(s): 2310 - 2320
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (589 KB)  

    This paper studies the blind estimation of single-input-single-output channels with finite impulse response (FIR) and nonminimum phase. Based on higher order statistics, we introduce a new algorithm that exploits a matrix pencil constructed from a set of cumulant matrices. By solving a generalized eigenvalue problem, channel estimates (up to a scalar ambiguity) can be obtained from nontrivial generalized eigenvectors of this cumulant matrix pencil. With multiple estimation results available, different schemes are given to extract channel information effectively. The proposed algorithm does not require exact knowledge of the channel length and can function properly under channel length overestimation. Numerical simulations demonstrate the robustness of this new algorithm to various adverse conditions. View full abstract»

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  • Framing pyramids

    Page(s): 2329 - 2342
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1002 KB)  

    Burt and Adelson (1983) introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filters is a tight frame, and thus, the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform. In more general cases, we propose an efficient filterbank (FB) for the reconstruction of the LP using projection that leads to a proved improvement over the usual method in the presence of noise. Setting up the LP as an oversampled FB, we offer a complete parameterization of all synthesis FBs that provide perfect reconstruction for the LP. Finally, we consider the situation where the LP scheme is iterated and derive the continuous-domain frames associated with the LP. View full abstract»

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  • Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization

    Page(s): 2381 - 2401
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1133 KB) |  | HTML iconHTML  

    This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multiple-input multiple-output (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schur-convex functions. Once the optimal structure of the transmit-receive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closed-form expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peak-to-average ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel water-filling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form. View full abstract»

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  • A numerically stable fast Newton-type adaptive filter based on order recursive least squares algorithm

    Page(s): 2357 - 2368
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (827 KB) |  | HTML iconHTML  

    This paper presents a numerically stable fast Newton-type adaptive filter algorithm. Two problems are dealt with in the paper. First, we derive the proposed algorithm from an order-recursive least squares algorithm. The result of the proposed algorithm is equivalent to that of the fast Newton transversal filter (FNTF) algorithm. However, the derivation process is different. Instead of extending a covariance matrix of the input based on the min-max and the max-min criteria, the derivation shown in this paper is to solve an optimum extension problem of the gain vector based on the information of the Mth-order forward or backward predictor. The derivation provides an intuitive explanation of the FNTF algorithm, which may be easier to understand. Second, we present stability analysis of the proposed algorithm using a linear time-variant state-space method. We show that the proposed algorithm has a well-analyzable stability structure, which is indicated by a transition matrix. The eigenvalues of the ensemble average of the transition matrix are proved all to be asymptotically less than unity. This results in a much-improved numerical performance of the proposed algorithm compared with the combination of the stabilized fast recursive least squares (SFRLS) and the FNTF algorithms. Computer simulations implemented by using a finite-precision arithmetic have confirmed the validity of our analysis. View full abstract»

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  • Robust adaptive beamforming for general-rank signal models

    Page(s): 2257 - 2269
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (784 KB) |  | HTML iconHTML  

    The performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal. Such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment, sources, or sensor array. This is especially true when the desired signal components are present in the beamformer "training" data snapshots because in this case, the adaptive array performance is very sensitive to array and model imperfections. The similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly, but the training sample size is small. We propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary-type mismatches of the desired signal array response. Our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank-one (point source) and higher rank (scattered source/fluctuating wavefront) desired signal models. The proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst-case performance optimization. Simple closed-form solutions to the considered robust adaptive beamforming problems are derived. Our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms, while, at the same time, offer a significantly improved robustness and faster convergence rates. View full abstract»

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  • Nonlinear filtering for state delayed systems with Markovian switching

    Page(s): 2321 - 2328
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (578 KB) |  | HTML iconHTML  

    This paper deals with the filtering problem for a general class of nonlinear time-delay systems with Markovian jumping parameters. The nonlinear time-delay stochastic systems may switch from one to the others according to the behavior of a Markov chain. The purpose of the problem addressed is to design a nonlinear full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially stable in the mean square. Both filter analysis and synthesis problems are investigated. Sufficient conditions are established for the existence of the desired exponential filters, which are expressed in terms of the solutions to a set of linear matrix inequalities (LMIs). The explicit expression of the desired filters is also provided. A simulation example is given to illustrate the design procedures and performances of the proposed method. View full abstract»

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  • Invertible deinterlacing with sampling-density preservation: theory and design

    Page(s): 2343 - 2356
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1808 KB) |  | HTML iconHTML  

