Showing papers by "Mats Viberg published in 1996"

Two decades of array signal processing research: the parametric approach

Abstract: The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

Blind separation of synchronous co-channel digital signals using an antenna array. I. Algorithms

Abstract: We propose a maximum-likelihood (ML) approach for separating and estimating multiple synchronous digital signals arriving at an antenna array at a cell site. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet property of digital signals to simultaneously estimate the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for BPSK signals. We introduce a signal detection technique based on the finite alphabet property that is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful In wireless communication systems. Simulation results demonstrate its promising performance.

Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions

Abstract: This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. The rank-reduced matrix of regression coefficients is parameterized as the product of two full-rank factor matrices. This parameterization is essentially constraint free, but it is not unique, which renders the associated ML estimation problem rather nonstandard. Nevertheless, the problem turns out to be tractable, and the following results are obtained. An explicit expression is derived for the ML estimate of the regression matrix in terms of the data covariances and their eigenelements. Furthermore, a detailed analysis of the statistical properties of the ML parameter estimate is performed. Additionally, a generalized likelihood ratio test (GLRT) is proposed for estimating the rank of the regression matrix. The paper also presents the results of some simulation exercises, which lend empirical support to the theoretical findings.

Maximum likelihood array processing for stochastic coherent sources

Abstract: Maximum likelihood (ML) estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature We focus on the equally relevant case of stochastic coherent signals Explicit large-sample realizations are derived for the ML estimates of the noise power and the (singular) signal covariance matrix The asymptotic properties of the estimates are examined, and some numerical examples are provided In addition, we show the surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ML estimates obtained by exploiting the coherent source information Thus, the ML signal parameter estimator derived for the noncoherent case (or its large-sample realizations) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound)

Maximum-likelihood bearing estimation with partly calibrated arrays in spatially correlated noise fields

Abstract: The problem of using a partly calibrated array for maximum likelihood (ML) bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions. More exactly, this paper assumes that the array contains some calibrated sensors, whose number is only required to be larger than the number of signals impinging on the array, and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors. These two noise vectors, however, may have arbitrary spatial autocovariance matrices. Under these assumptions the many nuisance parameters (viz., the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors) can be eliminated from the likelihood function, leaving a significantly simplified concentrated likelihood whose maximum yields the ML bearing estimates. The ML estimator introduced in this paper, and referred to as MLE, is shown to be asymptotically equivalent to a recently proposed subspace-based bearing estimator called UNCLE and rederived herein by a much simpler approach than in the original work. A statistical analysis derives the asymptotic distribution of the MLE and UNCLE estimates, and proves that they are asymptotically equivalent and statistically efficient. In a simulation study, the MLE and UNCLE methods are found to possess very similar finite-sample properties as well. As UNCLE is computationally more efficient, it may be the preferred technique in a given application.

Instrumental variable subspace tracking with applications to sensor array processing and frequency estimation

Abstract: Recursive methods for subspace tracking with applications to 'on-line' direction of arrival estimation, have lately drawn considerable interest. Instrumental variable (IV) generalizations of the projection approximation subspace tracking (PAST) algorithm are proposed. The IV-approach is motivated by the fact that PAST delivers biased estimates when the noise vectors are not spatially white. The resulting basic IV-algorithm has a computational complexity of 3mn+O(n/sup 2/) complex multiplications, where m is the dimension of the measurement vector and n is the subspace dimension. The performance of the proposed algorithms in tracking sinusoids in colored noise is illustrated by computer simulations.

Minimal continuous state-space parametrizations

Abstract: We present a minimal continuous parametrization of all multivariate rational contractive transfer functions. In contrast to traditional minimal parametrizations, this parametrization does not contain any structural indices, which makes it very suitable for identification algorithms that use nonlinear optimization to estimate the parameters.

Minimal Continuous State Space Parameterizations

Abstract: We present a minimal continuous parametrization of all multivariate rational contractive transfer functions. In contrast to traditional minimal parametrizations, this parametrization does not contain any structural indices, which makes it very suitable for identification algorithms that use nonlinear optimization to estimate the parameters.

Optimal array signal processing in the presence of coherent wavefronts

Abstract: The problem of estimating the parameters of several wavefronts from the measurements of multiple sensors is often referred to as array signal processing. The maximum likelihood (ML) estimator in array signal processing for the case of non-coherent signals has been studied extensively. The focus here is on the ML estimator for the case of stochastic coherent signals which arises due to, for example, specular multipath propagation. We show the very surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent, coincide in large samples with the ML estimates obtained by exploiting the coherent source information. Thus, the ML signal parameter estimator derived for the non-coherent case (or its large-sample realizations such as MODE os WSF) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound).

Reduced-rank linear regression

Abstract: This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. An explicit expression for the ML estimate of the regression matrix is derived. A generalized likelihood ratio (GLRT) test as also proposed, for estimating the rank of the regression matrix. Computer simulations and numerical examples indicate the superiority of the proposed estimator, as compared to a traditional least-squares approach that does not exploit the reduced rank property in an optimal way.

On Cramer Rao bounds and optimal beamspace transformation in radar array processing

Abstract: This paper treats a scenario where a sinusoidal target signal, of unknown amplitude, phase, and frequency impinges on an array of antenna elements. The signal is assumed to be disturbed by spatially colored, but temporally white, additive Gaussian noise. In array signal processing, a beamspace transformation, T, is often used in order to arrive at a reduced computational complexity. Conditioned on a particular T, the Cramer Rao bounds for the unknown parameters are computed, from which an optimality condition on how to choose the beamspace transformation is derived. Finally, some computer simulation results comparing different T:s are given.