Chair: Benjamin Freidlander, University of California at Davis (USA)
A. Swindlehurst, Brigham Young University (USA)
This paper is concerned with the problem of optimal (maximum likelihood) direction of arrival (DOA) estimation in situations where the sensor array is calibrated over only a portion of the DOA space. Situations such as this often arise in airborne direction finding when skywave multipath is present. A parameterization is proposed for partially calibrated arrays (PCAs), and the identifiability of the model is discussed for both uncorrelated and correlated signals. It is shown how the signal and noise subspace fitting algorithms are generalized to handle PCAs, and a detection scheme is proposed for individually determining the number of signals arriving from calibrated and uncalibrated directions. The results of several simulation examples are included to validate the analysis.
A. Flieller, L.E.Si.R E.N.S. Cachan U.R.A. C.N.R.S.
A. Ferreol, Thomson-CSF
P. Larzabal, L.E.SI.R. E.N.S. Cachan U.R.A. C.N.R.S.
H. Clergeot, L.T.S.M.M. Faculte de Technologie de Guyane (FRANCE)
This paper presents identifiability and treatment relative to bearing estimation in presence of modelling errors. It introduces the general case of direction- dependent modelling errors. The classical direction-independent case is only a particular case which takes into account a prior knowledge. This general case introduces the important issue of simultaneous sources and perturbation identifiability which is analysed in this paper. A new self-calibration technique based on MUSIC algorithm and able to treat direction- dependent errors is also proposed. For regularization purpose, a "cost term" is introduced in this algorithm. It confers good robustness to algorithm which usually fails in presence of great gap between model and reality. After reduction of the new multidimensional "increased function", values of azimuths are easily obtained on a monodimensional spectrum. Some simulations support results and verify improvements expected in theory.
Anthony J. Weiss, Tel-Aviv University (ISRAEL)
Benjamin Friedlander, University of California-Davis (USA)
David D. Feldman, Technion (ISRAEL)
We consider the problem of separating and estimating the waveforms of superimposed signals received using an array of uncalibrated sensors. The array elements are assumed to have the same unknown gain pattern, up to an unknown multiplicative factor. The phases of the elements are arbitrary and unknown. In this paper we analyze the quality of the estimated signal in terms of the output signal to interference ratio (SIRO) and output signal to noise ratio (SNRO). It is shown that uncalibrated arrays can be used successfully for signal separation and estimation using only second order moments. The analysis is verified by Monte Carlo experiments using an algorithm for steering vector estimation presented in the full version of the paper.
Patrick C. Yip, McMaster University (CANADA)
Yifeng Zhou, McMaster University (CANADA)
In this paper, a self-calibration DOA estimation algorithm for cyclostationary source signals is presented in which the effects of the sensor gain and phase shift uncertainty have been eliminated. The uniqueness conditions and the asymptotic consistency of the estimates are discussed. An alternating projecting optimization algorithm is provided which lessens the computational load involved in the nonlinear multivariate optimization problem much less. A numerical example is presented to show the effectiveness of the algorithm.
Frank C. Robey, MIT Lincoln Laboratory (USA)
Edward J. Baranoski, MIT Lincoln Laboratory (USA)
For an airborne radar array, beamforming and detection are problems in both space and time. To null clutter, it is necessary to exploit both dimensions, and to do so optimally requires knowledge of the full space-time covariance matrix and the array steering vectors. This paper derives an Expectation-Maximization (EM) algorithm for the estimation of full space-time covariance matrices while simultaneously estimating array steering vectors. The EM approach iterates between estimating the spatial steering vectors and power associated with clutter scattering from different angles and the formation of a full space-time covariance matrix. The final result is an estimate of the set of array steering vectors and an estimate of the space-time covariance matrix. In practice, one would never need to form this covariance since all calculations could be performed using the SVD of the appropriately weighted clutter space-time steering vector matrix. The technique is capable of providing a positive definite estimate of the space-time covariance and complete array calibration with only a single space-time data sample.
J.W. Pierre, University of Wyoming
D.R. Fuhrmann, Washington University (USA)
This paper develops a calibration procedure for gain and phase imbalances in quadrature receivers. Quadrature demodulation has many applications in communications and array processing. Frequently, the output of the in-phase (I) and quadrature (Q) channels are considered the real and imaginary parts, respectively, of a complex random process which belongs to the Goodman class. Mismatch in the gain and phase of the I and Q channels results in a departure from this statistical model and a degradation in the performance of subsequent signal processing algorithms. The calibration algorithm presented in this paper estimates the relative imbalance between the I and Q channels, based on data from a sinusoid of known frequency but unknown amplitude and phase.
Saeed Gazor, Telecom Paris (FRANCE)
Sofiene Affes, Telecom Paris (FRANCE)
Yves Grenier, Telecom Paris (FRANCE)
We present a novel adaptive algorithm in the frequency domain with a low order of arithmetic complexity for simultaneously performing beamforming, source direction finding and array shape calibration. The algorithm is proposed for multiple wideband sources, but could be applied to the narrowband case or to a single wideband source. The source signals are first estimated using a set of beamformers. These estimates are processed with the observation signals to track the steering vectors within the signal subspace. The adapted steering vectors are projected over the array manifold, to finally estimate the source directions and sensor positions. Simulations show the efficiency of the algorithm to achieve the proposed tasks.
Egemen Gonen, University of Southern California (USA)
Jerry M. Mendel, University of Southern California (USA)
We propose an optimum cumulant-based blind beamforming method for signal recovery in coherent signal environments. Our approach is applicable to any array configuration having arbitrary and unknown response. There is no need to estimate the directions of arrival. A comparable result does not exist using second-order statistics.
Antoine Souloumiac, Schlumberger Industries (FRANCE)
We address the problem of using an array of sensors for detecting a narrow band source and separating its signal from unwanted disturbance signals, that is jammers and noise. The power of the desired signal is assumed to move from one level to another. This second order non-stationarity occurs, for instance, in frequency jumping systems, and, more generally, at the beginning or at the end of any communication. We derive a method based on the generalized eigenstructure of two covariance matrices which requires no a priori knowledge of the array manifold, but only second order stationarity of the disturbance signals. The loss in signal to interference plus noise ratio due to finite sample effect is calculated in closed form at the first order and validated by simulations. This last result shows that the method gives interesting performance in a wide range of situations.
J. Yang, Brigham Young University (USA)
A. Swindlehurst, Brigham Young University (USA)
In this paper, we consider the signal-to-interference plus noise ratio (SINR) performance of several beamforming algorithms, taking particular account of the contribution of sources correlated with the desired signal. In addition, we derive an optimal method that maximizes SINR by combining with the desired signal estimate any components of the interference/multipaths that are correlated with it. To facilitate performance comparisons, we will only consider the case where the signal directions of arrival (DOAs) are precisely known. The extension to unknown DOAs is straightforward. Our analysis includes the first order effects of array calibration errors, and is verified by numerical simulation.