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Hanks H. Zeng, University of Connecticut (U.S.A.)
Lang Tong, University of Connecticut (U.S.A.)
The constant modulus algorithm (CMA) is an effective technique for blind receiver design in practice. Treating CMA as a linear estimation problem, effects of noise and channel conditions are investigated. For the class of channels with arbitary finite impulse responses, an analytical description of locations of constant modulus receivers and an upper bound of their mean squared errors (MSE) are derived. We show that, with proper initializations, CMA can achieve almost the same performance as the (nonblind) minimum mean square error (MMSE) receiver. Our analysis reveals a strong relationship between the (blind) constant modulus and the (nonblind) MMSE receivers. It also highlights the significance of initialization/reinitialization schemes. The approach developed in this paper also applies to CMA blind beamforming in array signal processing.
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Channarong Tontiruttananon, Auburn University (U.S.A.)
Jitendra K. Tugnait, Auburn University (U.S.A.)
We consider a frequency-domain solution to the least-squares equation error identification problem using the power spectrum and the cross-spectrum of the IO (input-output) data to estimate the IO parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identification in colored noise and sufficient-order case, and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. Computer simulation results are presented to illustrate the proposed approach.
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Joel Grouffaud, LESIR - ENS de CACHAN (France)
Pascal Larzabal, LESIR - ENS de CACHAN (France)
Henri Clergeot, LESIR - ENS de CACHAN (France)
Transmissions through multipath channels suffer from Rayleigh fading and intersymbol interference. This can be overcome by sending a (known) training sequence and identifying the channel (active identification). However, in a nonstationary context, the channel model has to be updated by periodically sending the training sequence, thus reducing the transmission rate. We address herein the problem of blind identification, which does not require such a sequence and allows a higher transmission rate. In order to track nonstationary channels, we have derived an adaptive (Kalman) algorithm which directly estimates the entire set of characteristic parameters. An original adaptive estimation of the noise model has been proposed for this investigation. Monte-Carlo simulations confirm the expected results and demonstrate the performance.
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Dieter Boss, University of Bremen (Germany)
Karl-Dirk Kammeyer, University of Bremen (Germany)
We investigate the applicability of two algorithms for the blind identification of mixed-phase linear time-invariant FIR systems to the estimation of mobile radio channels on GSM conditions. One approach is based on Second Order Cyclostationary Statistics (SOCS), whereas the other exploits Higher Order Stationary Statistics (HOSS) of the received signal. While the former class of algorithms suffers from "singular" systems which can not be identified, the latter class is said to require an excessive number of samples of the received signal to achieve comparable performance levels. The purpose of this paper is two-fold: first, we demonstrate that "singular" systems represent a severe limitation to SOCS-based methods when it comes to the estimation of time-variant mobile radio channels from a small number of received samples. Secondly, we reveal that the approach relying on 4th order statistics yields a superior estimation performance: At a signal-to-noise-ratio of 10dB, all channel examples can be identified from 142 samples of a GSM burst within a normalized mean square error bound of 7 per cent.
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Elisabeth de Carvalho, Eurecom Institute (France)
Dirk T.M. Slock, Eurecom Institute (France)
We present two approaches to stochastic Maximum Likelihood identification of multiple FIR channels, where the input symbols are assumed Gaussian and the channel deterministic. These methods allow semi-blind identification, as they accommodate a priori knowledge in the form of a (short) training sequence and appears to be more relevant in practice than purely blind techniques. The two approaches are parameterized both in terms of channel coefficients and in terms of prediction filter coefficients. Corresponding methods are presented and some are simulated. Furthermore, Cramer-Rao Bounds for semi-blind ML are presented: a significant improvement of the performance for a moderate number of known symbols can be noticed.
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Michail K. Tsatsanis, Steven Institute of Technology (U.S.A.)
Georgios B. Giannakis, University of Virginia (U.S.A.)
When fractional samples are available at the receiver, blind channel estimation methods can be developed exploiting the cyclostationary nature of the received signal. In this paper, we show that different solutions are possible if cyclostationarity is introduced at the transmitter instead of the receiver. We propose specific coding and interleaving strategies at the transmitter which induce cyclostationarity and facilitate the equalization task. Novel subspace equalization algorithms are derived which make no assumptions whatsoever on the channel zeros locations. Synchronization issues are briefly discussed and some simulation examples are presented.