    A novel class of deinterlacing for intra-frame/field-based motion-picture coding, such as Motion JPEG2000, as well as an inter-frame-based coding without the support of interlaced scanning video, such as MPEG-1, is developed. This technique has two features: sampling-density preservation and invertibility. These features mean that the amount of deinterlaced pictures is not increased, and the original pictures can be perfectly reconstructed. This deinterlacing technique is a kind of sampling-lattice alteration and is regarded as a generalization of conventional field interleaving and field separation. With the help of multidimensional (M-D) multirate theory, it is shown that the design problem of such a system, that is, invertible deinterlacer with sampling-density preservation, can be replaced to finding a 2×2 multivariable polynomial matrix with a monomial determinant. This problem resembles the design of two-channel M-D maximally decimated perfect-reconstruction finite-impulse-response (FIR) filterbanks. The inverse system, which is referred to as a reinterlacer , is given as FIR when the dual deinterlacing system is FIR. A practical design procedure is provided by suggesting three constraints considered to be preferable: normalization, regularity, and vertical symmetry. The significance of the procedure is verified by showing some design examples of deinterlacing and reinterlacing filters. Simulation results show that the developed method causes fewer comb-shaped artifacts than conventional field interleaving. View full abstract»

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  • Extended RLS lattice adaptive filters

    Page(s): 2294 - 2309
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1212 KB) |  | HTML iconHTML  

    This paper solves the problem of developing exact fast weighted RLS lattice adaptive filters for input signals induced by general orthonormal filter models. The resulting algorithm can be viewed as a counterpart of the extended fast fixed-order RLS adaptive filters previously derived. View full abstract»

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  • OFDM transmitters: analog representation and DFT-based implementation

    Page(s): 2450 - 2453
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    The implementation of orthogonal frequency division multiplexing (OFDM) transmitters typically consists of a discrete DFT matrix and a digital-to-analog (DAC) converter. Many existing results on the analysis of OFDM systems, e.g., spectral roll-off, are based on a convenient analog representation. We show that the analog representation and the DFT-based OFDM transmitters are equivalent only in special cases. Using the analog system to analyze the DFT-based OFDM system may not be valid if there is no equivalent analog representation. View full abstract»

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  • MMSE design of redundant FIR precoders for arbitrary channel lengths

    Page(s): 2402 - 2409
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (534 KB) |  | HTML iconHTML  

    The joint design of transmitter and receiver for multichannel data transmission over dispersive channels is considered. The design criterion is the minimization of the mean squared error (MSE) at the receiver output under the constraint of a fixed transmit power. The focus is on the practically important case where the transmitter employs finite impulse response (FIR) filters, and the channel impulse response has arbitrary length. The proposed algorithm allows a straightforward transmitter design and generally yields near-optimal solutions for the transmit filters. Under certain conditions, the exact solutions for optimum block transmission, as known from the literature, are obtained. View full abstract»

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  • The use of fake algebraic Riccati equations for co-channel demodulation

    Page(s): 2288 - 2293
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (396 KB)  

    This paper describes a method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system. A fake algebraic Riccati equation is employed in the calculation of the filter gain. The design procedure attempts to produce a stable filter at the expense of optimality. This contrasts with the extended Kalman filter (EKF), which attempts to preserve optimality via its linearization procedure, at the expense of stability. A passivity approach is applied to deduce stability conditions for the filter error system. The performance is compared with an EKF for a co-channel frequency demodulation application. View full abstract»

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  • A near-optimal multiuser detector for DS-CDMA systems using semidefinite programming relaxation

    Page(s): 2446 - 2450
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (331 KB)  

    A multiuser detector for direct-sequence code-division multiple-access systems based on semidefinite programming (SDP) is proposed. It is shown that maximum likelihood (ML) detection can be carried out by "relaxing" the associated integer programming problem to a dual SDP problem, which leads to a detector of polynomial complexity. Computer simulations that demonstrate that the proposed detector offers near-optimal performance with considerably reduced computational complexity compared with that of existing primal-SDP-relaxation based detectors are presented. View full abstract»

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  • Minimum BER block precoders for zero-forcing equalization

    Page(s): 2410 - 2423
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (994 KB) |  | HTML iconHTML  

    We determine the linear precoder that minimizes the bit error rate (BER) at moderate-to-high signal-to-noise ratios (SNRs) for block transmission systems with zero-forcing (ZF) equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference, viz, zero padding (ZP) and cyclic prefix (CP). We show that both the ZP minimum BER precoder and the CP minimum BER precoder provide substantially lower error rates than standard block transmission schemes, such as orthogonal frequency division multiplexing (OFDM). The corresponding SNR gains can be on the order of several decibels. We also show that the CP minimum BER precoder can be obtained by a two-stage modification of the water-filling discrete multitone modulation (DMT) scheme in which the diagonal water-filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete Fourier transform (DFT) matrix. View full abstract»

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  • Detection and visualization of tandem repeats in DNA sequences

    Page(s): 2280 - 2287
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (555 KB)  

