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Signal Processing, IEEE Transactions on

Issue 5 • Date May 2004

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Displaying Results 1 - 25 of 37
  • Table of contents

    Page(s): c1 - c4
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    Freely Available from IEEE
  • IEEE Transactions on Signal Processing publication information

    Page(s): c2
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  • Multichannel post-filtering in nonstationary noise environments

    Page(s): 1149 - 1160
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (448 KB) |  | HTML iconHTML  

    In this paper, we present a multichannel post-filtering approach for minimizing the log-spectral amplitude distortion in nonstationary noise environments. The beamformer is realistically assumed to have a steering error, a blocking matrix that is unable to block all of the desired signal components, and a noise canceller that is adapted to the pseudo-stationary noise but not modified during transient interferences. A mild assumption is made that a desired signal component is stronger at the beamformer output than at any reference noise signal, and a noise component is strongest at one of the reference signals. The ratio between the transient power at the beamformer output and the transient power at the reference noise signals is used to indicate whether such a transient is desired or interfering. Based on a Gaussian statistical model and combined with an appropriate spectral enhancement technique, we derive estimators for the signal presence probability, the noise power spectral density, and the clean signal. The proposed method is tested in various nonstationary noise environments. Compared with single-channel post-filtering, a significantly reduced level of nonstationary noise is achieved without further distorting the desired signal components. View full abstract»

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  • ESPRIT-like estimation of real-valued sinusoidal frequencies

    Page(s): 1161 - 1170
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

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

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  • An information theoretic approach to source enumeration in array signal processing

    Page(s): 1171 - 1178
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    In this paper, a new information theoretic algorithm is proposed for signal enumeration in array processing. The approach is based on predictive description length (PDL) that is defined as the length of a predictive code for the set of observations. We assume that several models, with each model representing a certain number of sources, will compete. The PDL criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals. In the proposed method, the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces. The maximum likelihood (ML) estimates of the angles-of-arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces. The summation of the ML estimates of these matrices is the ML estimate of the correlation matrix. This method can detect both coherent and noncoherent signals. The proposed method can be used online and can be applied to time-varying systems and target tracking. View full abstract»

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  • Optimum linear joint transmit-receive processing for MIMO channels with QoS constraints

    Page(s): 1179 - 1197
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (576 KB) |  | HTML iconHTML  

    This paper considers vector communications through multiple-input multiple-output (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmit-receive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrix-valued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel water-filling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmit-receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. View full abstract»

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  • Polynomial spline-approximation of Clarke's model

    Page(s): 1198 - 1208
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB) |  | HTML iconHTML  

    We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling factor increases, the optimal and interpolation splines of even order tend to provide the same accuracy. To build such splines, the process to be approximated needs to be known for all time, which is impractical. Local splines, on the other hand, may be used where the process is known only over a finite interval. We first consider local splines with quasioptimal spline coefficients. Then, we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients. In practice, approximation with a low processing delay is of interest; we investigate local spline extrapolation with a zero-processing delay. The results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error; the error can be very close to the minimum error provided by optimal splines. Thus, local splines can be effectively used for channel estimation in multipath fast fading channels. View full abstract»

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  • The hierarchical timing pair model for multirate DSP applications

    Page(s): 1209 - 1217
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    The problem of representing timing information associated with functions in a dataflow graph is considered. This information is used for constraint analysis during behavioral synthesis of appropriate architectures for implementing the graph. Conventional models for timing suffer from shortcomings that make it difficult to represent timing information in a hierarchical manner for sequential and multirate systems. Some of these shortcomings are identified, and an alternate timing model that does not have these problems for hardware implementations is provided. We introduce the concept of timing pairs to model delay elements in sequential and multirate circuits and show how this allows us to derive hierarchical timing information for complex circuits. The resulting compact representation of the timing information can be used to streamline system performance analysis. In addition, several analytical results that previously applied only to single rate systems can now be extended to multirate systems. We present an algorithm to compute the timing parameters and have used this to compute timing parameters for a number of benchmark circuits. The results obtained on several ISCAS benchmark circuits as well as several multirate dataflow graphs corresponding to useful signal processing applications are presented. These results show that the new representation model can result in large reductions in the amount of information required to represent timing for hierarchical systems. View full abstract»

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  • The uncertainty principle: global, local, or both?

