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Lang Tong, University of Connecticut (U.S.A.)
Dan Liu, University of Connecticut (U.S.A.)
The noise predictive structure of DFE is attractive for the equalization of the coded modulation signals. In this paper, a blind predictive constant modulus (CM) decision feedback equalizer (PCM-DFE) is presented and analyzed. The PCM-DFE employs the CM linear equalizer as its forward filter and a feedback filter that optimizes the CM cost of the decision variable. It is shown that for any fixed forward filter with reasonable small residue intersymbol interference, the CM cost function for the feedback filter is approximately convex and its global minimum can be approximated in closed form. We demonstrate that the convergence rate of the feedback filter is similar to the least mean square (LMS) algorithm used in the nonblind design. We show that the PCM-DFE performs better than the nonblind linear MMSE equalizer in simulations.
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Alexei Y. Gorokhov, Télécom Paris (France)
Philippe Loubaton, Université de MLV (France)
Our contribution addresses the identification of multiple convolutive FIR channels. Many recently proposed blind techniques suffer from the imperfect knowledge of the channel order. Meanwhile the major part of the existing communication systems requires periodically transmitted reference sequences known at the reception site. This information can be used to ensure the robustness the existing blind approaches. We consider here joint utilization of the referenced snapshots with the non-referenced data and construct a combined estimator originating from the blind subspace based technique applied to the Single Input Multiple Output (SIMO) systems identification. The statistical efficiency analysis and numerical examples are presented.
ic973905.pdf ic973905.pdf TOPAnthony Quinn, Trinity College Dublin (Ireland)
The problem of eliciting priors on the parameter space of a signal hypothesis is considered in this paper, and two lesser-known approaches are emphasized. Each yields conservative priors appropriate for data-dominated Bayesian parameter inference. They are based, respectively, on the principles of (i) a posteriori transformation invariance, and (ii) a priori maximum entropy. Novel priors on a wide class of signal models are deduced. Their ability to regularize inference of the difference frequency between closely spaced tones is considered, and they are compared with the Ockham Prior which was studied in previous work.
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Lianming Sun, Keio University (Japan)
Wenjiang Liu, Xi'an Jiaotong University (China)
Akira Sano, Keio University (Japan)
A new identification algorithm based on over-sampling scheme is proposed for a Hammerstein type model which consists of a nonlinear element followed by a linear dynamic model. The unknown linear transfer function model can be identified by making use of the information obtained from the over-sampled output, and the intermediate input to the linear part can also be estimated as well as the arbitrary continuous or discontinuous function type of nonlinear element by deconvolution approach. The priori information of the nonlinear element is not needed for the new algorithm.
ic973913.pdf TOPAapo Hyvärinen, Helsinki University of Technology (Finland)
Independent Component Analysis (ICA) is a statistical signal processing technique whose main applications are blind source separation, blind deconvolution, and feature extraction. Estimation of ICA is usually performed by optimizing a 'contrast' function based on higher-order cumulants. In this paper, it is shown how almost any error function can be used to construct a contrast function to perform the ICA estimation. In particular, this means that one can use contrast functions that are robust against outliers. As a practical method for finding the relevant extrema of such contrast functions, a fixed-point iteration scheme is then introduced. The resulting algorithms are quite simple and converge fast and reliably. These algorithms also enable estimation of the independent components one-by-one, using a simple deflation scheme.
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Linda M. Davis, University of Melbourne (Australia)
Iain B. Collings, University of Melbourne (Australia)
Robin J. Evans, University of Melbourne (Australia)
In this paper, we present a new method for on-line identification of time-varying FIR channels. Two conditionally coupled estimators are proposed. In both cases an augmented-state adaptive Kalman filter is employed for tracking the time-varying channel and estimating the mean channel response. Coupled to the Kalman filter is an algorithm for estimating the parameters of the underlying auto-regressive (AR) model which describes the time evolution of the channel. For the first coupled estimator, we propose a new recursive least squares algorithm for estimation of these AR parameters directly from the channel observations. An alternative algorithm based on estimation of the channel covariance is used in the second coupled estimator. A simulation example demonstrates the performance of the proposed estimators.
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Jonathon C. Ralston, CSIRO (Australia)
Boualem Boashash, Queensland University of Technology (Australia)
This paper considers the identification of time-invariant bilinear models using observed input--output data. Bilinear models represent a parsimonious class of nonlinear parameterisations and have been used in a variety of applications. However the performance of the bilinear model can be limited in practice when standard least-squares techniques are used, as this leads to biased parameter estimates. Most existing solutions for this problem are restrictive, suboptimal, or computationally intensive. We propose an alternative approach to this identification task by utilising a robust regression technique, known as bandlimited regression, to obtain bilinear parameter estimates with reduced bias. The approach is numerically stable and computationally inexpensive. Simulations are given to demonstrate the usefulness of the technique for bilinear system identification.
