Chair: Hagit Messer, Tel-Aviv University (ISRAEL)
Ilan Reuven, Tel-Aviv University (ISRAEL)
Hagit Messer, Tel-Aviv University (ISRAEL)
In this paper we report results of a research in which we studied the problem of determining the threshold signal to noise ratio (S N R) between large and small errors estimation of the direction of arrival (DOA) of a radiating, far-field source in the presence of another. Using the Barankin lower bound (BB) we examine the conditions under which achievable mean square error (mse) performance of any unbiased DOA estimator deviates substantially from the Carmer-Rao lower bount (CRB). We present expressions for the threshold S N R as a function of the source-array geometry and the sources S N R where one and two sources, of known/unknown spectral parameters and DOA's, are present.
Kristine L. Bell, George Mason University (USA)
Yariv Ephraim, George Mason University (USA)
Harry L. Van Trees, George Mason University (USA)
Bounds on the MSE in estimating the bearing of a planewave signal is of considerable interest in many fields. Of particular importance are the ability of a bound to closely characterize performance in the small error or asymptotic region, and the large error or ambiguity region, and to accurately predict the location of the threshold between the regions. In this paper, the vector Ziv-Zakai bound is applied to the problem of estimating two-dimensional bearing with planar arrays of arbitrary geometry. The bound is calculated for square and circular arrays, and compared with the Weiss-Weinstein bound. The Ziv-Zakai bound is shown to be tighter than the Weiss- Weinstein bound in the threshold and asymptotic regions.
Wenyuan Xu, University of Minnesota (USA)
Mostafa Kaveh, University of Minnesota (USA)
Many MUSIC-like DOA estimators, such as Min-Norm, Beamspace MUSIC, Likelihood MUSIC, FINE and FINES, have been proposed to improve the performance of MUSIC. Since in the difficult estimation situations the large-sample bias of MUSIC may become the dominant estimation error, a comparative study of biases of MUSIC-like estimators in these cases is necessary for their performance evaluation. This paper first identifies the dominant part of the bias of MUSIC for two closely-spaced sources. Then the paper presents a theoretical analysis of a hierarchy of the performances of these MUSIC-like estimators based on their abilities at reducing this major part of the bias and maintaining the asymptotic variance of MUSIC. The theoretical results in the paper explain analytically many previous observations resulting from simulations and numerical computations and may be useful for developing new MUSIC-like algorithms with reduced resolution threshold over that of MUSIC.
D. Linebarger, University of Texas at Dallas (USA)
R. DeGroat, University of Texas at Dallas (USA)
E. Dowling, University of Texas at Dallas (USA)
G. Fudge, University of Texas at Dallas (USA)
Petre Stoica, Chalmers University of Technology (SWEDEN)
We perform analysis of constrained and unconstrained MUSIC demonstrating that (asymptotically) improved subspace estimates always result from the use of constraints, and (asymptotically) the variance of constrained MUSIC is less than that of unconstrained MUSIC under either high coherence, large numbers of sensors, or high SNR conditions. As part of this analysis, we study the effects of coherence on MUSIC and derive best/worst case coherences in terms of the variance of MUSIC. We also demonstrate that those conditions where the variance of MUSIC is predicted to be less than that of constrained MUSIC generally correspond to conditions where MUSIC is in breakdown (and constrained MUSIC is not). So, unconstrained MUSIC does not achieve its predicted advantage in those cases.
Yosef Anu, RAFAEL (ISRAEL)
Mati Wax, RAFAEL (ISRAEL)
We present an analysis of the Signal-to-Interference-plus-Noise Ratio (SINR) at the output of the Minimum Variance beamformer. The analysis yields an explicit expression for the SINR in terms of the different parameters affecting the performance, including the Signal-to-Noise Ratio (SNR), the Interference-to-Noise Ratio (INR), the Signal-to-Interference Ratio (SIR), the angular separation between the desired signal and the interference, the array size and shape, the correlation between the desired signal and the interference, and the finite sample size.
Chandra Vaidyanathan, University of Minnesota (USA)
Kevin M. Buckley, University of Minnesota (USA)
A comparative study of the statistical performance of the MUSIC and minimum variance distortionless response (MVDR) direction of arrival (DOA) estimators is presented. Their relative performance due to given modeling errors is studied. In particular, we study the sensitivity of the estimators to modeling errors in the signal and noise structures.
Yinong Ding, Joint E-mu/Creative Tech Center
Richard J. Vaccaro, University of Rhode Island (USA)
This paper studies the Cramer-Rao (CR) bound for the problem of estimating the directions of arrival of narrow-band plane waves impinging on an ESPRIT array with overlapping subarrays. The overlapping subarray situation occurs when multiple invariances exist in the array. It is found through numerical example that ESPRIT is not efficient when overlapped subarrays are chosen, which is in contrast to the previous result in [1], where it is shown numerically that ESPRIT is asymptomatically efficient when the subarrays do not show any elements. Numerical example also shows that a recently proposed new algorithm called Weighted Subspace Estimation achieves the ESPRIT-CR bound derived in this paper.
Malcolm Hawkes, Yale University (USA)
Arye Nehorai, Yale University (USA)
We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic vector sensors. We derive an expression for the Cramer-Rao bound (CRB) on the DOA parameters of a single source. Using this, we give conditions that minimize the lower bound on the asymptotic mean-square angular error, and conditions that ensure it is isotropic. The asymptotic performance of the Capon and beamforming estimators is analyzed and compared with a scalar-sensor array. The vector-sensor array is seen to have improved performance due to its elements' directional sensitivity. Large sample approximations for the mean-square error (MSE) matrices of the estimators are derived. Throughout, we compare vector-sensor arrays with their scalar-sensor counterparts.
Ariela Zeira, Signal Processing Technology Ltd.
Benjamin Friedlander, University of California (USA)
This paper attempts to assess the potential performance gain of spatial-temporal processing relative to conventional spatial processing, for signals obeying a deterministic parametric model. The Cramer-Rao bound (CRB) on the estimates of the source directions of arrival (DOA) is used to quantify this gain. Spatial-temporal processing does not yield any such gain in the single source case, or for multiple coherent signals. However, significant gains can be achieved for multiple non-coherent signals.
Kah-Chye Tan, Defence Science Organization (SINGAPORE)
Kwok-Chiang-Ho, Defence Science Organization (SINGAPORE)
Arye Nehorai, Yale University (USA)
In this paper, we investigate linear dependence of steering vectors of one electromagnetic vector sensor. We show that every 3 steering vectors with distinct DOA's are linearly independent. We also show that 4 steering vectors with distinct DOA's are linearly independent if the ellipticity angles of the signals associated with any 2 of the 4 steering vectors are distinct. We then establish that 5 steering vectors are linearly independent if exactly 2 or 3 of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any 5 steering vectors, then for any DOA there exists a steering vector which is linearly dependent on the 5 steering vectors.