    Page(s): 1218 - 1227
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    We address the issue of the relation between local quantities and the uncertainty principle. We approach the problem by defining local quantities as conditional standard deviations, and we relate these to the uncertainty product appearing in the standard uncertainty principle. We show that the uncertainty product for the average local standard deviations is always less than or equal to the standard uncertainty product and that it can be arbitrarily small. We apply these results to the short-time Fourier transform/spectrogram to explore the commonly held notion that the uncertainty principle somehow limits local quantities. We show that, indeed, for the spectrogram, there is a lower bound on the local uncertainty product of the spectrogram due to the windowing operation of this method. This limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit. We also examine the local uncertainty product for a large class of time-frequency distributions that satisfy the usual uncertainty principle, including the Wigner distribution, the Choi-Williams distribution, and many other commonly used distributions. We obtain an expression for the local uncertainty product in terms of the signal and show that for these distributions, the local uncertainty product is less than that of the spectrogram and can be arbitrarily small. Extension of our approach to an entropy formulation of the uncertainty principle is also considered. View full abstract»

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  • Performance analysis of the adaptive algorithm for bias-to-variance tradeoff

    Page(s): 1228 - 1234
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB) |  | HTML iconHTML  

    An algorithm for the mean squared error (MSE) minimization, through the bias-to-variance ratio optimization, has been recently proposed and used in the literature. This algorithm is based on the analysis of the intersection of confidence intervals (ICIs). The algorithm does not require explicit knowledge of the estimation bias for a "near to optimal" parameter estimation. This paper presents a detailed analysis of the algorithm performances, including procedures and relations that can be used for a fine adjustment of the algorithm parameters. Reliability of the algorithm is studied for various kinds of estimation noise. Results are confirmed on a simulated example with uniform, Gaussian, and Laplacian noise. An illustration of the algorithm application on a simple filtering example is given. View full abstract»

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  • Asymptotically minimum variance second-order estimation for noncircular signals with application to DOA estimation

    Page(s): 1235 - 1241
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    This paper addresses asymptotically minimum variance (AMV) algorithms within the class of algorithms based on second-order statistics for estimating direction-of-arrival (DOA) parameters of possibly spatially correlated (even coherent) narrowband noncircular sources impinging on arbitrary array structures. To reduce the computational complexity due to the nonlinear minimization required by the matching approach, the covariance matching estimation technique (COMET) is included in the algorithm. Numerical examples illustrate the performance of the AMV algorithm. View full abstract»

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  • Reduced-complexity estimation for large-scale hidden Markov models

    Page(s): 1242 - 1249
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB) |  | HTML iconHTML  

    In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models (HMMs) with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes O(ε) (where ε is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm. View full abstract»

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  • CuBICA: independent component analysis by simultaneous third- and fourth-order cumulant diagonalization

    Page(s): 1250 - 1256
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    CuBICA, which is an improved method for independent component analysis (ICA) based on the diagonalization of cumulant tensors is proposed. It is based on Comon's algorithm, but it takes third- and fourth-order cumulant tensors into account simultaneously. The underlying contrast function is also mathematically much simpler and has a more intuitive interpretation. It is therefore easier to optimize and approximate. A comparison with Comon's and three other ICA algorithms on different data sets demonstrates its performance. View full abstract»

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  • Exponential condition number of solutions of the discrete Lyapunov equation

    Page(s): 1257 - 1265
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    The condition number of the n×n matrix P is examined, where P solves P-APA*=BB*, and B is a n×d matrix. Lower bounds on the condition number κ of P are given when A is normal, a single Jordan block, or in Frobenius form. The bounds show that the ill-conditioning of P grows as exp(n/d)≫1. These bounds are related to the condition number of the transformation that takes A to input normal (IN) form. A simulation shows that P is typically ill-conditioned in the case of n≫1 and d=1. When Aij has an independent Gaussian distribution (subject to restrictions), we observe that κ(P)1n/∼3.3. The effect of autocorrelated forcing on the conditioning on state space systems is examined. View full abstract»

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  • Robust filtering for discrete-time systems with saturation and its application to transmultiplexers

    Page(s): 1266 - 1277
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB) |  | HTML iconHTML  

    This paper considers the problem of robust filtering for discrete-time linear systems subject to saturation. A generalized dynamic filter architecture is proposed, and a filter design method is developed. Our approach incorporates the conventional linear H2 and H filtering as well as a regional l2 gain filtering feature developed specially for the saturation nonlinearity and is applicable to the digital transmultiplexer systems for the purpose of separating filterbank design. It turns out that our filter design can be carried out by solving a constrained optimization problem with linear matrix inequality (LMI) constraints. Simulations show that the resultant separating filters possess satisfactory reconstruction performance while working in the linear range and less degraded reconstruction performance in the presence of saturation. View full abstract»

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  • Design of high-resolution cosine-modulated transmultiplexers with sharp transition band

    Page(s): 1278 - 1288
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB) |  | HTML iconHTML  

