Peter Stoica

Covariance Matching Estimation Techniques for Array Signal Processing Applications

A class of covariance matching estimation techniques (COMET) has recently attracted interest in the signal processing community. These techniques have their roots in the statistical literature where they are sometimes referred to as generalized least squares methods. Covariance matching is an alternative to maximum likelihood estimation, providing the same large sample properties often at a lower computational cost. Herein, we present a general framework for covariance matching techniques and show that they are well suited to solve several problems arising in array signal processing. A straightforward derivation of the COMET criterion from first principles is presented, which also establishes the large sample properties of the estimator. Closed form compact expressions for the asymptotic covariance of the estimates of the parameters of interest are also derived. Some detection schemes are reviewed and two COMET-based detection schemes are proposed. The main part of the paper treats three applications where the COMET approach proves interesting. First, we consider the localization of underwater sources using a hydro-acoustic array. The background noise is often spatially correlated in such an application and this must be taken into account in the estimation procedure. Second, the problem of channel estimation in wireless communications is treated. In digital communications, an estimate of the channel is often required to perform accurate demodulation as well as spatially selective transmission. Finally, a radar detection problem is formulated and the proposed detection schemes are evaluated.

Cyclic minimizers, majorization techniques, and the expectation-maximization algorithm: a refresher

Many parameter estimation problems in signal processing can be reduced to the task of minimizing a function of the unknown parameters. This task is difficult owing to the existence of possibly local minima and the sharpness of the global minimum. In this article we review three approaches that can be used to minimize functions of the type encountered in parameter estimation problems. The first two approaches, the cyclic minimization and the majorization technique, are quite general, whereas the third one, the expectation-maximization (EM) algorithm, is tied to the use of the maximum likelihood (ML) method for parameter estimation. The article provides a quick refresher of the aforementioned approaches for a wide readership.

Maximum likelihood array processing in spatially correlated noise fields using parameterized signals

This paper deals with the problem of estimating signal parameters using an array of sensors. This problem is of interest in a variety of applications, such as radar and sonar source localization. A vast number of estimation techniques have been proposed in the literature during the past two decades. Most of these can deliver consistent estimates only if the covariance matrix of the background noise is known. In many applications, the aforementioned assumption is unrealistic. Recently, a number of contributions have addressed the problem of signal parameter estimation in unknown noise environments based on various assumptions on the noise. Herein, a different approach is taken. We assume instead that the signals are partially known. The received signals are modeled as linear combinations of certain known basis functions. The exact maximum likelihood (ML) estimator for the problem at hand is derived, as well as computationally more attractive approximation. The Cramer-Rao lower bound (CRB) on the estimation error variance is also derived and found to coincide with the CRB, assuming an arbitrary deterministic model and known noise covariance.

Microwave Imaging via Adaptive Beamforming Methods for Breast Cancer Detection

Ultra-wideband (UWB) Microwave imaging (MWI) is a promising breast cancer detection technology which exploits the significant contrast in dielectric properties between normal breast tissue and tumor. Previously, data-independent methods, such as delay-and-sum (DAS) and space-time (ST) beamforming, have been used for microwave imaging. However, the low resolution and the poor interference suppression capability associated with the data-independent methods restrict their use in practice, especially when the noise is high and the backscattered signals are weak. In this paper, we develop two data-adaptive methods for microwave imaging, which are referred to as the robust weighted Capon beamforming (RWCB) method and the amplitude and phase estimation (APES) method. Due to their data-adaptive nature, these methods outperform their data-independent counterparts in terms of improved resolution and reduced sidelobe levels.

Automatic robust adaptive beamforming via ridge regression

In this paper we derive a class of new parameter free robust adaptive beamformers using the generalized sidelobe canceler reparameterization of the unit gain constrained minimum variance problem. In this parameterization the minimum variance beamformer is obtained as the solution of a linear least squares (LS) problem. In the case of an inaccurate steering vector and/or few data snapshots this marginally overdetermined system gives an ill fit causing signal cancellation in the standard minimum variance (LS) solution. By regularizing the LS problem using ridge regression techniques we get a whole class of robust adaptive beamformers, none of which requires the choice of a user parameter, as opposed to many existing methods. In this context we also propose a parameter free empirical Bayes-based ridge regression technique which, to the best of our knowledge, is novel. The performance of our approach is illustrated by numerical simulations and compared to other robust adaptive beamformers.

Time Reversal and Zero-Forcing Equalization for Fixed Wireless Access Channels

We consider a wideband system with an M -element transmit array. In this paper we combine conventional zeroforcing pre-equalization and time reversal: we present a beamformer that perfectly equalizes the channel and preserves the spatial focusing properties of time reversal. We compare it to a pure zero-forcing beamformer and a pure time reversal system and demonstrate its superior bit error rate performance and low probability of intercept properties using actual measurements of a fixed wireless access system in an urban environment.

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>>

On nonexistence of the maximum likelihood estimate in blind multichannel identification

In this paper, a blind multichannel identification problem for which the maximum likelihood estimate (MLE) does not exist is considered. More specifically, the likelihood function associated with this problem turns out to have no maximum but only saddle points. This interesting instance of nonexistence of the MLE for a practically relevant problem was first presented in the statistical literature on errors-in-variables regression (M. Solari, 1969). New insights into this result are presented in this paper, along with a direct proof based on the indefiniteness of the Hessian matrix.

Mathematical modeling and grey-box identification of the human smooth pursuit mechanism

A mathematical model of the human eye smooth pursuit mechanism was constructed by combining a fourth order nonlinear biomechanical model of the eye plant with a dynamic gain controller model. The biomechanical model was derived based on knowledge of the anatomical properties and characteristics of the extraocular motor system. The controller model structure was chosen empirically to agree with experimental data. With the parameters of the eye plant obtained from the literature, the controller parameters were estimated through grey-box identification. Randomly generated and smoothly moving visual stimuli projected on a computer monitor were used as input data while the output data were the resulting eye movements of test subjects tracking the stimuli. The model was evaluated in terms of accuracy in reproducing eye movements registered over time periods longer than 10 seconds, frequency characteristics and angular velocity step responses. It was found to perform better than earlier models for the extended time data sets used in this study.

Efficient sparse Bayesian learning via Gibbs sampling

Sparse Bayesian learning (SBL) has been used as a signal recovery algorithm for compressed sensing. It has been shown that SBL is easy to use and can recover sparse signals more accurately than the well-known Basis Pursuit (BP) algorithm. However, the computational complexity of SBL is quite high, which limits its use in large-scale problems. We propose herein an efficient Gibbs sampling approach, referred to as GS-SBL, for compressed sensing. Numerical examples show that GS-SBL can be faster and perform better than the existing SBL approaches.