Coherent Signal Subspace Method Research Articles

AR models for wideband source location

Wideband source location in array signal processing has received much attention in the literature lately. Methods such as the Coherent Signal Subspace (CSS) method proposed by Wang and Kaveh [12], and the signal subspace method used by Cadzow [3], are typical of the approaches used to tackle the multiple wideband source location problem. Most of these methods are variations of the narrowband high-resolution methods. Grenier [5], on the other hand, has applied the idea of time-dependent Auto-Regressive (AR) modeling [7] for a nonstationary process to the frequency domain AR modeling of the sensor outputs in a linear array and has been able to produce good results for a wideband signal. The AR coefficients in the model are expanded in a set of frequency-dependent basis functions. The choice of the basis functions was deemed immaterial and the method works even when only one snapshot of the array output is available. In this paper, we re-examine this method and present an extension of the frequency-dependent AR modeling approach to a planar array. It is shown that the use of a set of sinc functions for representing the frequency-dependent AR coefficients accurately tracks their evolution in the frequency domain, and gives superior performance compared to that when power or Legendre functions are used. We also propose two methods for smoothing the spatial spectra, from which the source locations are determined. Comparison with the CSS method are also presented.

Wideband array processing using a two-sided correlation transformation

A new method for broadband array processing is proposed. The method is based on unitary transformation of the signal subspaces. We apply a two-sided transformation on the correlation matrices of the array. It is shown that the two-sided correlation transformation (TCT) has a smaller subspace fitting error than the coherent signal-subspace method (CSM). It is also shown that unlike CSM, the TCT algorithm can generate unbiased estimates of the directions-of-arrival, regardless of the bandwidth of the signals. The capability of the TCT and CSM methods for resolving two closely spaced sources is compared. The resolution threshold for the new technique is much smaller than that for CSM. >

Wideband source location through frequency-dependent modeling

This paper describes a method for locating multiple wideband sources using the signals received by an array of sensors. In the present approach, the problem of source location is treated as a frequency dependent estimation problem. Each wideband source is received by the array as a vector signal. The spatial spectrum of this signal has a linear frequency modulation (with respect to the usual frequency) which is characteristic of the source location. The frequency modulation may be recovered by frequency dependent modeling over the entire frequency band. The models are estimated by a technique of "model expansion," which consists in the replacement of the data by their projections on a basis of functions of frequency. An invariant expanded model is fitted to these projections. It expresses the evolution of a spatial model with respect to frequency. An estimator based upon an eigen-decomposition of a covariance matrix built from the observations, is discussed. This estimator leads to wideband versions of the high resolution estimators (minimum norm solution and MUSIC). Simulations will conclude the paper and compare this estimator with the coherent signal subspace method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust coherent signal-subspace processing for directions-of-arrival estimation of wideband sources

The authors propose a class of robust focusing matrices for the coherent signal-subspace method, a novel approach for the estimation of directions-of-arrival of wideband sources. The new class of focusing matrices has robustness against size variations of focusing sectors obtained by preliminary group angle estimates. To quantify information loss due to source focusing, a new measure, termed 'relative efficiency index', is introduced and its properties are proved. This index is then used to assess statistical sufficiency of the coherently averaged covariance matrix, a data-reduced statistic on which the coherent signal-subspace method is based. Sensitivity issue as well as estimation performance comparisons for various classes of focusing matrices, based on simulations and relative efficiency index, are also presented.

Directions-of-arrival estimations of multiple coherent broadband signals

In the problems of estimating the directions-of-arrival (DOAs) of multiple coherent broadband signals, the coherent signal-subspace (CSS) method (H. Wang and M. Kaveh, 1990) and the coherent interpolation (CI) method (M. Wax et al., 1985) have been proposed. The performances of the two methods and that of total least squares estimation (LSE) of signal parameters via rotational invariance techniques (TLS-ESPRIT) (Y.H. Chen and F.P. Yu, 1991) which is a high-resolution narrowband signal-subspace approach to an array system with a translation invariant structure, are compared. In the case of unequal-signal powers, the CSS method is not as good as the CI method. Since CI has the disadvantage of larger estimation errors for larger arrival angles, a new spatial phase-shifting technique to improve its performance is presented. Simulation results show the effectiveness of the proposed method. >

Fisher information matrix of the coherently averaged covariance matrix

Novel expressions are derived for the asymptotic Fisher information matrix which is used to investigate the degree of statistical sufficiency of the approximately coherently averaged covariance matrix in the coherent signal-subspace method. These results correct previous ones given by the authors (see Proc. ICASSP-87, Dallas, TX, Apr. 1987). The reasons for the previous erroneous results are discussed. >

Coherent signal-subspace processing in a sector

The determination of the number of wideband signals impinging on a passive sensor array in the form of multiple groups (clusters), and the estimation of their directions of arrival is addressed. The idea of preprocessing by a set of orthogonal beamformers for dimensionality reduction is used to simplify wideband processing. The effectiveness of this approach is demonstrated with the use of discrete prolate spheroidal sequences (DPSSs) as the beamformers for linear uniform arrays. A weighting gain as an indicator of the improvement in the signal-to-noise ratio due to such preprocessing is introduced. Two versions of an algorithm that combines preprocessing/prefiltering and the coherent signal subspace method in the frequency domain are developed, and comparative performance evaluations are carried out. The relative effects of beamspace prefiltering on optimum and suboptimum estimators are explored. >

Coherent wide-band ESPRIT method for directions-of-arrival estimation of multiple wide-band sources

A strategy extending the coherent signal-subspace method (CSM) is proposed for estimating directions of arrival of multiple wideband sources. The proposed method, coherent wideband ESPRIT, extends the ESPRIT algorithm to a framework based on the CSM. A simulation example is provided to illustrate the effectiveness of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm

A novel direction-of-arrival estimation algorithm is proposed that applies to wideband emitter signals. A sensor array with a translation invariance structure is assumed, and an extension of the ESPRIT algorithm for narrowband emitter signals is obtained. The emitter signals are modeled as the stationary output of a finite-dimensional linear system driven by white noise. The array response to a unit impulse from a given direction is represented as the impulse response of a linear system. The measured data from the sensor array can then be seen as the output of a multidimensional linear system driven by white noise sources and corrupted by additive noise. The emitter signals and the array output are characterized by the modes of the linear system. The ESPRIT algorithm is applied at the poles of the system, the power of the signals sharing the pole is captured, and the effect of noise is reduced. The algorithm requires no knowledge, storage, or search of the array manifold, as opposed to wideband extensions of the MUSIC algorithm. This results in a computationally efficient algorithm that is insensitive to array perturbations. Simulations are presented comparing the wideband and ESPRIT algorithm to the modal signal subspace method and the coherent signal subspace method. >

Focussing matrices for coherent signal-subspace processing

A class of focussing matrices is proposed for use in the coherent signal-subspace method (CSM) (H. Wang and M. Kaveh, ibid., vol.ASSP-33, Aug. 1985). When the directions-of-arrival of wideband sources fall into more than one group of one beamwidth each, this class leads to performance substantially better than those suggested in previous studies on direction-of-arrival estimation. New insight into the structures of various focussing matrices and their effect on the performance of CSM is presented. The performance of CSM is compared for several classes of these matrices on the simulations as well as relative sufficiency analyses. >