    Due to the growing importance of multichannel modulation, there has been great interest in the design of high-performance transmultiplex systems. In this paper, a new cosine-modulated transmultiplex structure is proposed based on a prototype filter designed with the frequency-response masking (FRM) approach. This new structure leads to substantial reduction in the computational complexity (number of multiplications per output sample) of the prototype filters having sharp transition band and equivalently small roll-off values. The relation between the interpolation factor used in the FRM prototype filter and the decimation factor in the subbands leads to distinct structures. Examples included indicate that the reduction in computational complexity can be higher than 50% of the current state-of-art designs, whereas the reduction on the number of distinct coefficients of the prototype filter can be reduced even further (over 75%). As a result, the proposed approach allows the design of very selective subfilters for transmultiplexes with a very large number of subchannels. View full abstract»

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  • Results on the factorization of multidimensional matrices for paraunitary filterbanks over the complex field

    Page(s): 1289 - 1303
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    This paper undertakes the study of multidimensional finite impulse response (FIR) filterbanks. One way to design a filterbank is to factorize its polyphase matrices in terms of elementary building blocks that are fully parameterized. Factorization of one-dimensional (1-D) paraunitary (PU) filterbanks has been successfully accomplished, but its generalization to the multidimensional case has been an open problem. In this paper, a complete factorization for multichannel, two-dimensional (2-D), FIR PU filterbanks is presented. This factorization is based on considering a two-variable FIR PU matrix as a polynomial in one variable whose coefficients are matrices with entries from the ring of polynomials in the other variable. This representation allows the polyphase matrix to be treated as a one-variable matrix polynomial. To perform the factorization, the definition of paraunitariness is generalized to the ring of polynomials. In addition, a new degree-one building block in the ring setting is defined. This results in a building block that generates all two-variable FIR PU matrices. A similar approach is taken for PU matrices with higher dimensions. However, only a first-level factorization is always possible in such cases. Further factorization depends on the structure of the factors obtained in the first level. View full abstract»

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  • The double-density dual-tree DWT

    Page(s): 1304 - 1314
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant. View full abstract»

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  • Efficient architectures for 1-D and 2-D lifting-based wavelet transforms

    Page(s): 1315 - 1326
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (960 KB) |  | HTML iconHTML  

    The lifting scheme reduces the computational complexity of the discrete wavelet transform (DWT) by factoring the wavelet filters into cascades of simple lifting steps that process the input samples in pairs. We propose four compact and efficient hardware architectures for implementing lifting-based DWTs, namely, one-dimensional (1-D) and two-dimensional (2-D) versions of what we call recursive and dual scan architectures. The 1-D recursive architecture exploits interdependencies among the wavelet coefficients by interleaving, on alternate clock cycles using the same datapath hardware, the calculation of higher order coefficients along with that of the first-stage coefficients. The resulting hardware utilization exceeds 90% in the typical case of a five-stage 1-D DWT operating on 1024 samples. The 1-D dual scan architecture achieves 100% datapath hardware utilization by processing two independent data streams together using shared functional blocks. The recursive and dual scan architectures can be readily extended to the 2-D case. The 2-D recursive architecture is roughly 25% faster than conventional implementations, and it requires a buffer that stores only a few rows of the data array instead of a fixed fraction (typically 25% or more) of the entire array. The 2-D dual scan architecture processes the column and row transforms simultaneously, and the memory buffer size is comparable to existing architectures. View full abstract»

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  • Noise-enhanced performance for an optimal Bayesian estimator

    Page(s): 1327 - 1334
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    A novel instance of a stochastic resonance effect, under the form of a noise-improved performance, is shown to be possible for an optimal Bayesian estimator. Estimation of the frequency of a periodic signal corrupted by a phase noise is considered. The optimal Bayesian estimator, achieving the minimum of the mean square estimation error, is explicitly derived. Conditions are exhibited where this minimal error is reduced when the noise level is raised, over some ranges, where this occurs essentially with non-Gaussian noise, in the tested configurations. These results contribute a new step in the exploration of stochastic resonance and its potentialities for signal processing. View full abstract»

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  • An H optimization and its fast algorithm for time-variant system identification

    Page(s): 1335 - 1342
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (392 KB) |  | HTML iconHTML  

    In some estimation or identification techniques, a forgetting factor ρ has been used to improve the tracking performance for time-varying systems. However, the value of ρ has been typically determined empirically, without any evidence of optimality. In our previous work, this open problem is solved using the framework of H optimization. The resultant H filter enables the forgetting factor ρ to be optimized through a process noise that is determined by the filter Riccati equation. This paper seeks to further explain the previously derived H filter, giving an H interpretation of its tracking capability. Additionally, a fast algorithm of the H filter, called the fast H filter, is presented when the observation matrix has a shifting property. Finally, the effectiveness of the derived fast algorithm is illustrated for time-variant system identification using several computer simulations. Here, the fast H filter is shown to outperform the well known least-mean-square algorithm and the fast Kalman filter in convergence rate. View full abstract»