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Vikram Krishnamurthy, University of Melbourne (Australia)
Kutluyl Dogançay, University of Melbourne (Australia)
The paper presents a maximum likelihood (ML) blind channel equalisation algorithm based on the expectation-maximisation (EM) algorithm. We assume that the channel input sequence is a finite-state Markov chain and the channel output sequence is obtained from the continuous-time channel output by oversampling it at a rate higher than the channel input symbol rate, which leads to a fractionally-spaced channel equalisation problem. The objective of blind channel equalisation is to estimate the channel input symbols without explicit knowledge of the channel characteristics and the requirement of training data. The availability of multichannel outputs for the same channel input improves the reliability of the estimates. A reduced-cost blind equalisation algorithm which draws on aggregation by stochastic complementation is also proposed. A simulation example is presented to demonstrate the performance of the proposed algorithms.
ic973929.pdf ic973929.pdf TOPR. Lynn Kirlin, ECE Department, University of Victoria (Canada)
We derive a technique for estimating a small number of parameters of a spatially or temporally varying transfer function for which a parametric model is known. Such systems occur in transmission lines with faults or mismatches, ultrasonic imaging, semiconductor layering and tomography in various applications. We assume that it is important not only to know that a boundary exists but also to estimate the spatially varying parameters of the medium across the boundary. The method does not require that the input need be known, but it must be applied to the diverse paths simultaneously, such as with a plane wave hitting a plane surface. The output signals at the various points are time synchronous unless delay is the varying parameter. (In the case of temporal variation the same input must be applied to diverse time windows with corresponding delays.) The transfer function model may be nonlinear in the parameters, and we may also have to estimate the nominal values around which the parameters are locally
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Azzedine Touzni, ETIS / ENSEA (France)
I. Fijalkow, ETIS / ENSEA (France)
In this contribution, we address the comparison of Subspace (SS), Linear Prediction (LP) and Constant Modulus (CM) identificaton / equalization algorithms in terms of robustness to loss of Fractionally-Spaced channel disparity. We show that SS procedure leads to an inconsistent channel estimation. Investigating a left-inverse channel estimation, we show that LP results in the estimation of the so-called minimum-phase multivariate channel factorization. We show that CM criterion still perform reasonable channel estimation, even if proper algorithm initialization is still a critical subject.
ic973937.pdf ic973937.pdf TOPConstantinos B. Papadias, Stanford University (U.S.A.)
We consider the problem of global convergence of Godard equalizers in the special case of binary (2-PAM) input signals, when the channel impulse response is complex. We present a class of global minima of all Godard equalizers for this case, which do not correspond to settings free of intersymbol-interference (ISI). The equalizer output corresponding to these global minima appears as a four-point constellation in the complex plane, however it is easily shown that the decomposition in its real and imaginary part provides two ISI-free versions of the transmitted signal. In the case of multi-user constant modulus algorithms, the situation is somewhat more complicated: the real and imaginary parts of each equalizer output after convergence, may correspond to different user signals. These results can be extended to other types of real input signals.
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Abdelhak M. Zoubir, SPRC, Queensland University of Technology (Australia)
Jonathan C. Ralston, SPRC, Queensland University of Technology (Australia)
Robert Iskander, SPRC, Queensland University of Technology (Australia)
Nonlinear system identification involves selecting the order of the given model based on the input-output data. A bootstrap model selection procedure which selects the model by minimising bootstrap estimates of the prediction error is developed. Bootstrap based model selection procedures are attractive because the bootstrap observations generated for the model selection can also be used in subsequent inference procedures. The proposed method is simple and computationally efficient.
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Sylvie Icart, University of Nice (France)
Joël LeRoux, University of Nice (France)
Luc Pronzato, University of Nice (France)
Eric Thierry, University of Nice (France)
Anatoly Zhigljavsky, St. Petersburg University (Russia)
This communication presents a new approach to blind equalization of a FIR channel. It is based on a bounded-error assumption and takes into account the fact that the input signal is in a finite alphabet. We show that even in the noisy case, identifiability can be guaranteed in finite time, provided that the support of the noise density is suitably bounded. We then present some simulation. Keywords: Blind Equalization - Bounded Error - Finite Alphabet
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