    One conspicuous feature of DNA is the extent to which nucleotide subsequences repeat in the genome. Several strongly repetitive tandem (or contiguous) repeats are known to be associated with genetic diseases, while weaker repetitive structures are thought to be representative of historical events associated with sequence repetition. Thus, it is important to develop sensitive and rapid automation of the detection and identification of repeat sequences. A new algorithm for examining periodic patterns in DNA sequences is developed. The algorithm uses the short-time periodicity transform to compute the closest periodic sequence of fixed length at each nucleotide position in a given sequence to be analyzed. Each such subsequence is then compared to its closest periodic sequence to provide a quantitative measure of the amount of repetition within the sequence. In addition to being used to detect the presence of repeat subsequences in DNA, the periodicity explorer algorithm provides a potentially useful visualization of periodic patterns in a DNA sequence through a graphical display of the relative energy in the optimal periodic projections of the analyzed sequences, i.e., the DNA periodogram. Computationally, the algorithm is linear in the length of the analyzed sequence. View full abstract»

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  • Separate/joint optimization of error feedback and coordinate transformation for roundoff noise minimization in two-dimensional state-space digital filters

    Page(s): 2436 - 2445
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (921 KB) |  | HTML iconHTML  

    This paper is concerned with the minimization of roundoff noise subject to l2-norm dynamic-range scaling constraints in two-dimensional (2-D) state-space digital filters. Two methods are proposed, with the first one using error feedback alone and the second one using joint error feedback and coordinate transformation optimization. In the first method, several techniques for the determination of optimal full-scale, block-diagonal, diagonal, and scalar error-feedback matrices for a given 2-D state-space digital filter are proposed. In the second method, an iterative approach for minimizing the roundoff noise under l2-norm dynamic-range scaling constraints is developed by jointly optimizing a scalar error-feedback matrix and a coordinate transformation matrix, which may be regarded as an alternative approach to the conventional method for synthesizing the optimal 2-D filter structure with minimum roundoff noise. An analytical method for the joint optimization of a general error-feedback matrix and a coordinate transformation matrix under the scaling constraints is also proposed. A numerical example is presented to illustrate the utility of the proposed techniques. View full abstract»

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  • BER minimized OFDM systems with channel independent precoders

    Page(s): 2369 - 2380
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (777 KB) |  | HTML iconHTML  

    We consider the minimization of uncoded bit error rate (BER) for the orthogonal frequency division multiplexing (OFDM) system with an orthogonal precoder. We analyze the BER performance of precoded OFDM systems with zero forcing and minimum mean squared error (MMSE) receivers. In the case of MMSE receivers, we show that for quadrature phase shift keying (QPSK), there exists a class of optimal precoders that are channel independent. Examples of this class include the discrete Fourier transform (DFT) matrix and the Hadamard matrix. When the precoder is the DFT matrix, the resulting optimal transceiver becomes the single carrier system with cyclic prefix (SC-CP) system. We also show that the worst solution corresponds to the conventional OFDM system; the conventional OFDM system has the largest BER. In the case of zero forcing receivers, the design of optimal transceiver depends on the signal-to-noise ratio (SNR). For higher SNR, solutions of optimal precoders are the same as those of MMSE receivers. View full abstract»

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  • Orthogonal, exactly periodic subspace decomposition

    Page(s): 2270 - 2279
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (874 KB) |  | HTML iconHTML  

    The detection and estimation of machine vibration multiperiodic signals of unknown periods in white Gaussian noise is investigated. New estimates for the subsignals (signals making up the received signal) and their periods are derived using an orthogonal subspace decomposition approach. The concept of exactly periodic signals is introduced. This in turn simplifies and enhances the understanding of periodic signals. View full abstract»

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  • Worst-case design for optimal channel equalization in filterbank transceivers

    Page(s): 2424 - 2435
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (929 KB)  

    A worst-case approach is adopted to tackle optimal channel equalization for multirate filterbank transceivers, which are widely used in data communication networks, such as discrete wavelet multitone (DWMT) systems in digital subscriber lines (DSL), orthogonal frequency multiplexing division (OFMD) in frequency division multiple access (FDMA) systems, applicable to direct-sequence/spread-spectrum (DS/SS) code division multiple access (CDMA) networks. It is assumed that the observation noise is nonwhite with bounded power-norm or root-mean-squared (RMS) value. Our objective is to design the optimal receiving filterbanks that not only achieve the zero-forcing (ZF) condition or channel equalization but also minimize the RMS error between the transmitted symbols and the received symbols in the presence of the worst-case nonwhite noise. All ZF receiving filterbanks will be parameterized, and optimal design for channel equalization will be converted into an equivalent optimal H filtering problem for the augmented receiving filterbanks with RMS error preserved. Our main results cover computation of the optimal RMS error achievable for the worst-case noise and an explicit design algorithm for suboptimal channel equalizers with the performance index arbitrarily close to the optimal one. A simulation example is used to illustrate the proposed optimal channel equalization algorithm. 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