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  • Multidimensional rational approximations with an application to linear transforms

    Page(s): 1343 - 1351
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (312 KB) |  | HTML iconHTML  

    We discuss two new algorithms for the calculation of simultaneous rational approximations with specific computational characteristics. These approximations are used for efficient calculation of linear transforms. We develop an application in compression using the discrete cosine transform (DCT); however, the methods are also applicable to other integer transforms. To facilitate efficient multiplierless implementation for small field programmable gate arrays (FPGAs) or other low-cost processing elements, the rational approximations must have controlled precision (bits), and the numerators must use a minimum number of adds and shifts over the coefficient vector (minimum "length" representation). Our first method uses successive approximation of the coefficients in a suboptimal algorithm with low computational complexity to achieve low-length representations. The convergence of this method is analyzed, along with the closeness of the approximations. The suitability of this method for computational implementation, along with the quality of its representations, are evaluated in the context of continued fraction algorithms. The method is shown to be suitable for real-time computation for algorithms such as JPEG-2000. The second method, which finds the lowest length representation, requires more computation but is tractable for offline computation. This method employs search tree pruning and provides a lower bound for the representation length at each iteration. The computational complexity of this method is analyzed and compared with experimental results. View full abstract»

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  • A rate-distortion optimal alternative to matching pursuit

    Page(s): 1352 - 1363
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (376 KB) |  | HTML iconHTML  

    This paper presents a method to find the operational rate-distortion optimal solution for an overcomplete signal decomposition. The idea of using overcomplete dictionaries, or frames, is to get a sparse representation of the signal. Traditionally, suboptimal algorithms, such as matching pursuit (MP), are used for this purpose. When using frames in a lossy compression scheme, the major issue is to find the best possible rate-distortion (RD) tradeoff. Given the frame and the variable length code (VLC) table embedded in the entropy coder, the solution to the problem of establishing the best RD tradeoff is highly complex. The proposed approach reduces this complexity significantly by structuring the solution approach such that the dependent quantizer allocation problem reduces to an independent one. In addition, the use of a solution tree further reduces the complexity. It is important to note that this large reduction in complexity is achieved without sacrificing optimality. The optimal rate-distortion solution depends on the selection of the frame and the VLC table embedded in the entropy coder. Thus, frame design and VLC optimization is part of this work. We experimentally demonstrate that the new approach outperforms rate-distortion optimized (RDO) matching pursuit, previously proposed by Gharavi-Alkhansari. View full abstract»

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  • Blind channel equalization using chirp modulating signals

    Page(s): 1364 - 1375
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB) |  | HTML iconHTML  

    This paper addresses the problem of blind channel equalization in the context of digital communications. Recent results have shown that certain operations applied to the source signal at the transmitter help in the blind identification and equalization of the channel at the receiver. In this paper, the baseband data signal is multiplied with a chirp sequence. Exploiting certain structural properties arising from this operation, a batch-type algorithm is obtained for calculating the equalizer's coefficients. Conditions on the chirp sequence parameters are obtained that guarantee an equalization solution. A low-complexity adaptive algorithm is also proposed. Finally, extensive simulations, and comparisons with other well-known blind techniques, illustrate the excellent performance of this algorithm. View full abstract»

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  • Adaptive asymptotic Bayesian equalization using a signal space partitioning technique

    Page(s): 1376 - 1386
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (480 KB) |  | HTML iconHTML  

    The Bayesian solution is known to be optimal for symbol-by-symbol equalizers; however, its computational complexity is usually very high. The signal space partitioning technique has been proposed to reduce complexity. It was shown that the decision boundary of the equalizer consists of a set of hyperplanes. The disadvantage of existing approaches is that the number of hyperplanes cannot be controlled. In addition, a state-search process, that is not efficient for time-varying channels, is required to find these hyperplanes. In this paper, we propose a new algorithm to remedy these problems. We propose an approximate Bayesian criterion that allows the number of hyperplanes to be arbitrarily set. As a consequence, a tradeoff can be made between performance and computational complexity. In many cases, the resulting performance loss is small, whereas the computational complexity reduction can be large. The proposed equalizer consists of a set of parallel linear discriminant functions and a maximum operation. An adaptive method using stochastic gradient descent has been developed to identify the functions. The proposed algorithm is thus inherently applicable to time-varying channels. The computational complexity of this adaptive algorithm is low and suitable for real-world implementation. 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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Meet Our Editors

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