Mats Viberg

Sensor array processing based on subspace fitting

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

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

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. >

Robust signal parameter estimation in the presence of array perturbations

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.<<ETX>>

A statistical perspective on state-space modeling using subspace methods

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.<<ETX>>

An instrumental variable approach to array processing in spatially correlated noise fields

Signal parameter estimation from sensor array data is of great interest in a variety of applications, including radar, sonar, and radio communication. A large number of high-resolution (i.e., model-based) techniques have been suggested in the literature. The vast majority of these require knowledge of the spatial noise correlation matrix, which constitutes a significant drawback. A novel instrumental variable (IV) approach to the sensor array problem is proposed. By exploiting temporal correlatedness of the source signals, knowledge of the spatial noise covariance is not required. The asymptotic properties of the IV estimator are examined, and an optimal IV method is derived. Simulations are presented examining the properties of the IV estimators in data segments of realistic lengths.<<ETX>>

Sensor array processing using gated signals

The author considers the problem of using an array of sensors for separating a desired signal from unwanted disturbance signals. The desired signal is assumed to be gated, either in time or in frequency. He derives an eigenstructure based method which requires no knowledge of the array manifold and which allows for coherent signals. >

Optimal localization of partially known signals in unknown noise fields

Most methods for sensor array signal processing require the covariance matrix of the background noise to be known. Various techniques for overcoming this limitation have recently been proposed. While most of these are based on assumptions on the noise, we present herein an alternative approach based on partial knowledge of the signals. Methods yielding minimum variance estimates for the model in question are presented and analyzed.<<ETX>>

Effects of Unknown Noise Covariance on Parametric Array Processing Algorithms

Abstract Signal parameter estimation from measurements on a sensor array is an important problem in many engineering applications. Recently, there has been a large interest in parametric methods in the literature. An important assumption in essentially all of these methods is that the spatial correlation structure of the background noise (i.e., the correlation from sensor to sensor) is known to within a multiplicative scalar. In practice, this is often achieved by measuring the array соvariance when no signals are present. This results unavoidably in errors in the noise model. In this paper, the effect of such model errors on parametric methods are examined. The methods in question are the deterministic and stochastic maximum likelihood methods, and the so-called weighted subspace fitting technique. First-order expressions for the mean square etror (MSE) of the parameter estimates are derived. The spatial noise correlation structures that lead to maximum performance loss are identified under different assumptions. In case of high signal to noise ratio (SNR), it is found that the MSE can be increased by a factor m , where m is the number of sensors in the array, as compared to spatially white noise. Simple expressions comparing the asymptotic (for large amounts of data) bias, resulting from a small noise covariance perturbation, with the asymptotic standard deviation are derived. Numerical examples are included to illustrate the obtained results.

A study of adaptive arrays for mobile communication systems

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.<<ETX>>