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Phillip A. Regalia, INT (France)
Mamadou Mboup, Université René Descartes (France)
Mehdi Ashari, Université René Descartes (France)
We establish existence of asymptotic stationary points for a class of adaptive IIR filtering algorithms, including (S)HARF, the Feintuch algorithm, and Landau's algorithm, for reduced-order cases. We show first that the nonlinear equations characterizing a stationary point admit a solution giving rise to a stable transfer function, when the input is white noise. We then show that an analytic procedure to construct the solution may be reduced to the Nevanlinna-Pick interpolation problem. The white noise assumption on the input simplifies the mathematics of an already difficult problem, although the existence proof appears extendable to correlated inputs as well.
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Thomas J. Endres, Cornell University (U.S.A.)
Brian D.O. Anderson, Australian National University (Australia)
C. Richard Johnson Jr., Cornell University (U.S.A.)
Michael Green, Australian National University (Australia)
This paper studies the constant modulus (CM) criterion specifically for the case where the time span of the fractionally-spaced equalizer (FSE) is less than that of the channel. Hence, there necessarily exists an error in the equalized signal. Results for the binary case (Part I) are extended to multi-level signalling. This analysis is connected with the previous work of Fijalkow et al. on misadjustment of a CM receiver to suggest a finite interval of acceptable FSE length which shows that a longer FSE may not be better than a shorter FSE--in some cases, matching the FSE length to that of the channel may not reduce the MSE to a prescribed threshold, while a shorter FSE may be successful in achieving this threshold.
ic973605.pdf ic973605.pdf TOPZhi Ding, Auburn University, Alabama (U.S.A.)
In a multi-user system where training is not available, blind channel identification and equalization become essential. In this paper, we present a new method that utilizes second order statistics for channel parameter estimation and optimum filtering. The identification algorithm is simple and relies on an outer-product decomposition and partial information of the desired signal channel. It allows the identification of individual user channels for which partial information is known under a specific condition. An optimum receiver structure can then be established for the desired signal channel.
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Sylvie Perreau, Research Division, Alcatel Telecom (France)
Pierre Duhamel, Research Division, Alcatel Telecom (France)
This paper is concerned with the blind equalisation of a communication system. We propose to realize the identification of the channel impulse response as well as the noise variance estimation and detection of the emitted sequence of symbols. The signal modelisation as a Hidden Markov Model (HMM) has the intrinsic potential for solving such a problem. However, the high performances of such methods are usually obtained at the cost of a high computational complexity and local minima problems. Both issues are addressed in this paper.
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Eric Moulines, Ecole Nationale Superieure des Telecommunications, CNRS / URA 820 (France)
Jean-François Cardoso, Ecole Nationale Superieure des Telecommunications, CNRS / URA 820 (France)
Elisabeth Gassiat, Ecole Nationale Superieure des Telecommunications, CNRS / URA 820 (France)
In this paper, an approximate maximum likelihood method for blind source separation and deconvolution of noisy signal is proposed. This technique relies upon a data augmentation scheme, where the (unobserved) input are viewed as the missing data. In the technique described in this contribution, the input signal distribution is modeled by a mixture of Gaussian distributions, enabling the use of explicit formula for computing the posterior density and conditional expectation and thus avoiding Monte-Carlo integrations. Because this technique is able to capture some salient features of the input signal distribution, it performs generally much better than third-order or fourth-order cumulant based techniques.
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David Gesbert, France Telecom CNET (France)
Pierre Duhamel, Telecom Paris (France)
This contribution deals with the problem of blind channel identification and equalization based on the (temporally or spatially) oversampled channel output. A novel algorithm is presented which builds on a multistep prediction (MSP) approach and can be viewed as a certain generalization of the initial Linear Prediction Algorithm (LPA) proposed three years ago. Our algorithm improves on most recent related works in that it is theoretically and practically unsensitive to the critical and expected problem of channel length mismatch. Moreover, the MSP scheme improves on the conventional LPA by increasing the robustness of this earlier algorithm. In contrast with the LPA, the proposed prediction scheme exploits the full channel structure, thus providing more statistical efficiency in channel identification. A direct symbol recovery algorithm (requiring no channel estimate) is also straightforwardly drawn from our approach.
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