Showing papers by "Mats Viberg published in 1991"

Sensor array processing based on subspace fitting

Abstract: Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. >

Detection and estimation in sensor arrays using weighted subspace fitting

Abstract: The problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed. A multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed. The method is based on the recently introduced weighted subspace fitting (WSF) criterion and includes schemes for both detecting the number of sources and estimating the signal parameters. A Gauss-Newton-type method is presented for solving the multidimensional WSF and maximum-likelihood optimization problems. The global and local properties of the search procedure are investigated through computer simulations. Most methods require knowledge of the number of coherent/noncoherent signals present. A scheme for consistently estimating this is proposed based on an asymptotic analysis of the WSF cost function. The performance of the detection scheme is also investigated through simulations. >

An adaptive array for mobile communication systems

Abstract: The use of adaptive antenna techniques to increase the channel capacity is discussed. Directional sensitivity is obtained by using an antenna array at the base station, possibly both in receiving and transmitting mode. A scheme for separating several signals at the same frequency is proposed. The method is based on high-resolution direction-finding followed by optimal combination of the antenna outputs. Comparison with a method based on reference signals is made. Computer simulations are carried out to test the applicability of the technique to scattering scenarios that typically arise in urban areas. The proposed scheme is found to have great potential in rejecting cochannel interference, albeit at the expense of high computational requirements. >

Performance analysis of the total least squares ESPRIT algorithm

Abstract: The asymptotic distribution of the estimation error for the total least squares (TLS) version of ESPRIT is derived. The application to a uniform linear array is treated in some detail, and a generalization of ESPRIT to include row weighting is discussed. The Cramer-Rao bound (CRB) for the ESPRIT problem formulation is derived and found to coincide with the asymptotic variance of the TLS ESPRIT estimates through numerical examples. A comparison of this method to least squares ESPRIT, MUSIC, and Root-MUSIC as well as to the CRB for a calibrated array is also presented. TLS ESPRIT is found to be competitive with the other methods, and the performance is close to the calibrated CRB for many cases of practical interest. For highly correlated signals, however, the performance deviates significantly from the calibrated CRB. Simulations are included to illustrate the applicability of the theoretical results to a finite number of data. >

Robust signal parameter estimation in the presence of array perturbations

Abstract: Signal parameter estimators which are less sensitive to perturbations in the array manifold are presented. A parametrized stochastic model for the array uncertainties is introduced. The unknown array parameters can include the individual gain and phase responses of the sensors as well as their positions. Based on this model, a maximum a posteriori (MAP) estimator is formulated. This results in a fairly complex optimization problem which is computationally expensive. The MAP estimator is simplified by exploiting properties of the weighted subspace fitting method. An approximate method that further reduces the complexity is also presented, assuming small array perturbations. A compact expression for the MAP Cramer-Rao bound (CRB) on the signal and array parameter estimates is derived. A simulation study indicates that the proposed robust estimation procedures achieve the MAP-CRB even for moderate sample sizes. >

A statistical perspective on state-space modeling using subspace methods

Abstract: The authors investigate aspects of subspace-based state-space identification techniques from a statistical perspective. They concentrate their efforts on a simple approach which is based on finding the range-space of the observability matrix of a state-space representation. The system description is then found using the shift-invariance property of the observability matrix. It is shown that this results in a consistent system description for multivariable output-error models if the measurement noise is white in time and independent from output to output. The asymptotic covariance of the estimated poles of the system is also derived. In the test case studied, the subspace technique performs comparably with the statistically efficient PE (prediction error) method, whereas the instrumental variable method does notably worse. Hence, the subspace technique may be a strong candidate for determining initial values for the optimization in the efficient PE method. >

Detection and Estimation in Sensor Arrays Using

Abstract: This paper addresses the problem of signal param- eter estimation of narrow-band emitter signals impinging on an array of sensors. A multidimensional estimation procedure is proposed, which applies to arbitrary array structures and sig- nal correlation. The method is based on the recently introduced weighted subspace fitting (WSF) criterion, and includes schemes for both detecting the number of sources and estimating the signal parameters. A Gauss-Newton type algorithm is sug- gested for minimizing the WSF criterion. A new detection scheme is also formulated based on the asymptotic distribution of the WSF cost function. Strong consistency of the detection algorithm is proved for arbitrary signal correlation, including coherence. The WSF detection method is compared to a re- cently proposed information theoretic approach, and found to provide a significant improvement for high signal correlation scenarios. Simulations are carried out comparing the proposed WSF technique to the deterministic maximum likelihood (ML) method. The WSF scheme is found to be limited only by the estimation accuracy and not by the initialization or detection. This does not appear to be true for the ML method.

Local modeling and robust estimation for high-resolution direction finding

Abstract: Many signal processing applications are concerned with estimating signal parameters with high accuracy from sensor array measurements. To obtain accurate location estimates, knowledge of the array response is required. Most estimation techniques are sensitive to perturbations in the array model and array calibration is often necessary. The authors discuss the issue of generating the array response parameterization from a finite number of noise-contaminated calibration vectors. An estimation technique based on local parametric modeling of the array response is proposed. The potential improvement using the suggested scheme rather than an ideal array model is demonstrated on real data collected from a full-scale hydroacoustic array. It is shown that, by applying the proposed technique together with a standard direction-of-arrival estimation procedure, a significant reduction in estimation bias can be obtained. >

A study of adaptive arrays for mobile communication systems

Abstract: The application of adaptive antenna techniques to increase the channel capacity in mobile radio communication is discussed. Directional sensitivity is obtained by using an antenna array at the base station, possibly both in receiving and transmitting mode. A scheme for separating several signals at the same frequency is proposed. The method is based on high-resolution direction finding following by optimal combination of the antenna outputs. Comparisons to a method based on reference signals are made. Computer simulations are carried out to test the applicability of the technique to scattering scenarios that typically arise in urban areas. The proposed scheme is found to have great potential in rejecting cochannel interference, albeit at the expense of high computational requirements. >

Estimation accuracy of maximum likelihood direction finding using large arrays

Abstract: The authors analyze the performance of methods for estimating the parameters of narrowband signals arriving at an array of sensors. The deterministic and stochastic maximum likelihood (ML) methods are considered. A performance analysis is carried out for a finite number of snapshots but assuming that the array is composed of a sufficiently large number, m, of sensors. Strong consistency of the parameter estimates is proved and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large (time) sample case, the present analysis shows that the accuracy is the same for the two ML methods. The covariance matrix of the estimation error attains the Cramer-Rao bound. For many array geometries of practical interest, the array propagation vectors become orthogonal as m as increased. It is shown that the traditional beamforming method provides consistent (but not necessarily efficient) estimates under the assumption. This is true also in the presence of perfectly correlated emitters. >