TY - JOUR

T1 - Performance Analysis of Direction Finding with Large Arrays and Finite Data

AU - Viberg, Mats

AU - Ottersten, Björn

AU - Nehorai, Arye

N1 - Funding Information:
Manuscript received May 14, 1992; revised July 11, 1994. This work was supported by the Swedish Research Council for Engineering Sciences, the Air Force Office of Scientific Research under Grant No. AFOSR-90-0164, the Office of Naval Research under Grant No. N00014-91-J-1298, and the National Science Foundation under Grant No. MIP-9122753. M. Viberg is with the Department of Applied Electronics, Chalmers University of Technology, Gothenburg, Sweden. B. Ottersten is with the School of Engineering, Royal Institute of Technology, Stockholm, Sweden. A. Nehorai is with the Department of Electrical Engineering, Yale University, New Haven, CT 06520 USA. IEEE Log Number 9407634.

PY - 1995/2

Y1 - 1995/2

N2 - This paper considers analysis of methods for estimating the parameters of narrow-band signals arriving at an array of sensors. This problem has important applications in, for instance, radar direction finding and underwater source localization. The so-called deterministic and stochastic maximum likelihood (ML) methods are the main focus of this paper. A performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors. Several thousands of antennas are not uncommon in, e.g., radar applications. Strong consistency of the parameter estimates is proved, and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large sample case, the present analysis shows that the accuracy is the same for the two ML methods. Furthermore, the asymptotic covariance matrix of the estimation error coincides with the deterministic Cramér-Rao bound. Under a certain assumption, the ML methods can be implemented by means of conventional beamforming for a large enough number of sensors. We also include a simple simulation study, which indicates that both ML methods provide efficient estimates for very moderate array sizes, whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem.

AB - This paper considers analysis of methods for estimating the parameters of narrow-band signals arriving at an array of sensors. This problem has important applications in, for instance, radar direction finding and underwater source localization. The so-called deterministic and stochastic maximum likelihood (ML) methods are the main focus of this paper. A performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors. Several thousands of antennas are not uncommon in, e.g., radar applications. Strong consistency of the parameter estimates is proved, and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large sample case, the present analysis shows that the accuracy is the same for the two ML methods. Furthermore, the asymptotic covariance matrix of the estimation error coincides with the deterministic Cramér-Rao bound. Under a certain assumption, the ML methods can be implemented by means of conventional beamforming for a large enough number of sensors. We also include a simple simulation study, which indicates that both ML methods provide efficient estimates for very moderate array sizes, whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem.

UR - http://www.scopus.com/inward/record.url?scp=0029255849&partnerID=8YFLogxK

U2 - 10.1109/78.348129

DO - 10.1109/78.348129

M3 - Article

AN - SCOPUS:0029255849

SN - 1053-587X

VL - 43

SP - 469

EP - 477

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 2

ER -