Showing papers by "Karim Abed-Meraim published in 1996"

Second-order near-field source localization: algorithm and performance analysis

Abstract: A new method for the estimation of the DOA and range parameters of near-field sources is introduced. The proposed method proceeds in two steps and uses only the second-order statistics of the observations collected from a uniform linear array. The first step is a signal pre-processing which consists in the computation of some properly chosen spatial correlation sequences of the observed signal. This correlation coefficients are shown to be time series harmonic sequences and their harmonic frequencies are nonlinear functions of DOAs and ranges of the source signals. The second step consists in the estimation of the harmonic components using a weighted least square criterion in terms of the linear prediction polynomial of the correlation sequence. The source azimuths and ranges are then calculated from the estimated harmonic components. Performance analysis and optimal weighting matrix are derived in terms of the source parameters and the array output second order statistics. The effectiveness of the proposed method is illustrated by some numerical simulations.

Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure

Abstract: In this paper, we address the problem of the blind identification of linear-quadratic instantaneous mixture of statistically independent random variables. This problem consists in the identification of an unknown linear-quadratic transmission channel excited by temporally correlated and mutually independent source signals, using only statistical information on the observations received by an array of sensors. Herein we propose a new technique of blind identification of this non-linear mixture based on joint diagonalization of a set of data correlation matrices. Several numerical simulations are presented to demonstrate the effectiveness of the method in the case of a quadratic phase-coupling mixture.

Fast discrete quadratic phase transform for estimating the parameters of chirp signals

Abstract: This paper is concerned with the problem of estimating the parameters of multicomponent chirp signals from a finite number of noisy discrete time observations. A new transform called quadratic phase transform and its discrete version called discrete quadratic phase transform (DQPT) are introduced which jointly estimate the phase parameters of chirp signals. The DQPT is shown to result in maximum likelihood estimates for a single component chirp signal. A fast implementation of the DQPT is also proposed that results in substantial savings in the computational cost.

Combining cyclostationarity and spatial diversity for blind system identification

Abstract: Second-order blind system identification has become an intense area of research. Recently, it has been shown that, by exploiting space diversity (i.e., multiple receivers) and/or time diversity (i.e., cyclostationarity) of communication signals, system identification using only the second order statistics (SOS) of the system output is possible. In this contribution, we propose to combine cyclostationarity and spatial diversity for the blind identification of p-input, q-output rational system. The basic idea consists in associating with each input signal a specific cyclo-frequency as a proper 'signature'. This will permit, in a first step, to separate the p input signals by selecting successively their respective cyclo-frequencies. In a second step, and thanks to the spatial diversity, we can estimate the channel transfer function using only the output SOS.

Blind equalization of multichannel IIR system using second order statistics

Abstract: Second order statistics based solutions to blind equalization of p-inputs/q-outputs (q>p) IIR (infinite impulse response) system are presented. Many interesting results have been developed for the blind identification of single-input multiple-outputs (SIMO) FIR system. We show here, how to extend some of the existing results to the ARMA (autoregressive moving average) case. More precisely, two equalization methods, namely: (i) a linear prediction method and (ii) a noise subspace method are developed. Moreover, extension to the multi-inputs multi-outputs (MIMO) case is described for each of the two methods. Finally some simulation results are presented to compare and illustrate the effectiveness of the proposed methods.

Parameter estimation of exponentially damped sinusoids using second order statistics

Abstract: In this contribution, we present a new approach for the estimation of the parameters of exponentially damped sinusoids based on the second order statistics of the observations. The method may be seen as an extension of the minimum norm principal eigenvectors method (see [1]) to cydo-correlation statistics domain. The proposed method exploits the nullity property of the cy do-correlation of stationary processes at non-zero cyclo-frequencies [2], This property allows in a pre-processing step to get rid from stationary additive noise. This approach presents many advantages in comparison with existing higher order statistics based approaches [3]: (i) First it deals only with second order statistics which require generally few samples in contrast to higher-order methods, (ii) it deals either with Gaussian and non-Gaussian additive noise, and (iii) also deals either with white or temporally colored (with unknown autocorrelation sequence) additive noise. The effectiveness of the proposed method is illustrated by some numerical simulations.

Array processing in correlated noise fields based on joint eigen-decomposition of spatial-temporal correlation matrices

Abstract: Direction of arrival (DOA) estimation techniques require knowledge of the sensor-to-sensor correlation of the noise which constitutes a significant drawback. In the case of temporally correlated signals, it is possible to estimate the signal parameters without any assumptions made on the spatial covariance matrix of the noise. In this paper, we present a new method for the estimation of the signal subspace and noise subspace. The proposed approach is based on the joint eigendecomposition (JED) of a combined set of spatio-temporal correlation matrices. Once the signal and the noise subspaces are estimated, any subspace based approach can be applied for DOA estimation. Performance comparisons of the proposed approach with two existing techniques are provided.

A Linear Prediction-like Algorithm For Passive Localization Of Near-field Sources

Abstract: A new method for the estimation of the DOA and range parameters of near-field sources is introduced. The proposed method proceed in two steps and use only the second-order statistics of the observations collected from a uniform linear array. The first step is a signal pre-processing which consists in the computation of some properly chosen spatial correlation sequences of the observed signal. This correlation coefficients are shown to be time series harmonic sequences and their harmonic frequencies are nonlinear functions of DOAs and ranges of the source signals. The second step consists in the estimation of the harmonic components using a weighted least square criterion in terms of the linear prediction polynomial of the correlation sequence. The source azimuths and ranges are then calculated from the estimated harmonic components. The effectiveness of the proposed method is illustrated by some numerical simulations.

An iterative approach to the parametric estimation of chirp signals

Abstract: This paper considers the problem of estimating the parameters of a chirp signal from a finite number of noisy discrete time observations. A new iterative method is proposed that proceeds in two steps where the first step consists of estimating iteratively the second order phase coefficient using a properly chosen lagged sequence. The resulting sequence is shown to be time series harmonic, the harmonic frequency being a linear function of the chirp parameters. The iterative procedure is repeated until significantly accurate results are obtained. The second step consists of estimating (iteratively or not) the first order phase coefficient using a properly chosen quadratic transform of the chirp signal. The efficacy of the method is demonstrated by some numerical simulations.